Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Hasabel Naby, Mahmoud
Doctor of Philosophy - PhD
University of British Columbia
The rapid evolution of wireless communication networks demands evolved radio access network (RAN) architectures that can support massive connectivity and deliver high data rates. Collaborative signal processing, as seen in distributed antenna systems (DAS), is a promising approach, demonstrated by paradigms like Cloud RAN (C-RAN), Fog RAN (F-RAN), Cell-Free Massive MIMO (CF-mMIMO), and Open RAN (O-RAN). However, the effectiveness of DAS networks is constrained by the limited capacity of fronthaul links, connecting distributed antenna terminals to the central processing unit (CPU). This calls for the development of advanced signal processing and relaying techniques for efficient utilization of fronthaul links in both uplink and downlink transmissions. This dissertation makes a significant contribution by introducing a novel end-to-end multi-pair two-way computation paradigm tailored for DAS. It advocates a joint design approach for uplink and downlink transmissions, taking into consideration the source-destination message information. This idea is demonstrated in this dissertation through a pairwise message exchange paradigm among communicating users in the DAS, emphasizing the optimization of end-to-end spectral and energy efficiency. A lattice-based computation approach is adopted, wherein each antenna terminal quantizes its observed signal and transmits it to the CPU. The CPU decodes integer linear combinations of paired users' codewords, rather than linear combinations of individual codewords. The computed signals are then beamformed, compressed, and forwarded to the distributed antenna terminals, which subsequently decompress and transmit them to the users. This approach is applied in various scenarios, including C-RAN with intra-cloud communications and combined intra and inter-cloud scenarios, assuming perfect channel state information (CSI) and considering both real and complex-valued channel models. To address sensitivity to CSI estimation errors, a robust end-to-end multi-pair computation scheme is proposed to optimize energy efficiency under imperfect CSI, particularly relevant in CF-mMIMO networks due to their 'massive' nature. Additionally, to further alleviate communication overhead over limited-capacity fronthaul links, a distributed multi-pair computation scheme is introduced, wherein the computation of certain user-pair codewords is to be offloaded from the CPU to the distributed antenna terminals. The effectiveness of these proposed frameworks is rigorously evaluated through theoretical derivations and numerical simulations, demonstrating their superiority over state-of-the-art schemes.
Improving the Performance ofDistributed Antenna SystemsUsing Multi-Pair ComputationSchemesbyMahmoud Hasabel NabyB.Sc. Hons., Menoufia University, 2014M.Sc., Menoufia University, 2019A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE COLLEGE OF GRADUATE STUDIES(Electrical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)December 2023© Mahmoud Hasabel Naby, 2023The following individuals certify that they have read, and recommend to theCollege of Graduate Studies for acceptance, a dissertation entitled:Improving the Performance of Distributed Antenna Systems UsingMulti-Pair Computation Schemessubmitted by Mahmoud Hasabel Naby in partial fulfilment of the requirementsof the degree of Doctor of PhilosophyDr. Anas Chaaban, School of EngineeringSupervisorDr. Stephen O’Leary, School of EngineeringSupervisory Committee MemberDr. Jahangir Hossain, School of EngineeringSupervisory Committee MemberDr. Mahmudur Fatmi, School of EngineeringUniversity ExaminerDr. Halim Yanikomeroglu, Carleton UniversityExternal ExamineriiAbstractThe rapid evolution of wireless communication networks demands evolved radioaccess network (RAN) architectures that can support massive connectivity and de-liver high data rates. Collaborative signal processing, as seen in distributed antennasystems (DAS), is a promising approach, demonstrated by paradigms like CloudRAN (C-RAN), Fog RAN (F-RAN), Cell-Free Massive MIMO (CF-mMIMO), andOpen RAN (O-RAN). However, the effectiveness of DAS networks is constrained bythe limited capacity of fronthaul links, connecting distributed antenna terminals tothe central processing unit (CPU). This calls for the development of advanced signalprocessing and relaying techniques for efficient utilization of fronthaul links in bothuplink and downlink transmissions.This dissertation makes a significant contribution by introducing a novel end-to-end multi-pair two-way computation paradigm tailored for DAS. It advocates a jointdesign approach for uplink and downlink transmissions, taking into consideration thesource-destination message information. This idea is demonstrated in this disserta-tion through a pairwise message exchange paradigm among communicating users inthe DAS, emphasizing the optimization of end-to-end spectral and energy efficiency.A lattice-based computation approach is adopted, wherein each antenna terminalquantizes its observed signal and transmits it to the CPU. The CPU decodes integerlinear combinations of paired users’ codewords, rather than linear combinations ofindividual codewords. The computed signals are then beamformed, compressed, andforwarded to the distributed antenna terminals, which subsequently decompress andtransmit them to the users. This approach is applied in various scenarios, includingC-RAN with intra-cloud communications and combined intra and inter-cloud sce-narios, assuming perfect channel state information (CSI) and considering both realand complex-valued channel models.To address sensitivity to CSI estimation errors, a robust end-to-end multi-paircomputation scheme is proposed to optimize energy efficiency under imperfect CSI,particularly relevant in CF-mMIMO networks due to their ’massive’ nature. Addi-tionally, to further alleviate communication overhead over limited-capacity fronthaullinks, a distributed multi-pair computation scheme is introduced, wherein the com-putation of certain user-pair codewords is to be offloaded from the CPU to theiiiAbstractdistributed antenna terminals.The effectiveness of these proposed frameworks is rigorously evaluated throughtheoretical derivations and numerical simulations, demonstrating their superiorityover state-of-the-art schemes.ivLay SummaryThis dissertation aims to enhance wireless networks for faster, more reliableconnections. Imagine living a metaverse experience where virtual and real worldsseamlessly intertwine, offering boundless possibilities for exploration and social in-teraction. This vision demands high-speed connectivity wherever one ventures. Toachieve this, the study delves into advanced mobile network designs, focusing ondistributed antenna systems (DAS). These systems, when optimized, can signifi-cantly bolster high-speed connectivity and expansive coverage, pivotal for seamlessinteraction and content delivery. Introducing a novel end-to-end data transmissionapproach, the research simplifies data processing, proving more efficient than existingtechniques. The study also addresses challenges in estimating network conditions,especially in crowded networks, providing robust energy-efficient solutions. Further-more, by redistributing computational tasks within the network, the research aimsto reduce communication congestion. Ultimately, this work is a critical step towardsthe lightning-fast, dependable next-generation wireless networks we all rely on in ourincreasingly connected world.vPrefaceThis dissertation embodies research conducted under the supervision of Dr. AnasChaaban.Throughout the various chapters, I conducted comprehensive literature reviews,conceptualized research ideas, performed essential mathematical analyses, problemformulation, and optimization as well as executed simulations. Additionally, I au-thored the corresponding manuscripts. Dr. Chaaban offered valuable input on sys-tem models, solutions to problems, and their associated computational complexities,contributing to the refinement of all articles for scholarly dissemination.Some collaborations on part of this dissertation is conducted with Dr. MohanadObeed, Dr. Mohamed Saif, and Prof. Jahangir Hossain. We contributed in preparinga comprehensive survey paper that covers the road map of the evolution of radio-access networks.The following catalog enumerates the journal and conference publications per-tinent to the dissertation chapters. This compilation encompasses both publishedworks and those currently under review or submission. Additionally, it includesthe research and academic awards that I have been honored with during my Ph.D.studies.− Published, Submitted, and In-preparation Journal PapersJ1. Mahmoud A. Hasabelnaby and Anas Chaaban,“Hybrid D2D and Dis-tributed Multi-Pair Computation for Intra Cell-Free Massive MIMO Com-munications: Reinforcement Learning Approach”, in-preparation to besubmitted for publication at IEEE Transactions on Wireless Communi-catoins, (parts of Chapter 5).J2. Mahmoud A. Hasabelnaby, Mohamed Saif, Mohanad Obeed, AnasChaaban, and Jahangir Hossain, “Next-Generation Distributed AntennaSystems: Roadmap from Centralized RAN to Open RAN”, to be sub-mitted for publication at IEEE Communications Surveys and Tutorials(parts of Chapter 1).J3. Mahmoud A. Hasabelnaby and Anas Chaaban, “Energy-Efficient Multi-Pair Computation for Intra Cell-Free Massive MIMO Communications”,viPrefaceaccepted to appear at IEEE Wireless Communications Letters, December2023. (Chapter 4).J4. Mahmoud A. Hasabelnaby and Anas Chaaban, “Multi-Pair Compu-tation for C-RAN with Inter-Cloud and Intra-Cloud Communications”,IEEE Wireless Communications Letters, vol. 11, no. 12, pp. 2537-2541,December 2022 (Chapter 3).J5. Mahmoud A. Hasabelnaby and Anas Chaaban, “Multi-Pair Computa-tion for Two-Way Intra Cloud-Radio Access Network Communications”,IEEE Transactions on Wireless Communications, vol. 21, no. 7, pp.5586-5599, July 2022 (Chapter 2).− Referred Conference PublicationsC1. Mahmoud A. Hasabelnaby and Anas Chaaban, “Distributed Multi-Pair Computation for Intra C-RAN Bidirectional Communications”, 31thBiennial Symposium on Communications (BSC 2023), IEEE, Montreal,Canada, July 2023 (Chapter 5).C2. Mahmoud A. Hasabelnaby and Anas Chaaban, “Intra C-RAN Two-Way Multi-Pair Computation under Total Power and Fronthaul CapacityConstraints”, 17th Canadian Workshop on Information Theory (CWIT),IEEE, Ottawa, Canada, June 2022 (parts of Chapter 2).C3. Mahmoud A. Hasabelnaby, and Anas Chaaban, “End-to-End RateEnhancement in C-RAN Using Multi-Pair Two-Way Computation”, JointEuropean Conference on Networks and Communication and 6G Summit(EuCNC & 6G summit 2021), IEEE, Porto, Portugal, June 2021 (partsof Chapter 2).− Poster PresentationsP1. Mahmoud A. Hasabelnaby and Anas Chaaban, “Two-Way Multi-PairComputation for C-RAN Communications”, 2021 IEEE North AmericaSchool of Information Theory (NASIT 2021), Vancouver, Canada, June2021.− The following magazine paper has also been prepared during myPh.D. study; however, the materials of this paper are not includedin the dissertation.viiPrefaceJ. Abdullah Zayat, Mahmoud A. Hasabelnaby, Mohanad Obeed, andAnas Chaaban, “Transformer Masked Autoencoders for Next-GenerationWireless Communications: Architecture and Opportunities”, accepted toappear at IEEE Communications Magazine, October 2023.− Research and Academic AwardsA1. Oracle Research Project Award, Oracle Research, 2023.A2. UBC Okanagan Graduate Research Scholarship, University of BritishColumbia, 2023.A3. Internet for All competition: North American Second Place Winner, IEEECommunications Society, 2022.A4. UBC Okanagan Graduate Research Scholarship, , University of BritishColumbia, 2022.A5. The University Graduate Fellowship (UGF), University of British Columbia,2021.A6. The University Graduate Fellowship (UGF), University of British Columbia,2020.A7. International Four-Year Doctoral Partial Tuition Award (IDPT), Univer-sity of British Columbia, 2019.viiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxiiiChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Roadmap Evolution from Traditional de-Centralized RAN to DAS . . 21.1.1 Traditional de-Centralized RAN . . . . . . . . . . . . . . . . . 41.1.2 Distributed Antenna Systems . . . . . . . . . . . . . . . . . . 71.1.3 Design of Fronthaul Network in Distributed Antenna Systems 141.2 Literature Review for Uplink and Downlink Coding Strategies in DAS 181.2.1 Uplink Coding Strategies . . . . . . . . . . . . . . . . . . . . . 191.2.2 Downlink Coding Strategies . . . . . . . . . . . . . . . . . . . 241.3 Learned Lessons and Research Gaps . . . . . . . . . . . . . . . . . . . 271.4 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.5 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 29ixTABLE OF CONTENTS1.6 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321.7 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Chapter 2: Multi-Pair Computation for Two-Way Intra Cloud Radio-Access Network Communications . . . . . . . . . . . . . . 352.1 Accomplished Works and Research Contributions . . . . . . . . . . . 352.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.3 Toy Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.4 Uplink Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.4.1 Encoding at the users . . . . . . . . . . . . . . . . . . . . . . . 412.4.2 Compression at the RRHs . . . . . . . . . . . . . . . . . . . . 422.4.3 Decompression at the BBU pool . . . . . . . . . . . . . . . . . 432.4.4 Multi-Pair Computation at the BBU pool . . . . . . . . . . . 452.5 Downlink Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . 472.5.1 Compression at the BBU pool . . . . . . . . . . . . . . . . . . 472.5.2 Decompression at the RRHs . . . . . . . . . . . . . . . . . . . 482.5.3 Decoding at the users . . . . . . . . . . . . . . . . . . . . . . . 502.6 End-to-End Rate Optimization . . . . . . . . . . . . . . . . . . . . . 522.6.1 Uplink Rate Optimization . . . . . . . . . . . . . . . . . . . . 522.6.2 Downlink Rate Optimization . . . . . . . . . . . . . . . . . . . 562.6.3 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . 572.7 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Chapter 3: Multi-Pair Computation for C-RAN With Intra-Cloudand Inter-Cloud Communications . . . . . . . . . . . . . . 653.1 Accomplished Works and Research Contributions . . . . . . . . . . . 653.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.3 Uplink Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.4 Downlink Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . 713.5 Uplink and Downlink Sum-rate Optimization . . . . . . . . . . . . . . 743.5.1 Uplink Rate Optimization . . . . . . . . . . . . . . . . . . . . 753.5.2 Downlink Rate Optimization . . . . . . . . . . . . . . . . . . . 753.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Chapter 4: Energy-Efficient Multi-Pair Computation for Intra Cell-Free Massive MIMO Communications . . . . . . . . . . . 824.1 Accomplished Works and Research Contributions . . . . . . . . . . . 82xTABLE OF CONTENTS4.2 System Model and Assumptions . . . . . . . . . . . . . . . . . . . . . 834.3 End-to-End Transmission Scheme . . . . . . . . . . . . . . . . . . . . 844.3.1 Phase (a) Processing . . . . . . . . . . . . . . . . . . . . . . . 844.3.2 Phase (b) Processing . . . . . . . . . . . . . . . . . . . . . . . 874.4 Total Energy Efficiency Optimization . . . . . . . . . . . . . . . . . . 904.4.1 Optimizing Transmission Parameters for Phase (a) . . . . . . 914.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Chapter 5: Distributed Multi-Pair Computation for Intra C-RANBidirectional Communications . . . . . . . . . . . . . . . . 1005.1 Accomplished Works and Research Contributions . . . . . . . . . . . 1005.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015.3 Uplink Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025.3.1 Lattice encoding at users . . . . . . . . . . . . . . . . . . . . . 1025.3.2 Low-Level and High-level Compression at the distributed RUs 1035.3.3 Decompression and computations at the CPU . . . . . . . . . 1055.3.4 Multi-Pair Computation at the CPU . . . . . . . . . . . . . . 1065.4 Downlink Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.4.1 Compression at the CPU . . . . . . . . . . . . . . . . . . . . . 1085.4.2 Decompression at the distributed RUs . . . . . . . . . . . . . 1095.5 Distributed Multi-Pair Computation Optimization . . . . . . . . . . . 1115.5.1 Uplink and Downlink Rate Optimization . . . . . . . . . . . . 1125.5.2 Local User-Pair Processing Assignment . . . . . . . . . . . . . 1155.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Chapter 6: Conclusions and Future Works . . . . . . . . . . . . . . . . 1186.1 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.2 Current Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216.3 Suggested Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.3.1 Integrating Device-to-Device Communications with DMPC forFurther Relaxing Fronthaul Communications Overhead . . . . 1226.3.2 Designing Efficient Data Collection Models for Open RadioAccess Network Service Management Orchestration . . . . . . 1236.3.3 Multi-Pair Computation Linear Receiver for QAM Symbol De-tection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126xiTABLE OF CONTENTSAppendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Appendix A: Lattice Preliminaries . . . . . . . . . . . . . . . . . . . . . . 145Appendix B: Proof of Equation (2.27) . . . . . . . . . . . . . . . . . . . . 148xiiList of TablesTable 1.1 Required CPRI fronthaul data rate in fully centralized DAS [1] 17Table 1.2 Comparison of the uplink coding strategies in DAS . . . . . . 25Table 1.3 Comparison of the downlink coding strategies in DAS . . . . . 27xiiiList of FiguresFigure 1.1 Evolution of mobile generations KPIs: A comparative evalu-ation from 4G KPIs to 6G KPIs. . . . . . . . . . . . . . . . . 4Figure 1.2 Evolution of Radio Access Network (RAN) Architectures: AComparative Evaluation from de-Centralized RAN to Central-ized RAN to 5G Split RAN. . . . . . . . . . . . . . . . . . . . 5Figure 1.3 CPRI RAN functional split: fully separating RF functions indistributed RUs (RE) and all L1/L2/L3 processing functionsof the OSI protocol stack in the CPU (REC). . . . . . . . . . 16Figure 2.1 A C-RAN with multi-pair intra-cloud communication [2, Fig-ure 1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 2.2 Uplink Transmission: (a) User k encodes its message into uulkusing lattice coding, then scales it and transmits xulk to allRRHs. (b) RRH ` compresses its dithered observed signalusing lattice-based vector quantization, then maps its com-pressed signal to an index eul` , and forwards it to the BBUpool via its fronthaul link. (c) The BBU pool decompressesthe received signals and proceeds to decode M integer linearcombinations of the sum of user-pairs’ codewords [2, Figure 2]. 42Figure 2.3 Downlink Transmission: (a) The BBU compresses the com-puted combinations vulψ,m, maps each compressed linear com-bination to an index, and forwards indices to RRHs. (b) RRH` recovers its desired signal and broadcasts it to all users. (c)User k decodes its desired signal using its own codeword asside information [2, Figure 3]. . . . . . . . . . . . . . . . . . . 47Figure 2.4 Convergence of bisection search at L = 2, K = 4, transmittedpower = −5 dBm, and C` = 400 Mbps [2, Figure 4]. . . . . . 58Figure 2.5 Convergence of the uplink iterative algorithm at L = 2, K =4, transmitted power = −5 dBm, and C` = 400 Mbps [2,Figure 5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59xivLIST OF FIGURESFigure 2.6 End-to-End sum rate versus transmitted power in dBm atL = 2, K = 4 (M = 2), and C` = 400 Mbps [2, Figure 6]. . . 60Figure 2.7 End-to-End sum rate versus transmitted power in dBm atdifferent numbers of RRHs and users, and C` = 400 Mbps [2,Figure 7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Figure 2.8 End-to-End sum rate versus C` in Mbps at L = 2, K = 4(M = 2), and transmitted power = −5 dBm [2, Figure 8]. . . 62Figure 2.9 End-to-End sum rate versus C` in Mbps at different numbersof RRHs and users, and transmitted power = −5 dBm [2,Figure 9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Figure 3.1 A C-RAN with inter and intra-cloud communicating users. . . 66Figure 3.2 Uplink Transmission Model: (a) User κ encodes its mes-sage into uulκ using lattice coding, then scales it and transmitsxulκ to all RRHs. (b) RRH λ compresses its dithered observedsignal using lattice-based vector quantization, then maps itscompressed signal to an index eulλ , and forwards it to the BBUpool via its fronthaul link. (c) The BBU pool decompressesthe received signals and proceeds to decode 2M integer linearcombinations of user-pairs’ codewords for intra-cloud commu-nicating users, and individual codewords for inter-cloud com-municating ones. In the end, the BBU pool recovers the code-word sums Sulψ = WSul by multiplying the decoded equationswith the inverse of the uplink integer linear coefficient matrix. 68Figure 3.3 Downlink Transmission Model: (a) The CU precodes thecomputed equations, maps each compressed linear equation toan index, and forwards them to RUs. (b) RU λ recovers itsdesired signal and broadcasts it to all users. (c) Intra-cloudcommunicating user κ ∈ Kintra decodes its desired signal us-ing its own codeword as side information, whereas inter-cloudcommunicating user κ ∈ Kinter decodes its desired messagedirectly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Figure 3.4 Achievable uplink sum-rate versus uplink transmitted powerper user P¯ ulκ at Cλ = 400 Mbps [3, Figure 1a]. . . . . . . . . . 77Figure 3.5 Uplink outage percentage versus P¯ ulκ at Rulth = 50 Mbps andCλ = 400 Mbps [3, Figure 1b]. . . . . . . . . . . . . . . . . . 78Figure 3.6 Achievable uplink sum-rate versus Cλ at P¯ulκ = −5 dBm [3,Figure 1c]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79xvLIST OF FIGURESFigure 3.7 Achievable downlink sum-rate versus uplink transmitted powerper user P¯ ulκ at Cλ = 400 Mbps. . . . . . . . . . . . . . . . . . 80Figure 3.8 Achievable downlink sum-rate versus Cλ at P¯ulκ = −5 dBm. . 81Figure 4.1 Total energy efficiency versus the number of iterations. . . . . 93Figure 4.2 Total energy efficiency versus number of APs at K = 4 usersand C` = 400 Mbps. . . . . . . . . . . . . . . . . . . . . . . . 94Figure 4.3 Total energy efficiency versus number of K at L = 32 APsand C` = 400 Mbps. . . . . . . . . . . . . . . . . . . . . . . . 95Figure 4.4 Total energy efficiency versus C` at K = 4 users and L = 64APs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Figure 4.5 Total energy efficiency versus number of APs at K = 4 usersand C` = 400 Mbps [4, Figure 1b]. . . . . . . . . . . . . . . . 97Figure 4.6 Total energy efficiency versus C` at K = 4 users and L = 64APs [4, Figure 1d]. . . . . . . . . . . . . . . . . . . . . . . . . 98Figure 5.1 Uplink Transmission. . . . . . . . . . . . . . . . . . . . . . . . 102Figure 5.2 Downlink Transmission. . . . . . . . . . . . . . . . . . . . . . 108Figure 5.3 End-to-End sum-rate versus SNR in dB at C` = 4 bits/transmission[5, Figure 1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure 5.4 End-to-End sum-rate versus C` in bits/transmission at SNR= 40 dB [5, Figure 2]. . . . . . . . . . . . . . . . . . . . . . . 117xviList of AcronymsAcronyms Definitions5G Fifth Generation5G NR 5G New Radio6G Sixth GenerationAF Amplify-and-ForwardAWGN Additive White Gaussian NoiseB5G Beyond Fifth GenerationBBU Baseband Processing UnitC-RAN Centralized/Cloud Radio Access NetworkCAP Compress-After-PrecodingCCoF Compute-Compress-and-ForwardCF Compress-and-ForwardCF-mMIMO Cell-Free Massive Multi-Input-Multi-OutputCFE Compress-Forward-EstimateCoF Compute-and-ForwardCPU Central Processing UnitCU Centralized UnitD2D Device-to-DeviceDAS Distributed Antenna SystemDF Decode-and-ForwardDMPC Distributed Multi-Pair ComputationDU Distributed UnitECF Estimate-Compress-ForwardEEMPC Energy-Efficient Multi-Pair ComputationEMCF Estimate-Multiply-Compress-ForwardEMCFW Estimate-Multiply-Compress-Forward-WeightF-RAN Fog Radio Access NetworkIFCC Integer Forcing Channel CodingIFSC Integer Forcing Source CodingL1 Physical Layer in OSI ModelL2 Data-link Layer in OSI ModelxviiList of AcronymsL3 Network Layer in OSI ModelLTE Long Term EvolutionLLL Lenstra Lenstra Lovesz Lattice Reduction AlgorithmMAC Medium Access ControlMIMO Multi-Input-Multi-OutputMPC Multi-Pair ComputationMPTWC Multi Pair Two Way ComputationO-RAN Open Radio Access NetworkPAC Precoding-After-CompressRCoF Reverse-Compute-and-ForwardRQCoF Reverse-Quantize-Compute-and-ForwardRRH Remote Radio HeadRU Radio UnitSNR Signal-to-Noise RatioSU Single-User CompressionUE User EquipmentV-RAN Virtualized Radio Access NetworkWZ Wyner-Ziv CompressionxviiiList of SymbolsSymbols DefinitionsK Set of K usersL Set of L RRHsM Set of M user-pairsC` Fronthaul Capacity at RRH `W M ×K user-pairing matrixσ2 Additive white Gaussian noise (AWGN) powerΛc Coarse latticeΛf Fine latticeυΛc Fundamental Voronoi region of the coarse lattice ΛcCulk Nested lattice codebook at user kgk message to be transmitted by user ktulk a random dither added by user kHul L×K uplink perfect channel gain matrixYul Uplink received signals at the RRHsXul Uplink transmitted codewords by the usersZul L× n uplink additive white Gaussian noise matrixBul K ×K uplink scaling matrixDul L× L uplink compression distortion matrix.Aulr Uplink coefficient matrix of compressed signalsAulψ Uplink coefficient matrix of user-pairs’ codewordsRulr,` Uplink compression rate at RRH `Rulk Uplink computation rate at user kHdl K × L downlink perfect channel gain matrixYdl Downlink received signals at the usersXdl Downlink transmitted signals by the RRHsZdl K × n downlink additive white Gaussian noise matrixBdl K ×K downlink beamforming matrixDdl L× L downlink compression distortion matrixAdlr Downlink coefficient matrix of compressed signalsAulψ,inv. The inverse matrix of AulψxixList of SymbolsRdlr,` Downlink compression rate at RRH `Rdlk Downlink computation rate at user kHˆa L×K phase (a) imperfect channel gain matrixHˆb K × L phase (b) imperfect channel gain matrixEa L×K phase (a) channel estimation error matrixEb K × L phase (b) channel estimation error matrixHa L×K phase (a) perfect channel gain matrixYa Phase (a) received signals at the RUsXa Phase (a) transmitted codewords by the usersZa L× n phase (a) additive white Gaussian noise matrixBa K ×K phase (a) scaling matrixDa L× L phase (a) compression distortion matrix.Aar Phase (a) coefficient matrix of compressed signalsAaψ Phase (a) coefficient matrix of user-pairs’ codewordsRar,` Phase (a) compression rate at RRH `Rak Phase (a) computation rate at user kHb K × L phase (b) perfect channel gain matrixYb Phase (b) received signals at the usersXb Phase (b) transmitted signals by the RRHsZb K × n phase (b) additive white Gaussian noise matrixBb K ×K phase (b) beamforming matrixDb L× L phase (b) compression distortion matrixAbr Phase (b) coefficient matrix of compressed signalsRbr,` Phase (b) compression rate at RRH `Rbk Phase (b) computation rate at user kqp`,m Low-level quantization errorRp L×M a user-pair local processing matrixyp` Output of the low-level quantization process at RU `yc` Remaining signal to be forwarded by RU `Rp` The low-level quantization rate at RU `Wc M ×K centralized processing user-pair matrixxxAcknowledgementsFirst and foremost, I offer boundless praise and gratitude to Allah, the All-Knowing and the Most-Generous. I am profoundly thankful for His countless bless-ings, which provided me with the strength, purpose, and patience to reach thissignificant milestone in my life.I extend my deepest appreciation to my Ph.D. supervisor, Dr. Anas Chaaban, forhis exceptional guidance, unwavering encouragement, and constant support through-out my Ph.D. journey. Under his mentorship, I not only learned how to approachintricate research problems but also how to articulate ideas in a clear and concisemanner, be it in oral presentations or written documents. His dedication to refiningsystem models, polishing manuscripts, and guiding them towards submission hasbeen instrumental in the success of this research. Beyond academia, I am profoundlygrateful for his invaluable guidance in various aspects of life; his door was alwaysopen for discussion, demonstrating boundless patience and genuine interest.I am sincerely grateful to Prof. Jahangir Hossain for his invaluable feedbackand insightful discussions that greatly enriched our weekly group meetings, whichhave significantly contributed to the advancement of my research. Additionally, Ialso extend my deepest gratitude to Prof. Stephen O’Leary for his sincere feedback,discerning critiques, and invaluable suggestions during my research proposal exami-nation. I also extend my thanks to Prof. Halim Yanikomeroglu and Prof. MahmudurFatmi for their insightful contributions as members of my examination committee.I am immensely thankful to my labmates at the Communication Theory Lab,UBC Okanagan and my friends in Kelowna, BC, for the enlightening discussions andthe sense of camaraderie that has made this journey an enjoyable one.I must express my deepest gratitude to my family, whose support has been unwa-vering. Their endurance of my absence was a true sacrifice, and I am acutely awarethat I cannot repay this. I could not have reached this stage in my career withouttheir guidance and prayers. Their steadfast belief in my abilities has been the cor-nerstone of my achievements. My heartfelt thanks go to my parents, my brother andsisters, and especially in cherished memory of my father, whose fervor for learningignited my own academic pursuits. I extend my sincerest thanks to my extraordinarymother, whose unwavering strength has been a perennial source of inspiration.xxiAcknowledgementsI express my deepest gratitude to my wife, the radiant beacon in my life, forher unconditional love and unwavering support. Her encouragement, in moments oftriumph and adversity alike, has been immeasurable.Lastly, I extend my heartfelt gratitude to my cherished son, Yaseen. His laughterand presence have been the guiding stars of this endeavor.Each of you has contributed immeasurably to my journey, and for that, I ameternally grateful.xxiiDedicationTo my beloved late father, my incredible mother, my supportive family, my de-voted wife, and my cherished son Yaseen, you are the heartbeat of my journey.xxiiiChapter 1IntroductionThe rapid evolution of next-generation wireless communication networks demandsadvanced radio access network (RAN) architectures capable of delivering high datarates and accommodating a diverse array of connected devices. This thesis exploresthe potential of evolved radio-access networks, specifically focusing on collabora-tive signal processing akin to distributed antenna systems (DAS), exemplified byparadigms like Cloud RAN (C-RAN), Fog RAN (F-RAN), Cell-Free massive MIMO(CF-mMIMO), and Open RAN (O-RAN). This transformation holds the promiseof interference mitigation, ultimately enhancing overall performance. However, theeffectiveness of distributed antenna systems is hindered by restricted radio inter-faces and fronthaul links, which impose limitations on the volume of data exchangebetween the distributed antenna terminals and the central processing unit (CPU).These constraints can impact the overall performance and efficiency of the distributedantenna system. As such, the development of advanced signal processing and relay-ing techniques is crucial for efficient fronthaul link utilization in both uplink anddownlink transmissions.A significant contribution of this thesis is the introduction of novel end-to-endmulti-pair two-way computation approaches tailored for DAS. We advocate for ajoint design strategy encompassing uplink and downlink transmissions, incorporat-ing message source-destination information. This concept is exemplified through apairwise message exchange paradigm among communicating users within the DAS,with a focal point on optimizing end-to-end spectral and energy efficiency.This chapter is structured as follows: Section 1.1 delves into the evolutionaryjourney from the traditional de-Centralized RAN to DAS, covering different DAS ar-chitecture models and the design of the fronthaul network along with its constraints.Section 1.2 scrutinizes existing coding schemes in literature for both uplink anddownlink transmissions in DAS systems. In Section 1.3, we distill the key insightsfrom existing works, introducing the research gaps and persistent challenges. Thethesis objectives and contributions are outlined in Sections 1.4 and 1.5, respectively.Finally, we present the notations and an outline of the thesis in Sections 1.6 and 1.7.11.1. Roadmap Evolution from Traditional de-Centralized RAN to DAS1.1 Roadmap Evolution from Traditionalde-Centralized RAN to DASAccording to the International Telecommunication Union Radio CommunicationSector (ITU-R), the rapid growth of smart Internet-of-Things (IoT) devices and asso-ciated use cases is poised to strain the existing 5G networks in the near future. Thisaligns seamlessly with recent statistical projections by Ericsson emphasizing that theanticipated mobile traffic load for the year 2030 and beyond is expected to skyrocket,reaching an astonishing 5016 exabytes per month, underscoring the surging demandfor data-centric services and applications [6]. Concurrently, this surge in data con-sumption is accompanied by the substantial energy consumption footprint associatedwith operating mobile networks, globally estimated at approximately USD 25 bil-lion [7]. This estimation, however, is further compounded by contemporary globaleconomic challenges, marked by burgeoning inflation and a mounting energy crisis.Consequently, it becomes evident that a comprehensive response is indispensable,involving both the evolution of communication protocols and technologies as well asa paradigm shift in the design and configuration of existing RANs.Compared to 5G networks, the transition to 6G networks holds immense promisefor enabling unprecedented levels of connectivity, capacity, and intelligence. Withdata-intensive applications such as augmented reality, virtual reality, Internet ofThings (IoT), and autonomous systems on the horizon, 6G networks must possessthe capability to support efficient network management, low-complex resource allo-cation, and enhanced user experiences, while reducing total operational costs andenergy consumption. This development has paved the way for the exploration of6G wireless networks, aimed at supporting stringent Key Performance Indicators(KPIs) including a connection density of 107 users per square kilometer with a 1Gbps downlink data rate, coupled with network reliability exceeding 99.99999% andcommunication latency as low as 0.1 msec [8]. Additionally, in the realm of 6G,communication scenarios have evolved to meet the burgeoning demands of users,introducing immersive communication, massive communication, hyper-reliable andlow-latency communication (URLLC), and ubiquitous connectivity. Immersive com-munication, pushing beyond the boundaries of 5G’s enhanced mobile broadband,encompasses technologies like extended reality and holographic communications, de-manding substantial transmission bandwidth for seamless virtual experiences. Mas-sive communication, an evolution from 5G’s massive machine-type communications,envisions supporting an extensive array of devices in concentrated areas, necessi-tating extremely high-speed connectivity for the diverse and numerous connectionsinherent to this paradigm as well as covering the network with massive number of21.1. Roadmap Evolution from Traditional de-Centralized RAN to DASantennas. URLLC, a critical advancement, addresses mission-critical applicationssuch as remote tele-surgery and autonomous driving, relying on extremely high-speed connectivity for near-instantaneous responsiveness and unwavering reliability.Ubiquitous connectivity, bridging digital divides, aims to enhance connectivity inunderserved areas, relying on interworking with other access systems. The commonthread weaving through these scenarios is the imperative of extremely high-speedconnectivity, serving as the linchpin for unlocking the transformative potential of 6Gtechnologies.Consequently, mobile operators are currently facing increasing pressure to en-hance their network performance capabilities, prompting them to explore novel so-lutions in order to keep up with the requirements of 6G networks. This typicallyinvolves either adding new network equipment/modules or adopting more efficient,flexible, and scalable alternatives. Quantitatively, the radio access network (RAN)represents a substantial portion (approximately 65%-70%) of total network capi-tal expenditures, according to Ericsson. To effectively address the confluence ofthese challenges and opportunities, a revolutionized synergistic approach is required,wherein architectural innovations align harmoniously with robust energy-efficientstrategies and sophisticated QoS provisions. In light of this transformative impera-tive for the future, next-generation mobile networks necessitate a meticulous designapproach that adeptly harnesses the limited radio resources, navigates the intrica-cies of optimizing network parameters, and accommodates the unprecedented surgein mobile data traffic demands. As we embark on the 6G evolution, these challengeshave become even more intricate, requiring innovative solutions that are uniquely tai-lored to the complexities and requirements of future network paradigms. The mainconclusion emphasized by RAN experts is that the ultimate challenge of current mo-bile network architectures is its design itself. This has driven researchers to proposeadvanced RAN architectures with efficient and powerful processing techniques thatcan dramatically improve network performance.Understanding the RAN architecture could help in determining the most appro-priate evolution to keep up with the requirements of next-generation mobile networks.The landscape of mobile communication has witnessed a remarkable evolution overthe years, with each generation bringing forth new demands and technological chal-lenges. One pivotal aspect of this evolution has been the continuous transformationof Radio Access Networks (RANs) to meet the diverse Key Performance Indicators(KPIs) associated with different mobile generations as shown in Fig. 1.1. This fig-ure demonstrates that the evolution of RAN architectures is crucial to ensure thatmobile networks meet the evolving demands of different mobile generations. Each ar-chitecture represents a step forward in addressing specific challenges and optimizing31.1. Roadmap Evolution from Traditional de-Centralized RAN to DASFigure 1.1: Evolution of mobile generations KPIs: A comparative evaluation from4G KPIs to 6G KPIs.performance, ultimately shaping the future of wireless communication. Researchersand network operators must continue to assess and innovate in this field to meet thediverse needs of modern mobile communication. Next, we investigate the roadmapevolution journey from the traditional de-Centralized RAN to DAS, covering theDAS’s different architecture models.1.1.1 Traditional de-Centralized RANIn general, a RAN consists mainly of radio units (RUs) which perform all the ra-dio transmission functions, and baseband processing units (BBUs) which support allother protocol layers of the RAN. The BBU has been largely designed as a combina-tion of dedicated physical processing functions, such as source coding/decoding, mod-ulation/demodulation, channel estimation, equalization, and channel coding/decoding.It also includes other medium access, radio link, and radio recourse control functions.For every transmit interval, the medium access control (MAC) layer defines the sizeof the packet to be used. This transmit interval is referred to as a transmit block.The MAC is also responsible for the reliable transfer of data over the air by per-forming a hybrid automatic repeat request (HARQ) procedure, which uses ACK andNACK feedback from the receiver. HARQ allows the transmitter to retransmit the41.1. Roadmap Evolution from Traditional de-Centralized RAN to DASFigure 1.2: Evolution of Radio Access Network (RAN) Architectures: A ComparativeEvaluation from de-Centralized RAN to Centralized RAN to 5G Split RAN.data packet if the packet is not correctly received. The MAC layer is further usedfor implementing fast control signaling, for example, activating carrier aggregation.Fast control activation is required because other signaling mechanisms through theupper radio resource controller (RRC) can be almost 10 times slower. The radio linkcontroller (RLC) layer processes the data arriving from the upper layers into packetsthat fit into the transmit block defined by the MAC layer. An incoming packet maybe segmented into smaller packets or multiple packets may be concatenated into alarger packet. The packet data convergence protocol (PDCP) provides optional IPpacket header compression and security features. It encrypts the data that is sentover the air and protects the integrity of signaling messages to protect against ma-licious tempering. The radio resource control (RRC) is the top protocol layer usedfor major RAN functions, such as connection establishment, handover procedures,paging an idle user equipment, uplink power control, and so on. The PHY, MAC,and RLC layers are involved in tasks that are very delay-sensitive (of the order of afew milliseconds), such as HARQ operations and fast control signaling. In contrast,the higher layer PDCP and RRC protocols undertake tasks that are more delaytolerant and can take tens of milliseconds. Each function in the BBU is designedeither independently or jointly with another function based on systematic modelsthat determine the network behavior and the required mobile data traffic [9].51.1. Roadmap Evolution from Traditional de-Centralized RAN to DASIn the 2G and 3G networks as well as initial long-term evolution (LTE) installa-tion, de-Centralized RAN was deployed as the nascent phase of mobile networks. Inde-Centralized RAN, base stations (BSs) are distributed across the service area, eachserving a specific cell. The BBU was placed at the bottom of the antenna tower andconnected to its RU using a short fiber run or coaxial cable as shown in Fig. 1.2. Thisconfiguration is referred to as traditional or de-Centralized RAN which ensures a lowRU-BBU latency for procedures such as providing timely acknowledgment (ACK) ornon-acknowledgment (NACK) in response to the reception of downlink data packets.In this traditional RAN, the complicated scheduling task in the BBU can onlyfocus on active users supported by the RUs in the serving cells with little or nocoordination with other cells. This means that the BBU manages and schedulesresources independently for each cell without significant coordination with othercells in the network. As a result, resources may not be efficiently distributed acrossthe entire network. Some cells might be underutilized while others may experiencecongestion, leading to suboptimal network performance. Additionally, the BBU’soperation needs to remain operational 24 hours/7 days with its full power capabilities,regardless of the number of users actively using the network. This underutilizes theBBU resources and increases power consumption, thereby upsurging the total RANcosts.Moreover, with the deployment of massive machine-type communications (m-MTC), vehicle communications (V2X), industrial internet of things (IIoT), large-scale intelligent reconfigurable surfaces (IRSs), ultra-massive multiple-input multiple-output (UM-MIMO) networks, and other applications included in the third genera-tion partnership project (3GPP) Releases 15 through 18, designing the RAN networkbased on the traditional de-centralized architecture becomes extremely difficult andwith unreasonably high computational complexity. For instance, one of the key po-tentials of beyond 5G (B5G) technologies is network densification through planninga massive deployment of small cells and implementing their corresponding low-powerBSs. However, managing the BSs in a massive number of small decentralized cellsis challenging [9]. Furthermore, the diversity of recent communication protocols andtechnologies, increasing traffic demands, and convergence requirements make tradi-tional RANs far too expensive to be competitive in the current mobile data world.Consequently, it is anticipated that de-Centralized RAN architectures will not becapable of adapting to emerging technologies and providing the required dramaticperformance enhancement in next-generation mobile networks.Evidently, it became paramount to have revolutionized RAN architectures thatcan tackle the aforementioned de-centralized architecture limitations and supportB5G mobile networks. This triggered the need for more advanced architecture, lead-61.1. Roadmap Evolution from Traditional de-Centralized RAN to DASing to the emergence of distributed antenna systems (DAS) as discussed next.1.1.2 Distributed Antenna SystemsIn order to overcome the challenges in the de-Cendtralized RAN architectures andto address the requirements of next-generation wireless networks, one viable approachis to pool some (or possibly all) BBU functions into a physical infrastructure or acloud-based central processing unit (CPU). This architecture is called ”CentralizedDistributed Antenna Systems” (DAS). While the theoretical interest in DistributedAntenna Systems (DAS) originated in the 1990s [10, 11], the practical deploymentwithin mobile networks experienced significant growth toward the end of the 3G erain the late 2000s [12].DAS comprises three main fundamental components: Baseband processing Unit(BBU) pool, Remote Radio Heads (RRHs) (can also be referred as radio units (RUs)or access points (APs)) functioning as distributed remote antenna elements, andfronthaul links connecting the BBU pool and RRHs as shown in Fig. 1.2. Central-ized signal processing in DAS allows for facilitating the deployment of distributedRRHs in the service area, upgrading the equipment, resources, and operations sharingamong different RUs, saving power consumption, and maximizing network coverage[13]. Additionally, this configuration enables the dynamic sharing of radio resourcesamong various BBUs in the BBU pool to meet fluctuating user demands. The cen-tralized BBU pool assumes control over all RRHs in the service area and is adaptable,allowing for changes in the number of active BBUs in the pool over time and allocat-ing signal processing resources dynamically as needed [14, 15]. Further, with closeproximity between BBUs, advanced LTE and 5G New Rdio (5G NR) features such asinterference coordination, cancellation, and carrier aggregation across BBUs becamepossible [16].DAS concept encapsulating a range of innovative network architectures. Theseencompass Cloud RAN (C-RAN), Fog RAN (F-RAN), Cell-Free Massive MIMO(CF-mMIMO), and Open RAN (O-RAN) frameworks. Each of these paradigmsintroduces unique collaborative signal processing methods, which in turn, presentdistinct challenges in terms of fronthaul network design. Through this comprehensiveexamination, we can better grasp the complexities involved and devise more effectivesolutions for optimizing fronthaul networks in these diverse RAN setups.1.1.2.1 Cloud RANA C-RAN can have different configurations depending on the split of BBU pro-cessing functions between the RRHs (locally) and the BBU pool (centrally) [17].71.1. Roadmap Evolution from Traditional de-Centralized RAN to DASOne extreme which can decrease RAN costs is to pool all BBU processing func-tions into central hubs or baseband ’hotels’, while limiting the RRHs’ functionalityto transmission/reception only. This approach is referred to as a fully centralizedRAN, which enables fully-centralized signal processing capabilities in advanced LTEnetworks. Functions like modulation, coding, fast Fourier transform, and channelselection are executed in the BBU pool. Conversely, RRHs represent distributedantenna terminals responsible for transmitting radio signals from the BBU pool tousers in the downlink and forwarding baseband signals from users to the BBU poolfor uplink processing. RRHs handle functions such as radio frequency (RF) amplifi-cation, up/down conversion, filtering, digital processing, analog-to-digital conversion,digital-to-analog conversion, and interface adaptation. With most signal processingperformed in the BBU pool, RRHs can have simplified designs and can be deployedefficiently over large-scale scenarios.Technically, in a C-RAN, the BBU pool coordinates the different transmit framesof the connected RRHs and shares users’ data among all (or a subset of) theseRRHs (depending on the level of coordination, i.e., signal-level or scheduling-level).In signal-level coordination [18, 19], users’ data is shared among various RRHs us-ing a data-sharing, reverse-compute-and-forward, or compression-based strategies.However, signal-level coordination in C-RANs requires high fronthaul link capacitiesas well as optimization over different factors, such as RRH’s beamforming vectors,user-RRH association, and message traffic over the fronthaul links. This makes theC-RAN’s design complex [20]. On the other hand, in scheduling-level coordination[21, 22], the BBU pool allocates users to the radio resources of the different RUs,under the constraint that each user can be connected to at most a single RRH. Thissystem constraint not only overcomes sharing users’ data among multiple RRHs butalso manages interference in a C-RAN [23, 24]. As a result, scheduling-level coordi-nation in C-RAN offers a simplified, yet efficient, resource coordination framework[25, 26].Although C-RAN is anticipated to usher in significant enhancements in wirelessmobile networks, its practical implementation faces notable limitations. A criticalconcern within C-RAN is the consolidation of Baseband Units (BBUs) in a singlepool over cloud architecture heightens the risk of a single-point failure, potentiallyresulting in a complete network outage. Additionally, C-RAN introduces a substan-tial fronthaul overhead in the communication links connecting RRHs and the BBUpool, often exceeding fronthaul requirements by an order of magnitude [13]. This el-evated fronthaul demand is exacerbated by concerns regarding fronthaul latency andjitter, which can be significant limitations for future C-RAN-based wireless systems.In specific scenarios, centralized signal processing may increase latency, leading to81.1. Roadmap Evolution from Traditional de-Centralized RAN to DASsuboptimal C-RAN performance.1.1.2.2 Cell-Free Massive MIMO (CF-mMIMO)Another DAS candidate for B5G technology is the cell-free massive MIMO (CF-mMIMO) architecture (also known as distributed massive MIMO), where a very largenumber of access points (APs) distributed in a large area coordinate their transmis-sion to serve a small number of user devices [27, 28]. The cooperation betweenAPs in a CF-mMIMO network reduces interference and increases spectral efficiency.As such, CF-mMIMO network is conceptually similar to a C-RAN, with the maindifference being the massive number of APs leading to channel hardening and favor-able propagation, which consequently improves the performance of linear precodingschemes [29]. In addition, through employing time division duplex (TDD) massiveMIMO and user-centric design techniques, scalable CF-mMIMO can be realized [30].Massive MIMO technology can be implemented in either collocated or distributedconfigurations. Collocated setups concentrate antennas on a base station or withina limited space, while distributed setups scatter antennas across a wide area. Orig-inally devised to address indoor dead spots, distributed antenna networks evolvedto enhance data rates and coverage. Collocated architecture excels in low back-haul link requirements, while distributed setups offer advantages in diversity gainand shadowing effect, notably heightening coverage probability. This section scruti-nizes the realm of distributed massive MIMO, also known as cell-free massive MIMO(CF-massive MIMO). CF-massive MIMO employs numerous controllable antennas,or access points (APs), dispersed across a large expanse, coordinating transmissionsfor a small pool of user devices. This approach holds immense promise for next-generation technology, ensuring equitable service quality with simplified signal pro-cessing [31]. Cooperation among APs minimizes interference and bolsters spectralefficiency, while antenna dispersion amplifies diversity gain for improved coverage.CF-massive MIMO amalgamates TDD massive MIMO, a distributed ultra-densenetwork topology, and user-centric design, ensuring scalability. Breaking free fromtraditional cell boundaries, CF-massive MIMO maximizes the advantages of bothmassive MIMO and small cells, presenting a powerful solution for future wirelessnetworks. A radio stripes structure can be employed for deployment, wherein anten-nas and their processing units are serially connected, sharing synchronization, dataexchange, and power. This structure enhances synchronization among APs, furtheroptimizing system performance [32].Comparatively, collocated massive MIMO, with antennas confined to the basestation, entails lower data-sharing overhead and fronthaul requirements compared91.1. Roadmap Evolution from Traditional de-Centralized RAN to DASto CF-massive MIMO. However, CF-massive MIMO offers distinct advantages, in-cluding expanded coverage and improved channel decorrelation, even in proximity toother users. Moreover, CF-massive MIMO ensures each user benefits from a multi-tude of APs, guaranteeing robust channel quality and equitable service. By dispers-ing antennas widely, CF-massive MIMO eliminates scenarios where some users arein close proximity to the base station while others are distant, resulting in a moreequitable system [33].A series of studies have delved into the performance of cell-free massive MIMOin comparison to both collocated massive MIMO and small cell networks [34]. Whenperfect CSI is available at both APs and users, distributed antenna networks offerhigher per-user rates in asymptotic scenarios, particularly with a large number of an-tennas. Additionally, CF-massive MIMO outperforms centralized solutions in termsof average rate, affirming its efficacy in real-world scenarios [35, 36].In contrast to small cells, where each AP serves a single user, CF-massive MIMOleverages AP cooperation to serve multiple users, mitigating inter-cell interference.This grants CF-massive MIMO a significant advantage in per-user rate and coverageprobability. With perfect CSI at both APs and users, CF-massive MIMO surpassessmall cell systems, demonstrating superior per-antenna rates, particularly as thenumber of small cells increases. In the presence of imperfect CSI, CF-massive MIMOremains dominant, showcasing substantial improvements in per-user throughput [31,37].While Cloud RAN (C-RAN) and Cell-Free Massive MIMO (CF-mMIMO) ar-chitectures offer notable advantages, their effectiveness is hindered by the tangibleconstraints of fronthaul links. This is particularly evident in densely populated wire-less networks where the sheer volume of data transmission poses a challenge [13, 28].To address this, a viable approach is to distribute certain processing tasks from thecentral processing unit (CPU) to the Remote Units (RUs), which will be furtherelaborated on in the subsequent discussion. This method aims to alleviate the strainon the fronthaul links, ultimately enhancing the overall performance of the network.1.1.2.3 Fog RAN (F-RAN)To reduce the fronthaul traffic of C-RAN in ultra-dense networking scenarios,edge-caching (EC) has emerged [38, 39]. EC was motivated by the observationthat a large portion of mobile multimedia traffic is generated by many duplicatedownloads of particular popular content (audio, photo, or video) within a shortperiod of time [38–40]. Instead of causing unnecessary traffic on the fronthaul links,such popular content is cached at edge nodes (local storage of RUs) during off-peak101.1. Roadmap Evolution from Traditional de-Centralized RAN to DAShours. This way, RUs can transmit cached content to requesting users with littleto no intervention from the cloud. In addition to reducing fronthaul traffic, EC canenable cooperative transmission if common content is cached at multiple edge nodes,and is an effective way for reducing content delivery time [40, 41]. These cachingRUs are henceforth referred to as enhanced RUs (eRUs). EC introduced a paradigmshift in wireless network design and optimization featuring a transition from content-agnostic schemes to content-specific ones. The resulting wireless network architectureis referred to as Fog RAN (F-RAN) [42, 43]. An F-RAN exploits the centralizedprocessing advantages of C-RAN and the fast content delivery of EC [44]. Indeed,harvesting these advantages requires careful design of content distribution amongeRUs (including cache placement, cache capacity, and request-to-cache routing) andcontent delivery to users (including resource utilization and efficient transmission)[45].Long-range wireless communication between eRUs and users is subject to fading,shadowing, and other propagation effects. This occasionally leads to link failures.However, in when users are close to each other, communication with eRUs is notnecessary if users can communicate directly with each other. Motivated by this,device-to-device (D2D) communication was proposed as a key enabler of 5G networks[46, 47]. Due to its short-range communication, cooperation, and data exchange be-tween connected devices, D2D communication offloads the traffic from the eRUs andCPU and frees their resources to serve other users [46]. This can be used to enhanceF-RANs, where caching at the eRUs is combined with user cooperation via D2Dcommunications, leading to the so-called D2D-aided F-RAN [48]. The performanceof F-RAN can be further improved by pushing some popular content to the usersnear the eRUs. This can be beneficial in B5G where the size of the popular contentswill be too large to cache at the eRUs due to cost/memory issues. Instead, caching atdevices can be employed [49, 50]. With distributed caching at eRUs and devices, notonly do the eRUs transmit their cached content to requesting devices, but devices canalso deliver their cached content to other devices via D2D communications. Besidesits integration with F-RANs for content delivery, D2D communications is also a corecomponent in many mobile cloud/fog computing systems that distribute heavy pro-cessing tasks, e.g., distributed optimization and computation, over a computationallylimited CPU [51, 52].To address the 5G low delay requirements, the 3GPP introduced a split RANarchitecture, where the CPU is effectively split into two units: the centralized unit(CU) and the distributed unit (DU). The DU is placed close to the RU, but theCU is located far away from the DU. Larger or multiple CUs can be placed in acentralized manner to facilitate a cost-effective cloud-based implementation. The111.1. Roadmap Evolution from Traditional de-Centralized RAN to DASDU implementation may be a mixture of physical and virtual technologies. One ofthe primary benefits of the split RAN architecture is that it utilizes network resourcesefficiently. By separating low-level from high-level (define high/low-level) functions,this split RAN architecture allows for a more effective allocation of resources to wherethey are needed most. This can lead to reduced latency and communication overheadover the RAN interfaces, thus improving network performance, as discussed next.1.1.2.4 Open RANThe evolution from Cloud RAN (C-RAN) to the split RAN architecture (is alsoreferred as Open RAN (O-RAN)), as shown in Fig. 1.2, emphasizes two key princi-ples: Openness and Intelligence. Openness focuses on accessible interfaces, enablingsmaller vendors and operators to innovate and tailor networks to their needs. It alsoencourages multi-vendor RAN setups, fostering a dynamic ecosystem. Open-sourcesoftware and hardware play a crucial role in rapid innovation while maintainingcompatibility with legacy systems. As wireless systems like 5G grow in complex-ity, mobile network operators and vendors must develop self-organizing capabilities,utilizing technologies like Machine Learning (ML) and Artificial Intelligence (AI) toautomate network operations and reduce costs. The deployment of an open vir-tualized RAN is considered a major step forward in the progression towards 5Gdeployment [53].The increasing interest in O-RAN is evident in the growing number of researchand development initiatives under the O-RAN alliance. This initiative is built onthree key principles: promoting open, interoperable interfaces, virtualizing the Ra-dio Access Network (RAN), and leveraging big data for RAN intelligence. It alsooutlines the specification of APIs and interfaces, driving standardization efforts andexploring open-source solutions where applicable. Additionally, it advocates for themaximal use of Commercial Off-The-Shelf (COTS) hardware and merchant siliconwhile minimizing reliance on proprietary hardware.The increasing interest in O-RAN is evident in the growing number of researchand development initiatives under the O-RAN alliance. This initiative is built onthree key principles: promoting open, interoperable interfaces, virtualizing the Ra-dio Access Network (RAN), and leveraging big data for RAN intelligence. It alsooutlines the specification of APIs and interfaces, driving standardization efforts andexploring open-source solutions where applicable. Additionally, it advocates for themaximal use of Commercial Off-The-Shelf (COTS) hardware and merchant siliconwhile minimizing reliance on proprietary hardware.O-RAN introduces a more flexible functional split between the radio units (RUs),121.1. Roadmap Evolution from Traditional de-Centralized RAN to DASdistributed unit (DU), and the central unit (CU). This allows for a greater degree oflocalized processing at the RU and DU levels, thereby mitigating the necessity forfrequent and high-capacity communication with the CU.Additionally, the O-RAN initiative employs advanced technologies including Soft-ware Defined Networking (SDN), AI-enabled RAN Intelligent Controllers, RAN Vir-tualization, Open Interfaces, White Box hardware, and Open Source software. TheSoftware Defined, AI-Enabled RAN Intelligent Controller extends the SDN paradigmby separating the control plane (CP) from the user plane (UP) within the Radio Ac-cess Network (RAN). This separation enhances traditional Radio Resource Manage-ment (RRM) functions with embedded intelligence provided by the RAN IntelligentController (RIC). This brings benefits such as standardized UP, enabling seamlessscalability, and cost-effective solutions. It also introduces advanced control func-tionalities, contributing to enhanced efficiency and superior radio resource manage-ment and intelligent traffic routing algorithms through analytics and data-driven ap-proaches, including sophisticated Machine Learning (ML) and Artificial Intelligence(AI) tools. O-RAN is dedicated to leading the development of AI-enabled RICs,ensuring that only essential data is transmitted over the fronthaul links, therebyoptimizing fronthaul bandwidth usage. It envisions that even complex networks em-bracing the O-RAN AI-enabled RIC will inherently deliver efficient, optimized radioresource management through closed-loop control [54].Another critical aspect of the O-RAN architecture is RAN Virtualization. O-RAN places particular emphasis on delivering the prerequisites for Network FunctionVirtualization Infrastructure/Virtualized Infrastructure Manager (NFVI/VIM), en-hancing virtualization platforms to support various protocol stack splits, includingnetwork slicing. By doing so, O-RAN enables the dynamic allocation and scalingof computational resources [55]. This strategic allocation allows for resources to besituated in closer proximity to the edge of the radio access network (RAN), wherethey are most crucial, ultimately minimizing the need for extensive fronthaul com-munication. This approach enhances the efficiency and responsiveness of the networkto better meet the demands of users [56, 57].It is essential to underscore that the O-RAN initiative remains in its nascentstages of development. The realization of its envisioned goals is an ongoing processthat is expected to evolve through various stages of development, shaped by in-creasingly pragmatic engagement with C-RAN, V-RAN, and O-RAN. In light of thistrajectory, it is imperative that forthcoming research endeavors prioritize practicaland real-world trials specifically centered on virtualized RAN concepts.In light of the preceding subsections, it becomes evident that the optimizationof resource allocation and effective data transmission is pivotal for enhancing the131.1. Roadmap Evolution from Traditional de-Centralized RAN to DASperformance metrics of diverse DAS architectures, encompassing C-RAN, V-RAN,CF-mMIMO, and O-RAN. Distributing antennas in these systems yields substantialbenefits, including amplified achievable rates, heightened energy efficiency, expandedcoverage, reduced latency, and equitable system fairness. However, a significant chal-lenge faced by DAS systems arises from the limited fronthaul capacity linking RemoteUnits (RU) with Central Processing Units (CPU). This constraint imposes restric-tions on the volume of traffic that can traverse between RU and CPU, consequentlylimiting network performance. Thus, it is imperative to delve deeper into the intri-cacies of fronthaul link design, underscoring their inherent constraints, and subse-quently explore strategies to surmount these limitations. This proactive approach isessential to align fronthaul capabilities with the evolving demands of next-generationRAN, a discussion we undertake in the ensuing subsection.1.1.3 Design of Fronthaul Network in Distributed AntennaSystemsThe communication between the distributed antenna terminals and the BBU poolin DAS systems is normally realized over a digital high-speed fronthaul interface, aninternal interface for serial data transfer between the distributed RUs and CPU. Thisinterface is responsible for forwarding the digitized in-phase and quadrature (I/Q)samples resulting from the sampling and quantization of radio signals at the RUs.It also transmits other synchronization, management, and control signals that areemployed for operations and maintenance (OAM) purposes [58]. These fronthaullinks can be deployed using various technologies, including optical fiber, standardwireless, or microwave/millimeter-wave communication. Optical fiber offers hightransmission capacity but comes at a higher cost and lacks flexibility, while wirelessfronthaul is cost-effective and flexible but offers reduced capacity and reliability.Because of the centralized nature of the processing resources in the CPU andthe distributed nature of the antenna terminals in the service area, fronthaul linksbetween the distributed RUs and the CPU are of critical importance in the designof DAS architectures. In order to build a high-reliability fronthaul network, it isnecessary to take into account some interdependent technical requirements such asthe RU configuration, required data rate, bit error rate (BER), latency, synchroniza-tion, and jitter, and operations administration and maintenance (OAM) constraints.It is also important to consider business aspects in terms of obtaining low-cost im-plementation from a mobile operator point of view [59]. In this section, we startby presenting traditional fronthaul interface standards and highlighting their con-straints, followed by how we can overcome their limitations to keep up with the141.1. Roadmap Evolution from Traditional de-Centralized RAN to DASrequirements of next-generation RAN as discussed next.The conventional fronthaul interface has been standardized by the common pub-lic radio interface (CPRI) and open base station standard architecture initiative(OBSAI) specifications [60]. Both protocols include different RAN vendor-specificgroups, thereby, full interoperability between them is not guaranteed [61].The first version of the CPRI protocol was published in 2003 as a result of cooper-ation between leading RAN technologies vendors, e.g. Ericsson, Huawei TechnologiesCo. Ltd, NEC Corporation, and Nokia. Further improved versions have been re-leased until version 7.0 in 2015 [62]. CPRI specifications divide the BS into two partsincluding a baseband unit (BBU), or a radio equipment control (REC) unit (can bereferred to as CPU), and a radio frequency unit (RU) or radio access equipment(RE). The CPRI interface separates between the radio frequency (RF) signal andbaseband signal using the physical layer (L1) and data-link layer (L2) protocols ofthe open standard interconnection (OSI) protocol stack [58, 63]. However, CPRI hasa stringent BER constraint, where each fronthaul link must operate with at most aBER value of 10−12 [59, 64].In contrast, the OBSAI is another industry specification group resulting from thecollaboration of joining RAN vendors, and component and module manufacturers toreduce the cost of deploying RAN architectures [65]. OBSAI was first released in2002 and successively improved versions have been published afterwards as for CPRI.According to the OBSAI specifications, the BS is divided into four main modulesincluding radio frequency (RF), transmission, processing, and control modules. TheRF module transmits, receives, and amplifies RF signals and converts them fromanalog to digital and vice versa. The transmission module provides communicatinginterfaces between the different modules, as well as the conformance and interop-erability test specifications. In the processing module, the baseband signals arecomputed and processed. The control module supports system management, config-uration, and synchronization of all BS modules and generates reports to the OAMsystem [66]. Therefore, OBSAI specifications deal with the physical (L1), data-link(L2), transport (L4), and application (L7) layers protocols of the OSI protocol stack[67]. Also, the BER requirement in OBSAI is 10−15 which is more stringent thanthat in CPRI.Another industry specification group called open radio interface (ORI) was formedby the European Telecommunications Standards Institute (ETSI) in 2010 to intro-duce a fronthaul interface specification that can support multi-vendor interoperabilitybetween network elements in the RAN system [61, 68]. This interface is built overthe CPRI protocol by removing some functions and adding other options to supportthe full interoperability [59].151.1. Roadmap Evolution from Traditional de-Centralized RAN to DASFigure 1.3: CPRI RAN functional split: fully separating RF functions in distributedRUs (RE) and all L1/L2/L3 processing functions of the OSI protocol stack in theCPU (REC).Despite the differences between the CPRI, OBSAI, and ORI interfaces, they allprovide a constant bit rate in both uplink and downlink transmission. However,CPRI is the widely used protocol for the fronthaul interface by RAN vendors, es-pecially for conventional fully-centralized 4G C-RAN networks, due to its efficientone-to-one I/Q samples mapping techniques between the distributed RUs and theCPU [58, 69]. As a result, in this subsection, we confine our investigation to theCPRI specifications as a case study of the conventional fronthaul interfaces.In conventional 4G C-RAN networks, the CPRI fronthaul interface is used tofully separate the RF functions in distributed RUs and all the baseband processingfunctions in the CPU as shown in Fig. 1.3 [64]. This split allows the full centralizationof all L1/L2/L3 processing functions of the OSI protocol stack, at the expense ofextremely stringent fronthaul capacity and latency demands [70].CPRI can support constant data rate options from 614.4 Mbps up to 24330.24Mbps over one RU-CPU fronthaul connection [59, 71, 72]. Generally, informationflows at the higher layers of the OSI protocol stack are less data-intensive thanthose at the lowest. Processing functions in the physical (PHY) layer (e.g. cyclicredundancy check (CRC), modulation, mapping, and encoding) add extra overheadto the data blocks received from the higher MAC layer. Thus, incredibly higherdata rates are required as the information flows at the PHY layer towards the RUwhere RF functions are performed [62]. Practically, CPRI requires an overhead ofup to 30 times the 4G LTE baseband data rates, thus requiring the deployment ofone or more 10 Gbps optical fiber fronthaul links to support 4G LTE data rates161.1. Roadmap Evolution from Traditional de-Centralized RAN to DASTable 1.1: Required CPRI fronthaul data rate in fully centralized DAS [1]Number of antennasRF channel bandwidth10 MHz 20 MHz 50 MHz 100 MHz 1 GHz2 1 Gbps 2 Gbps 5 Gbps 10 Gbps 100 Gbps8 4 Gbps 8 Gbps 20 Gbps 40 Gbps 400 Gbps64 32 Gbps 64 Gbps 160 Gbps 320 Gbps 3200 Gbps256 128 Gbps 256 Gbps 640 Gbps 1280 Gbps 12800 Gbps[73]. As current 5G networks aim to support 10 times the data rates of LTE, thefronthaul rate needs an increase to over 100 Gbps, which is cost-prohibitive andoperationally challenging. Particularly, the required CPRI data rate RCPRI dependson the employed radio-access technology (RAT), MIMO implementation, and RFchannel bandwidth as shown in the following expression [59, 74]RCPRI = 2SnAfsbsCwC, (1.1)where Sn is the number of antenna sectors, A represents the number of antennaports per sector, fs is the sampling rate for RF signal digitization (30.72 Mega sam-ples/second per 20 MHz RF channel bandwidth) and bs is the number of bits persample (referred as the sample width and is typically 15 bits/sample for LTE sys-tems), Cw accounts for control word overhead in the CPRI frames (typically 16/15),and C denotes a line coding factor (either 10/8 for 8B/10B code or 66/64 for 64B/66Bcode) [1, 59]. Factor 2 is due to the in-phase and quadrature-phase components. Forinstance, for high bandwidth demanding services such as enhanced mobile broad-band (eMBB) or for massive MIMO distributed RUs, the CPRI protocol requiresunreasonably high fronthaul capacity with maximum latency between RU and CPUof a few hundred microseconds.Table 1.1 demonstrates the approximate required CPRI data rates without linecoding using various RF channel bandwidths and numbers of antennas in a conven-tional fully-centralized C-RAN network as given by the 3rd Generation PartnershipProject (3GPP) [1]. As shown in this table, with 20 MHz LTE and 2 antennasconfiguration, the required CPRI data rate without line coding is 2 Gbps (2.5 Gbpswith line coding 10/8) for one RU-CPU fronthaul connection. Therefore, extremelyhigh fronthaul capacity is needed in order to have a fully centralized C-RAN networkwhich is a major problem in the design of next-generation RAN networks [13, 75].Moreover, the 4G LTE RAN latency requirement of about 10 ms leaves a de-lay budget of 100 microseconds over the fronthaul link between the CPU and RU;171.2. Literature Review for Uplink and Downlink Coding Strategies in DASconversely, the maximum fronthaul distance is only around 15 km. With some 5G ap-plications, an RAN latency of 1 ms is required. This requirement forces the distancebetween the RU and the CPU to be around 1 km, requiring many more locations forthe CPUs, which is expensive [41].CPRI specifications have some other drawbacks that make them too far fromaccommodating the evolution in the RAN industry nowadays. First, CPRI has aconstant data rate regardless of the change of mobile traffic per the temporal/servicearea dimensions [62]. Even in situations when there is no active user traffic in the net-work, there are still CPRI streams forwarded between the CPU and distributed RUs.This underutilizes the fronthaul bandwidth thus decreasing efficiency. Second, as thenumber of antennas increases, the required CPRI data rate is incredibly increasing.This is a major impediment to the use of the CPRI interface in 5G networks as far asdeploying cell-free mMIMO networks is concerned. Moreover, advanced networkingand OAM features of data transport standards are required which are not supportedby CPRI specifications [76]. Finally, the cost of the fully centralized DAS networkssupported by the CPRI specifications is very high [69].With the current revolution in B5G networks, many mobile operators started toquestion the efficiency of CPRI specifications to keep up with the requirements ofnext-generation RAN. Currently, researchers and industry experts are working onproposing new techniques for lowering the extremely high capacity demands on thefronthaul network, while still keeping as many benefits as possible from the fullycentralized processing as in conventional C-RAN network.To efficiently utilize the fronthaul network resources and better support the evolv-ing needs of next-generation RAN, advanced functional split schemes, uplink anddownlink relaying techniques, hybrid DAS and other emerging technologies, and ma-chine learning (ML) and artificial intelligence (AI) approaches have been investigated.This thesis centers specifically on elucidating how the implementation of advancedcoding schemes in both uplink and downlink transmissions can facilitate the optimalutilization of fronthaul links in DAS systems, a subject that will be explored in thesubsequent section.1.2 Literature Review for Uplink and DownlinkCoding Strategies in DASOne way to limit the fronthaul signaling requirements is through using efficientuplink and downlink source and channel coding schemes. From an information-theoretic perspective, the DAS model is best understood as a relay network. The181.2. Literature Review for Uplink and Downlink Coding Strategies in DASRUs can be considered relaying nodes that facilitate communication between theCPU and the user terminals. A major drawback of DAS architectures is that theirperformance is constrained by the limited capacity of fronthaul links that connect thedistributed RUs with the CPU. This puts a constraint on the amount of exchangedtraffic between the RUs and the CPU. In order to tackle this problem, various uplinkrelaying schemes have been proposed to relay user data traffic from distributed RUsto the CPU, such as decode-and-forward (DF) [77], amplify-and-forward, compress-and-forward (CF) [78], compute-and-forward (CoF) [79], and noisy network coding[80]. Additionally, in the downlink, the CPU transmits data to users via the dis-tributed RUs using cooperative relaying schemes such as data-sharing techniques[81], compression-based strategies, [26], reverse compute-and-forward (RCoF) [82],and reverse quantized-compute-and-forward (RQCoF) [79]. These techniques havegained significant attention in recent years due to their potential to enhance over-all network performance. However, despite the ongoing effort, the optimal relayingstrategy is still to be found [83].The interesting but essential questions here are: What is the appropriate way forthe RUs to relay as much useful information as possible to the CPU while satisfyingthe limited fronthaul capacity constraints of the fronthaul links? Is it using localdetection, compression, or computation? How can the physical and data link layerdesign of a DAS architecture adapt to the capacity limitations of the fronthaul links?Also, what should the CPU do to recover the original messages? Should it usesuccessive or joint decoding?To properly answer these questions, in this section, we discuss various uplink anddownlink relaying strategies that utilize the limited fronthaul capacity constraintsin different ways for different DAS architectures, along with their correspondingoptimization methods and frameworks for finding appropriate solutions. We concludeby providing design insights learned from such optimization.1.2.1 Uplink Coding StrategiesIn the uplink, multiple users communicate their codewords with the CPU throughthe distributed RUs. In an ideal case with infinite-capacity fronthaul links, each RUcan forward its exact observed signal to the CPU, and the full joint-decoding gaincan be achieved. Therefore, the resulting uplink channel is modeled as an instanceof a single-input-multiple-output (SIMO) or multiple-input-multiple-output (MIMO)multiple-access channel. In practice, however, the fronthaul links have limited ca-pacity constraints, thus each RU should relay as much useful information as possiblefrom its observation to the CPU in order to mitigate the inter-cell interference and191.2. Literature Review for Uplink and Downlink Coding Strategies in DASimprove the overall network performance. As a result, from an information-theoreticpoint of view, the uplink channel is modeled in this case as a two-hop multiple-accessrelay channel [84].Different relaying strategies can be used to relay traffic from RUs to the CPU.The first typical approach is to make each RU decodes the codewords of its scheduledusers, and then re-encodes and forwards them for collaborative transmission to theCPU; this is the so-called Decode-and-Forward (DF) strategy [85]. Although thistechnique offers significant advantages, the RU is ultimately interference-limited asthe number of transmitted codewords increases. This also scarifies the potentialbenefits that the user terminals can gain from the jointly centralized processingcapability at the CPU [77]. In addition, it introduces additional delay and requireshigh signal processing capability at the distributed RUs which significantly increasesthe processing power as well as the network complexity and cost, which can bea disadvantage in systems with limited computational resources [86]. Also, DF issensitive to errors in the received signal. If the RU node is unable to correctlydecode the signal, it will not be able to forward it to the CPU, which can result intransmission errors and loss of data [87].Higher data rates can be attained by decoding integer linear combinations of si-multaneously transmitted users’ codewords that ’mimic’ the channel realization ateach RU, as long as they are all drawn from the same linear codebook; this is theso-called Compute-and-Forward (CoF) strategy. CoF has recently been employed inDAS systems [79] including C-RAN [88, 89] and cell-free mMIMO systems [90, 91]to significantly reduce the fronthaul load, increase the system throughput as well asoffer protection against noise and inter-cell interference [92]. The key idea of theCoF scheme is that user terminals encode their messages using nested lattice linearcodes, and an RU suppresses interference by not decoding the users’ codewords butrather computes a weighted sum function (integer linear combination) of them andforwards it to the CPU [93]. The advantage of using nested lattice codes is thatthey are closed under modulo-addition, and hence the (modulo-) integer linear com-bination of lattice codewords is still a valid lattice codeword [94]. A nested latticecodebook is constructed by nesting set of lattice points of a fine lattice confinedwithin the fundamental Voronoi region of a coarse shaping lattice [95]. At the CPU,after receiving all the linear combinations forwarded by the RUs, it uses the inverseof integer coefficient matrix to recover the codewords [79]. However, this strategyis sensitive to channel estimation errors and requires the integer coefficients matrixto be invertible [96]. In the original CF [93], all constructed nested lattice codes atuser terminals share a common coarse lattice, thereby all users are constrained by thesame power constraint. In [97, 98], asymmetric CoF schemes are proposed that allow201.2. Literature Review for Uplink and Downlink Coding Strategies in DASasymmetric construction of coarse lattices and unequal power allocation across users,as a result, this improves the achievable sum rate and computation rate [99, 100]. In[101], this asymmetric approach is employed in a cell-free mMIMO network whoseresults show a significant reduction in the required backhaul capacity compared to[93]. To solve the possibility of having a full-rank failure of the integer coefficientmatrix in CoF, references [102, 103] utilize the successive interference cancellation(SIC) strategy, where a successive computation of multiple codeword combinationsis required to enlarge the achievable rate and enhance system performance. In [104],power control algorithms are proposed for both parallel computation and succes-sive computation in a cell-free mMIMO network. Simulation results show that thesuccessive computation approach outperforms the parallel computation in terms ofachievable sum rate.Since the decoded integer linear combinations of users’ codewords at RUs are ingeneral correlated, the performance of the CoF can be improved if the computed in-teger linear combination of users’ codewords at each RU is further compressed usinga lattice-based quantizer before forwarding it to the CPU to reduce the informa-tion redundancy [105]; this is the so-called Compute-Compress-and-Forward (CCoF)strategy. Further improvements on CCoF have been proposed in [106], where thecomputed integer linear combinations at RUs are remapped to equations of the users’input symbols, forwarded compressed in a lossy manner to the CPU, and are notrequired to be linearly independent.As an alternative to the DF, CoF, and CCoF schemes, the RUs can offload thedecoding process to the CPU using Amplify-and-Forward (AF) or Compress-and-Forward (CF) strategies. As a result, the uplink channel is converted into a virtualMIMO multiple-access channel [107]. In the AF, the RU simply acts as a repeaterthat amplifies the observed signal it receives and forwards a scaled version of it tothe CPU, where beamforming gains can be exploited. However, the amplificationprocess can introduce noise and distortion into the transmitted signal as well asamplify the interference from other wireless devices or signals, which can degradethe performance of the system [108]. Additionally, AF requires the RU node to havea stable power supply in order to amplify the received signal. This can be challengingin some scenarios, such as in remote or inaccessible locations, where the power supplymay be unreliable or unavailable [109].In contrast, in the CF scheme, RUs first downconvert their observed RF signalsto baseband signals, which are analog in nature, then compress the baseband signalsand forward the corresponding compression indices, which are represented by digitalcodewords, via their fronthaul links to the CPU. Once the CPU receives all the in-dices, the CP decompresses these compressed signals in order to obtain a distorted211.2. Literature Review for Uplink and Downlink Coding Strategies in DASversion of the received signals across all the distributed RUs, then recovers the orig-inal users’ messages based on the entire set of decompressed signals [78]. Intuitively,the required resolution of the compression level at each RU is determined by the ca-pacity of the fronthaul link. A limited fronthaul link’s capacity would imply coarsercompression, which in the rate-distortion theory is reflected by a larger compressiondistortion and as a result, decreases the users’ achievable rates, and vise versa [110].In [111], the use of CF scheme for C-RAN is justified from an information-theoretic perspective. Results show that CF can achieve the information-theoreticcapacity of the network within a constant gap for a Gaussian multi-message mul-ticast network which depends only on the network topology and is independent ofother channel parameters. At the CPU, the original users’ messages can be re-covered by joint decompression (of the quantized signals forwarded by RUs) anddecoding (of the users’ codewords) using joint processing and decoding for both thedecompression and message decoding simultaneously. Although this technique isinformation-theoretically better justified, its computational complexity is extremelyhigh and increases exponentially with the number of user terminals [112]. Thus,several low-complexity distributed lossy compression techniques with comparableperformance have been proposed using sequential (successive) decompression anddecoding strategies, which differ based on the amount of utilized side informationin the decompression process at the CPU. One of these strategies is independentcompression or single-user (SU) compression in which RUs’ observed signals arecompressed and decompressed independently without capitalizing on the presence ofany side information at the CPU. [77]. This may lead to high compression distortionas it ignores any correlations among the received signals at the RUs [113]. Thus,by taking advantage of the correlated received signals at the CPU, once one of thecompressed signals is decompressed, it can serve as side information in decompress-ing the remaining compressed signals [110]. As a result, RUs can capitalize on thisside information, and the needed amount of fronthaul capacity for the compressionprocess can be reduced [107, 114]. This compression strategy is called Wyner-Ziv(WZ) compression [115], and can achieve users’ rates equal to that achieved by jointdecompression and decoding through using successive interference cancellation (SIC)for message decoding at the CPU [114, 116]. In [78], a robust compression methodis proposed to cope with uncertainties on the correlation of the received signals inC-RAN. Moreover, for further improvement in the performance of CF in a Gaussianchannel setting, lattice-based Wyner-Ziv compression schemes have been proposedin [117, 118]. This utilizes the benefits of structured coding with correlated-basedcompression [119].Inspired by the CoF scheme, a distributed lossy compression strategy called221.2. Literature Review for Uplink and Downlink Coding Strategies in DASinteger-forcing source coding (IFSC) has been proposed in [120], where the receiverestimates integer linear combinations of the compressed signals, and then recoversthe compressed signals themselves. Particularly, a full-rank integer coefficient ma-trix can be optimized by exploiting the correlations between the compressed signals.This technique has been studied in a C-RAN scenario and was shown to performsimilarly to Wyner-Ziv compression with SIC [121]. References [77, 121] show thatin an uplink C-RAN, CoF schemes are better than CF under small fronthaul capac-ity values. However, distributed lossy CF schemes outperform CoF at moderate andlarge fronthaul capacities.CF strategies are also favorable relaying schemes for CF-mMIMO. Due to thelarge number of antennas at the APs in CF-mMIMO systems, employing low-resolutionanalog-to-digital converters (ADCs) to quantize the observed signals at the AP is afeasible and practical solution to reduce the fronthaul load, power consumption, andsystem complexity as well as the hardware cost. Based on what information is quan-tized and forwarded to the CPU and where channel estimation is performed, severalCF scenarios have been studied in cell-free mMIMO systems [122, 123]. In the firstapproach, each AP compresses its observed pilot and data signals separately andsends their compressed versions over its limited-capacity fronthaul link to the CPU,and then, the CPU performs the channel estimation, the design of combining vec-tors, and the data detection; this is the so-called Compress-Forward-Estimate (CFE)strategy [124, 125]. Following this way, centralized combining methods can be im-plemented over a limited fronthaul network by compression at the APs [126, 127].The second approach is to first estimate the channel at each AP, and then each APcompresses the estimated channels and data signals separately and forwards theircompressed versions to the CPU that recovers the CSI and performs data recoveryusing centralized combining; this is the so-called Estimate-Compress-Forward (ECF)[127]. Since the compression is implemented at the APs, ECF reduces the fronthaulload in a distributed fashion. In the third approach, each AP first performs thechannel estimation, multiplies the observed data signals by a local combining vectorcomputed based on the local channel estimate, compresses and forwards the resultsto the CPU that only performs data recovery; this is the so-called Estimate-Multiply-Compress-Forward (EMCF) [128]. Therefore, by implementing the channel estima-tion and EMCF can further reduce the fronthaul load compared to other compressionapproaches. The four approach is similar to the EMCF. However, the received signalat the CPU is further multiplied by the receiver filter coefficients to minimize theinterference and improve the performance; this is the so-called Estimate-Multiply-Compress-Forward-Weight (EMCFW) [123, 124, 128]. The channel estimation anddesign of the combining vectors are also implemented at the APs in a distributed231.2. Literature Review for Uplink and Downlink Coding Strategies in DASway. As a result, EMCFW has a significant performance improvement in terms ofthe fronthaul load and the achievable uplink rates. Reference [129] studies the effectof different quantization approaches on the fronthaul link. In the first approach,the AP quantizes the CSI and data signals and forwards their digital representa-tions to the CPU, whereas the second scheme forwards only a quantized weightedsignal version to the CPU. Simulation results demonstrate that the first approachhas a slightly higher achievable uplink rate than the second one. As the number ofantennas per AP increases, this difference in performance between the two schemesdecreases. Moreover, under the network setup proposed in [129], results show thata performance near to that of a perfect fronthaul can be obtained if the number ofquantization bits is set to be greater than 7.Despite the efficiency and simplicity of CF schemes in reducing the fronthaul loadin DASs, the uniform quantization approach can result in quantization error, leadingto significant performance degradation. As a result, in an uplink DAS, CoF schemesare better than CF under small fronthaul capacity values. However, distributed lossyCF schemes outperform CoF at moderate and large fronthaul capacities [77, 121]. AComparison of the uplink coding strategies is illustrated in Table 1.2.Next, we investigate how the cooperative downlink coding strategies play a vitalrole in ensuring reliable and efficient data transmission from the CPU to the endusers in DAS.1.2.2 Downlink Coding StrategiesIn de-centralized RAN, each scheduled user is served by a single BS and ex-periences interference from all neighboring BSs. The benefit of centralized signalprocessing in DAS architectures arises from the ability of multiple RUs to cooper-atively serve users, which minimizes the effect of unwanted interference. Since themessages intended for different users in DAS, all originate from the CPU, the CPUcan relay useful information about the user messages to the distributed RUs viathe fronthaul links, thus allowing the RUs to perform network-wide beamformingin order to achieve interference mitigation and cooperative transmission. Similar tothe uplink, if the fronthaul links have infinite capacities, all the information of users’messages can be forwarded from the CPU to all RUs, thus achieving full cooperation.In this ideal case, the downlink channel can be modeled as a SIMO or MIMO broad-cast channel. However, practically, due to the finite fronthaul capacity, the amountof information that can be forwarded to RUs is limited. Here, the main question forthe CPU is to determine the most useful information about users’ messages to beconveyed to the RUs in order to minimize interference as possible. As a result, the241.2. Literature Review for Uplink and Downlink Coding Strategies in DASTable 1.2: Comparison of the uplink coding strategies in DASScheme Processing at RU Processing at CPU ReferencesDF Decode the codewords Recover the original messages [77, 86]CoFCompute integer linearcombinations of the codewordsRecover the codewords[79, 88–90],[93, 94, 96],[97–100, 102–104]CCoFCompute integer linearcombinations of the codewords,then compress these combinationsDecompress the compressed equationsand recover the codewords[105, 106]AF Amplify the received signal Recover the original messages [107–109]SU Compression Compress the observed signalDecompress the compressed signalsindependently[77, 113]WZ Compression Compress the observed signalUtilize side information todecompress the compressed signals[107, 110, 114],[78, 115–119]IFSC Compress the observed signalEstimate integer linear combinationsof the compressed signals, thensolve these equations[120, 121]CFE Compress observed signal and CSI Estimate channel and design combining [122–127]ECFEstimate the channel and compressobserved signal and CSIDesign combining [127]EMCFEstimate the channel, design combining,and compress observed signalRecover the original messages [128]EMCFWEstimate the channel, design combining,and compress observed signalDesign receiver filter andrecover the original messages[123, 124, 128]channel can be expressed as an instance of a two-hop broadcast-relay channel [130].Different cooperative transmission schemes that enable collaboration among RUscan be used to forward traffic from the CPU to RUs. A straightway method for theCPU to enable cooperation is by sharing each user’s message with multiple RUs toform a cooperative cluster, which then forms locally beamformed signals to servetheir scheduled users. This technique is commonly referred to as data sharing [131].Ideally, in order to achieve full cooperation among RUs, the CPU should share theusers’ messages with all serving RUs. The benefit of the data-sharing approachis that the RUs receive clean messages that can be utilized for joint transmission.However, such full cooperation may not be feasible to be achieved because of thelimited fronthaul capacity constraint, which imposes restrictions on the size of theRU cluster that can collaborate in serving a user [81]. A significant improvementcan be obtained using common messages and rate-splitting optimization techniques[130–132].Alternatively, since all the users’ data are available at the CPU, the encoded andbeamformed signals can be centrally constructed at the CPU. Subsequently, thesesignals can be compressed and transmitted to the RUs for further processing [26].Particularly, the signals beamformed at the CPU have the potential to emulate thebenefits of full cooperation. However, the beamformed signals become analog instead251.2. Literature Review for Uplink and Downlink Coding Strategies in DASof discrete like the raw data in the data-sharing strategy. Therefore, it is necessaryto compress these signals before transmitting them over digital fronthaul links withlimited capacity. The primary benefit of the compression-based approach is theefficient utilization of fronthaul capacity when transmitting beamformed signals con-taining multiple users’ messages over the fronthaul link. However, the downside ofthis approach is the introduced compression distortion, which leads to a decreasein the achievable downlink rates. In general, the reduction in the achievable ratesis influenced by the compression rate, which is determined by the capacity of thefronthaul links and the compression strategy implemented at the CPU [77]. Furtherimprovement can be achieved through the implementation of the multivariate com-pression, where the baseband signals are jointly compressed at the CPU [26]. Thisapproach enables correlation among the compression distortions in the signals of dif-ferent RUs. By designing the correlation to cancel out compression distortions atthe user side, the achievable rates for users can be improved as the added distortions(due to interference) are mitigated.In the context of downlink transmission in CF-mMIMO networks, compressionstrategies remain favorable. Two compression approaches have been explored in CF-mMIMO. The first approach is Compress-After-Precoding (CAP) [133, 134], wherethe centralized signal is first precoded and then compressed at the CPU before be-ing transmitted to the APs. This makes CAP suitable for centralized precoding[135]. The second approach is Precoding-After-Compress (PAC) [136], where simplecompression is performed at the CPU by separately quantizing the symbols for eachuser. Each AP then receives the symbols and designs precoding vectors for each user,making PAC suitable for distributed precoding.As another option inspired by CoF in the uplink transmission, the CPU can sendlinear combinations of the users’ codewords to the RUs using structured lattice codes.This strategy is called reverse-compute-and-forward (RCoF) [82]. Furthermore, avariant called reverse-quantized-compute-and-forward (RQCoF) [79] can be utilized,where the linear combinations of codewords are quantized at the CPU before beingtransmitted to the RUs.In general, when fronthaul capacities are moderate to high, the compression-based strategy consistently outperforms data-sharing, RCoF, and RQCoF strategies,as it achieves low compression distortion. However, in scenarios with small fronthaulcapacities, the data-sharing, RCoF, and RQCoF schemes are more practical and offerbetter performance compared to compression-based strategies, which suffer from highcompression distortion [82, 137].A Comparison of the downlink coding strategies is illustrated in Table 1.3.261.3. Learned Lessons and Research GapsTable 1.3: Comparison of the downlink coding strategies in DASScheme Processing at CPU Processing at RU ReferencesData SharingSharing users’ messageswith RUsBroadcast the codewords [81, 130–132]Independent CompressionEncode, beamform, andcompress users’ signalsDecompress the compressedsignals independently[26, 77]Multivariate CompressionJointly compress users’signalsJointly decompress thecompressed signals[26]CAPPrecoding design andcompressionDecompress the compressedsignals[133–135]PACSimple compression ofusers’ signalsPrecoding design andDecompression[136]RCoFCompute integer linearcombinations of the codewordsRecover the codewords [82]RQCoFCompute integer linearcombinations of the codewords,then compress these combinationsDecompress the compressedequation and recover thecodewords[79]1.3 Learned Lessons and Research GapsThe choice of a proper relaying strategy depends on the specific DAS architec-ture, fronthaul capacity constraints, and desired network performance. The previoussection has illustrated different uplink and downlink relaying strategies in DAS thataim to optimize network performance while considering the limited fronthaul capac-ity constraints. The fronthaul links connecting the distributed remote units (RUs)with the central processing unit (CPU) pose a limitation on the amount of traffic ex-changed between them. For the uplink transmission from users to the CPU, variousrelaying schemes have been proposed including Decode-and-Forward (DF), Amplify-and-Forward (AF), Compute-and-Forward (CoF), Compress-and-Forward (CF), andCompute-Compress-and-Forward (CCoF). Each strategy has its advantages and dis-advantages in terms of performance, computational complexity, and sensitivity tochannel conditions. In the downlink transmission from the CPU to users, cooper-ative relaying schemes are used. Techniques like data-sharing, compression-basedstrategies, reverse compute-and-forward (RCoF), and reverse quantized-compute-and-forward (RQCoF) have been studied. These techniques leverage the distributedRUs to improve network performance by relaying data from the CPU to users. Theoptimal relaying strategy is still an active area of research and an open researchquestion. Various optimization methods and frameworks have been proposed tofind appropriate solutions based on the specific requirements and constraints of thenetwork. These methods involve the optimization of coding schemes, power alloca-tion, compression levels, and decoding strategies. By studying and optimizing these271.3. Learned Lessons and Research Gapsstrategies, valuable insights have been gained on how to effectively utilize limitedfronthaul capacity in DAS and enhance network performance.The main research gap identified in this thesis revolves around the predominantfocus on either uplink or downlink transmissions in the aforementioned works in theliterature. This singular approach may inadvertently lead to a noticeable decline inthe overall system performance, especially in situations where there is a significantexchange of messages within the same cloud or network. Such scenarios are commonin local area network communications within venues like shopping centers, stadiums,and university campuses. This becomes particularly pertinent when a large numberof distributed antenna terminals are deployed across a wide geographic area. Giventhese circumstances, it is imperative to shift the research paradigm towards a morecomprehensive optimization strategy. This involves jointly addressing the uplink anddownlink transmissions in order to bolster the overall system performance by takingthe message source-destination information into consideration.Another challenge is that all aforementioned uplink and downlink transmissionschemes primarily rely on fully centralized processing. This centralized processingparadigm can potentially lead to fronthaul overload, as the sheer volume of data be-ing transmitted between the central processing unit (CPU) and the distributed radiounits (RUs) may exceed the capacity of the fronthaul links. However, there is anuntapped opportunity to significantly enhance system performance by transitioningtowards distributed processing. This paradigm shift entails enabling communicationbetween the CPU and RUs to be processed in a distributed manner. Such an ap-proach has the potential to effectively alleviate the communication overhead overthe fronthaul links, a critical aspect that has been insufficiently addressed in currentresearch endeavors. By incorporating this aspect into the optimization strategy, weaim to develop a more efficient and balanced system, harnessing the advantages ofjointly optimizing the uplink and downlink transmission parameters while relaxingthe constraints imposed by fronthaul communication.By bridging these research gaps, we aim to develop a holistic approach that notonly enhances communication efficiency within the cloud but also improves the end-to-end performance of the system as a whole. This research endeavor promises to bea pivotal advancement in the field of wireless communication networks, potentiallyyielding substantial improvements in system performance and resource utilization,particularly in densely populated and geographically expansive environments.281.4. Thesis Objectives1.4 Thesis ObjectivesGiven the aforementioned background and identified research gaps, this disserta-tion primarily focuses on developing novel end-to-end transmission strategies tailoredfor distributed antenna systems (DAS). These strategies leverage multi-pair compu-tation schemes while considering critical factors such as source-destination messageinformation. In particular, we consider multi-pair computation schemes for the fol-lowing DAS architectures: (i) two-way intra C-RAN communications; (ii) C-RANwith intra-cloud and inter-cloud communications; (iii) intra CF-mMIMO communica-tions; and (vi) distributed processing for intra C-RAN bidirectional communications.To this end, this dissertation is built on the following four research objectives.1. Design a multi-pair two-way computation scheme to optimize the end-to-endsum rate in intra-cloud C-RAN communications while accounting for the mes-sage source-destination information.2. Develop a joint and iterative multi-pair computation-based transmission schemefor C-RANs with combined intra-cloud and inter-cloud communications, wherethe uplink and downlink are designed jointly to maximize the achievable uplinkand downlink rates.3. Develop a robust multi-pair computation approach to optimize the total energyefficiency in intra Cell-Free Massive MIMO communications in the presence ofimperfect channel state information (CSI).4. Develop a distributed multi-pair computation approach framework for intraC-RAN bidirectional networks to minimize the communications overhead andmaximize the achievable end-to-end sum rate.1.5 Thesis ContributionsThe contributions of this thesis are strategically designed to address and alignwith the emerging scenarios anticipated in 6G communications. The key contribu-tion of this thesis is to design novel multi-pair computation transmission schemestailored for efficient resource allocation in DAS networks. The primary objectiveis to optimize various critical metrics including network reliability, achievable rates,and energy efficiency. Specifically, this thesis presents the following four significantcontributions.291.5. Thesis Contributions− Designing an end-to-end transmission scheme for intra-cloud C-RAN communi-cations: We delve into the potential advantages of jointly designing the uplinkand downlink transmissions, especially when considering the specific source-destination attributes of the messages. To illustrate this concept, we focus onpairwise message exchanges within a C-RAN framework, which caters to im-mersive communication scenarios, a key aspect of 6G. We introduce a multi-pairtwo-way transmission scheme aimed at maximizing the aggregate end-to-enddata rate. This is indeed well-suited for immersive applications like extendedreality (XR), where higher bandwidth is essential for seamless user experiences.In this proposed approach, we employ a lattice-based computation strategy,wherein the baseband processing unit (BBU) pool decodes integer linear combi-nations of paired users’ codewords, rather than decoding linear combinations ofindividual codewords. Subsequently, the BBU pool precodes the computed sig-nals, compresses them, and transmits them to the remote radio heads (RRHs).The RRHs then decompress the signals and relay them to the respective users.Each user then decodes its intended message with its own message serving assupplementary information. We derive the achievable end-to-end user datarate for this scheme, optimize it while accounting for constraints on power andfronthaul capacity, and conduct a numerical evaluation. Simulation results in-dicate an approximately 1.3-fold improvement in end-to-end data rate usingthe proposed scheme compared to existing approaches.− Developing a multi-pair computation scheme for C-RANs with combined intra-cloud and inter-cloud communications: We generalize the multi-pair computa-tion concept from intra-cloud C-RAN scenarios to encompass C-RAN setupswith simultaneous intra-cloud and inter-cloud communications. By segregatingusers’ traffic into these categories, we aim to enhance the overall performance ofthe C-RAN network. This stands in contrast to existing relaying schemes in theliterature that treat all user transmissions uniformly, irrespective of their na-ture as intra-cloud or inter-cloud communications. This extension allows us todevelop a multi-pair computation strategy tailored for C-RANs with inter-cloudand intra-cloud communications, taking into consideration source-destinationinformation for message exchange. Extending the multi-pair computation con-cept to C-RANs with combined intra-cloud and inter-cloud communicationsdirectly addresses the massive communication scenario in 6G. The scheme op-timizes network performance by distinguishing between intra-cloud and inter-cloud communications, supporting a large number of devices and emerging usecases such as metaverse and logistics. We adopt a complex-valued transmis-301.5. Thesis Contributionssion model utilizing real-valued vector representation (in contrast to real-valuedrepresentations in the intra-cloud scenario). Furthermore, we establish theachievable uplink and downlink rates for both types of communicating users,introduce an iterative algorithm for joint optimization of uplink and downlinktransmission parameters, and conduct performance evaluations across varyingnumbers of intra- and inter-cloud communicating users. The results demon-strate significant enhancements compared to the current state-of-the-art ap-proaches.− Developing a robust and energy-efficient multi-pair computation approach forintra CF-mMIMIO communications: We delve into a scenario involving intra-network two-way communication among user pairs within a CF-mMIMO net-work. This is indeed well-suited for massive communications scenarios in 6G.In this context, “massive communications” refers to supporting connectivityfor a large number of devices in a relatively small area served by a massivenumber of access points. This is particularly relevant for applications such asdenses sensor networks, metaverse, logistics, and transportation, aligning per-fectly with the 6G vision for massive communication scenarios. Our primaryfocus lies in situations where direct links are absent among the communicatingusers within the intra-cloud environment, often due to substantial distances.This necessitates that users engaged in intra-cloud communication relay theirmessages through the access points and take advantage of joint processing atthe CPU. Building upon the concept of multi-pair computation for intra-cloudC-RAN, we introduce a robust end-to-end lattice-based multi-pair computationscheme tailored for intra-network CF-mMIMO communications. This schemedeviates from the traditional split of communication into uplink and downlink,instead leveraging the decoding of codeword combinations at the CPU (as op-posed to decoding individual codewords in a classical uplink). Additionally, itleverages message source-destination information for communicating user-pairsto enhance performance. In contrast to the multi-pair computation approachfor intra-cloud C-RAN, which assumes perfect channel state information (CSI),we adopt the more realistic assumption of imperfect CSI, particularly relevantin CF-mMIMO networks due to their ’massive’ nature. This considerationis complemented by accounting for fronthaul capacity, spectral efficiency, andlimitations in user, access point (AP), and fronthaul power. We thoroughlycharacterize the achievable rate of this scheme and optimize its performance interms of energy efficiency, demonstrating its superior performance comparedto state-of-the-art schemes.311.6. Notations− Developing a distributed multi-pair computation approach framework for intraC-RAN bidirectional networks: We embark on a comprehensive investigation ofa distributed multi-pair computation framework designed specifically for intraC-RAN bidirectional networks. This innovative approach entails the delega-tion of multi-pair computation tasks for specific user-pairs, transitioning themfrom the BBU pool to the distributed RRHs. This scheme is well-suited forscenarios requiring low-complexity ultra-reliable and low-latency communica-tion (URLLC) in 6G, (e.g., autonomous vehicles and device-to-device com-munications). This task offloading is facilitated by employing a sophisticatedlow-level lattice-based quantization strategy, which culminates in a substantialreduction of the essential fronthaul traffic between RUs and the CPU. Our pro-posed framework, denoted as the Distributed Multi-Pair Computation (DMPC)scheme, is intricately tailored for C-RAN setups featuring intra-cloud bidirec-tional communication. Within this framework, certain user-pairs are attendedto locally by an RU, while others receive centralized processing from the CPU.We conduct rigorous derivations to ascertain the achievable end-to-end rates forboth locally and centrally processed user pairs, strategically optimizing theirprocessing locations to maximize these rates. Furthermore, we subject thenetwork performance to numerical evaluations under the constraints of limitedfronthaul capacity and power. The numerical assessments compellingly affirmthat the proposed scheme adeptly surmounts the fronthaul capacity limitation,leading to a notable enhancement in the achievable end-to-end sum-rate whenjuxtaposed with conventional centralized approaches.1.6 NotationsColumn vectors and matrices are denoted by boldface lowercase and uppercaseletters, such as x and X, respectively. The transpose of matrix X is denoted byX>. The Hermitian of matrix X is denoted by XH .The L × L identity matrix isdenoted IL, and a diagonal matrix with diagonal equal to x is denoted diag(x). Theeuclidean norm of a vector is represented by ‖·‖. Subscripts ul and dl are used todenote uplink and downlink variables, respectively. Subscripts a and b are used todenote phases (a) and (b) transmission parameters, respectively. All the logarithmsare base 2, and log+(x) = max(0, log(x)).321.7. Outline1.7 OutlineThe rest of this thesis is organized as follows. In Chapter 2, we demonstrate thebasic concept of multi-pair computation by considering A pairwise message exchangebetween users in intra-cloud C-RAN communications. Then, we propose a multi-pairtwo-way transmission scheme which targets maximizing the end-to-end sum rate. Inparticular, we drive the achievable end-to-end rate of this scheme, propose an iter-ative scheme that solves the end-to-end sum rate maximization problem efficiently,and analyze its computational complexity. Simulation results reveal that significantend-to-end rate improvement can be achieved using the proposed scheme comparedto the existing schemes. This chapter has been included in published journal articleand conference papers [3, 138, 139], respectively.In Chapter 3, we extend the multi-pair computation scheme to the case of aC-RAN with both inter-cloud and intra-cloud communications, while consideringcomplex-valued channels (versus real-valued ones in Chapter 2). We generalize themulti-pair computation scheme, derive its achievable rate, and evaluate its perfor-mance under varying numbers of intra- and inter-cloud communicating users showingsignificant improvements compared to the state-of-the-art. The materials presentedin this chapter have been included in a published journal article [3].In Chapter 4, we introduce a robust end-to-end lattice-based multi-pair computa-tion scheme for intra-network CF-mMIMO communications. We consider the morerealistic assumption of imperfect CSI. This is in addition to accounting for fronthaulcapacity, spectral efficiency, and user, AP, and fronthaul power limitations. We char-acterize the achievable rate of the scheme and optimize its performance in terms ofenergy efficiency, showing that it yields superior performance compared to state-of-the-art schemes. This chapter has been included in an accepted journal article [4].In Chapter 5, we extend the multi-pair computation framework to the scenariowith the multi-pair computation of some user-pair codewords can be relegated fromthe CPU to the distributed RUs, thereby reducing the communication overhead overthe limited-capacity fronthaul links. In particular, we propose a distributed multi-pair computation (DMPC) scheme in a C-RAN, that aims to maximize the achiev-able end-to-end sum rate. The achievable uplink and downlink rates are derived,optimized, and numerically evaluated under limited fronthaul capacity and powerconstraints. Numerical evaluations reveal the proposed scheme can significantly im-prove the achievable end-to-end sum-rate compared to conventional centralized ones.This chapter has been included in a published conference paper [5].Finally, Chapter 6 provides a summary of the key findings and accomplishmentspresented throughout the thesis. Furthermore, it delves into potential avenues for331.7. Outlinefuture research that are closely aligned with the topics explored in this thesis.34Chapter 2Multi-Pair Computation forTwo-Way Intra CloudRadio-Access NetworkCommunicationsIn this chapter, we aim to devise an end-to-end transmission methodology tailoredfor intra-cloud C-RAN communications. This involves a comprehensive explorationof the benefits yielded by co-designing both uplink and downlink transmissions, withparticular emphasis on the distinct characteristics of message sources and destina-tions. To illustrate this concept, our focus centers on pairwise message interactionswithin an intra-cloud C-RAN communications framework. Such work’s setup is prac-tically relevant to local area network communications, especially when a C-RANcovers a relatively large area (city, university campus, stadium, etc.).This chapter’s organization is given as follows. The accomplished works and re-search contributions are summarized in Section 2.1. The intra-cloud C-RAN systemmodel is introduced in Section 2.2. A toy example that illustrates the scheme ispresented in Section 2.3. The uplink and downlink transmission schemes are pro-posed and investigated in Section 2.4 and Section 2.5, respectively. The end-to-endMPTWC optimization algorithm is described in Section 2.6. Numerical results arepresented in Section 2.7, and finally, the chapter is concluded in Section 2.8.2.1 Accomplished Works and ResearchContributionsThe contributions of this chapter are summarized as follows. We introduce anovel multi-pair two-way transmission scheme with the primary goal of maximizingthe aggregate end-to-end data rate. Existing relaying schemes in literature studyeither the uplink or the downlink separately. This may incur performance loss, es-pecially in scenarios where intra-cloud message exchange takes place. This chapter352.1. Accomplished Works and Research Contributionsdemonstrates this idea by studying a C-RAN with intra-cloud pairwise communica-tion. We focus on the scenario where there are no direct links between the intra-cloudcommunicating users (due to distance e.g.). Therefore, the intra-cloud communicat-ing users must exchange their messages through the RRHs and the BBU pool. Sucha scenario is relevant when a C-RAN covers a relatively large area (city, universitycampus, stadium, etc.) [140]. In particular, the chapter has the following contribu-tions:− A multi-pair two-way computation (MPTWC) scheme is proposed to improvethe end-to-end sum rate in a C-RAN with intra-cloud communications.− The achievable uplink and downlink rates of the scheme are derived.− An iterative MPTWC optimization algorithm is proposed to maximize the end-to-end sum rate, where the uplink and downlink parameters of the scheme areoptimized.− The proposed scheme is evaluated numerically, showing superior performanceto existing schemes in the literature.The proposed MPTWC scheme relies on the idea of lattice-based multi-way re-laying to improve the end-to-end rate [93, 95]. It uses a lattice-based distributedlossy compression strategy for compression at the RRHs in the uplink and at theBBU pool in the downlink, and a lattice-based integer-forcing computation strategyfor decoding at the BBU pool and users. In the uplink, the RRHs compress theirobservations and forward them to the BBU pool, which in turn computes integerlinear combinations of sums of codeword-pairs. This reduces the required numberof computation steps at the BBU pool, thereby reducing the number of rate con-straints. In the downlink, the BBU pool precodes the decoded linear combinations,compresses, and forwards them to the RRHs, which decompress and transmit themto the users. Users then decode their desired message using their own messages asside information. After describing the scheme, we derive its achievable rate. Then,we formulate the uplink sum rate optimization as a mixed integer non-linear pro-gram (MINLP), where the objective is maximizing the uplink sum rate by jointlyadjusting the uplink distortion levels of RRHs, the integer coefficients of the decodedequations, and the power allocation per user until convergence. Afterwards, we for-mulate the downlink optimization where the objective is to obtain an achievabledownlink rate greater or equal to the achievable one in the uplink, by optimizingthe downlink beamforming matrix. In these optimizations, we take into account themaximum transmitted power per user, the fronthaul capacity constraint, and the362.2. System ModelFigure 2.1: A C-RAN with multi-pair intra-cloud communication [2, Figure 1].downlink power budget per RRH. Using numerical evaluations, we then show thatour proposed scheme achieves a significant advantage over existing schemes.2.2 System ModelWe consider a C-RAN consisting of M single-antenna user pairs (K = 2Musers), L single-antenna RRHs,1 and a central processor (BBU pool). Each RRH` ∈ {1, . . . , L}, is connected to the BBU pool via a digital noiseless fronthaul linkwith a limited capacity C`. User pairs wish to communicate with each other using theC-RAN architecture, where users k, k′ ∈ {1, . . . , K}, k 6= k′ , exchange messages witheach other as shown in Fig. 2.1. Therefore, we can consider the uplink and downlinktransmissions in the C-RAN network as a multi-hop two-way relay network (TWRN)[95]. In this context, the uplink transmission corresponds to the signal flow from theusers to the BBU pool, whereas the downlink transmission refers to the signal pathfrom the BBU pool to the users.1This is in line with cell-free massive MIMO assumptions. The results can be extended to dealwith multi-antenna RRHs.372.2. System ModelThe user pairing is represented by an M ×K pairing matrix W, where wm,k ∈{0, 1} is a user-pair association indicator, i.e., wm,k = 1 if user k belongs to pairm, and wm,k = 0 otherwise, such that∑Mm=1wm,k = 1 for all k ∈ {1, . . . , K} and∑Kk=1wm,k = 2 ∀ m ∈ {1, . . . ,M}. The message exchange among the user-pairs iscompleted in two stages over n channel uses each, an uplink phase and a downlinkphase. 2In the uplink, user k ∈ {1, . . . , K} encodes its message gk at rate Rk into acodeword xulk ∈ Rn and sends it to the RRHs. This codeword is subject to a powerconstraint P ulk . Note that we consider a real-valued transmission model for the sakeof simplicity, bearing in mind that a complex-valued model can be addressed usingthe real-valued vector representation [93, 141]. The received signal at the RRHs isgiven byYul = HulXul + Zul, (2.1)where Yul = [yul1 , . . . ,yulL ]>, yul` ∈ Rn is the received signal at RRH `, Hul =[hul1 , . . . ,hulL ]> ∈ RL×K is the uplink channel gain matrix between all users andRRHs, Xul = [xul1 , . . . ,xulK ]>, and Zul ∈ RL×n is additive white Gaussian noise withindependent and identically distributed (i.i.d.) components with zero mean and unitvariance N (0, 1). RRH ` ∈ {1, . . . , L} processes its received signal yul` into a messageeul` , and sends this message to the BBU pool using the fronthaul link.The downlink is described as follows. First, the BBU processes the receivedmessages from all RRHs, then constructs messages edl` , ` ∈ {1, . . . , L}, and sendsedl` to RRH ` using the fronthaul links. The RRH then processes edl` to constructa transmit signal xdl` ∈ Rn with power constraint pdl` ≤ P dl` for transmission to theusers. The received signals at the users can be written asYdl = HdlXdl + Zdl, (2.2)where Ydl = [ydl1 , . . . ,ydlK ]>, ydlk is the received signal at user k, Hdl ∈ RK×L is thedownlink channel gain matrix between all RRHs and users, Xdl = [xdl1 , . . . ,xdlL ]>,and Zdl ∈ RK×n is additive white Gaussian noise with i.i.d. N (0, 1) components.Finally, each user uses its received signal in combination with its own message todecode the message of the paired user.We assume channel reciprocity, i.e., Hdl = Hul>. We also assume that chan-nels are block fading, i.e., they remain fixed across the transmission of a completecodeword, and change independently between blocks according to some distribution2We assume that the uplink and downlink occur over the same frequency band using a half-duplex fashion.382.3. Toy Example(Rayleigh e.g.). To enable cooperative transmission and make the problem mathe-matically tractable, we assume that the BBU pool has full-perfect knowledge of theinstantaneous channel state information (CSI) of all RRHs3. The availability of full-perfect CSI allows the BBU pool to coordinate the RRHs’ signaling strategies (i.e.user scheduling, beamforming, power allocation, etc.). At this cooperation level, thesharing of channel state information, signal-level synchronization, or transmittingdata between the RRHs or users is not necessary. Hence, the amount of overheadplaced on the fronthaul link is relatively modest [146].The main goal is to design a two-way transmission scheme that takes the givenuser pairing into account, to derive its achievable rate, and to optimize the end-to-endsum rate Rt given byRt =K∑k=1Rk, (2.3)where Rk = min{Rulk , Rdlk } is the end-to-end user rate calculated following the ca-pacity of the compute-and-forward two-way relay network (CoF-TWRN) [147, 148]and Rulk and Rdlk are the uplink and downlink rates of user k, respectively. This isdiscussed in sections 2.4 and 2.5 which study the uplink phase and the downlinkphase, respectively.Note that we consider optimizing the end-to-end sum-rate to be consistent withthe performance criteria used in the existing schemes in the literature as in [102, 114,149, 150].Due to the intricate nature of the proposed scheme, we provide a toy examplenext which illustrates the main idea.2.3 Toy ExampleConsider a C-RAN as described in Sec. 2.2 with L = 2 RRHs and K = 4users communicating pairwise, with user 1 communicating with user 2, and user 3communicating with user 4. Assume a rather simplistic symmetric channel wherehul1 = [ha, ha, hb, hb]> and hul2 = [hb, hb, ha, ha]> for simplicity in this example,with non-zero ha and hb satisfying ha 6= hb 6= 0. If user i sends xuli in the uplink, the3Obviously, perfect CSI is not always available in practice, where CSI has to be estimated andtherefore may contain errors [142, 143]. In this case, the performance can be analyzed similar to[144, 145].392.3. Toy ExampleRRHs 1 and 2 receiveyul1 = ha(xul1 + xul2 ) + hb(xul3 + xul4 ) + zul1 . (2.4)yul2 = hb(xul1 + xul2 ) + ha(xul3 + xul4 ) + zul2 . (2.5)The RRHs compress these signals into indices eul1 and eul2 with a rate which is less thanor equal their associated fronthaul capacities C1 and C2, respectively. Upon receivingeul` , the BBU pool decompresses them to obtain yul` + qul` where qul` is a compressiondistortion. Then, the BBU pool intends to extract the signals xul12 = xul1 + xul2 andxul34 = xul3 + xul4 from the decompressed signals. To benefit from both decompressedsignals, it proceeds to combine them intovul1 = a11(yul1 + qul1 ) + a12(yul2 + qul2 ), (2.6)vul2 = a21(yul1 + qul1 ) + a22(yul2 + qul2 ). (2.7)Generally, aij here will be subject to optimization. For simplicity here, let a11 =a22 = 1 and a12 = a21 = 2. Then, the BBU pool obtainsvul1 = (ha + 2hb)xul12 + (hb + 2ha)xul34 + noise (2.8)vul2 = (2ha + hb)xul12 + (2hb + ha)xul34 + noise, (2.9)where we combined all noises and left out details to keep the exposition simple. If weignore the noise, then the BBU pool can invert the (full rank) matrix[ha + 2hb hb + 2ha2ha + hb 2hb + ha]to obtain xul12 and xul34. In the presence of noise, the BBU pool can decode xul12 andxul34 if xuli are generated using lattice codes [93, 95].Next, the BBU proceeds to precode xul12 and xul34 into b11xul12 + b12xul34 and b21xul12 +b22xul34, compresses these signals to edl1 and edl2 , and sends the compression indices toRRHs 1 and 2, respectively. The RRHs decompress these signals and send them tothe users. User 1 receivesydl1 = ha(b11xul12 + b12xul34) + hb(b21xul12 + b22xul34) + noise= (hab11 + hbb21)xul12 + (hab12 + hbb22)xul34 + noise.User 2 receives a similar signal. Similarly, user 3 receivesydl3 = (hbb11 + hab21)xul12 + (hbb12 + hab22)xul34 + noise,and user 4 receives a similar signal. Generally, bij will be optimized. For the sake ofthis example, let b11 = b22 = ha and b12 = b21 = −hb. Then, we obtainydl1 = (h2a − h2b)xul12 + noise, (2.10)ydl3 = (h2a − h2b)xul34 + noise. (2.11)402.4. Uplink TransmissionThese two users can use their signals (xul1 and xul3 ) to decode their desired signals(xul2 and xul4 ).We have applied a lot of simplifications in this example, but we tried to preservethe essence of the scheme. The most notable step is the computation of xul12 andxul34 done at the BBU pool. At this step, one can interpret (2.8) and (2.9) as a2× 2 MIMO channel with inputs xul12 and xul34 and outputs vul1 and vul2 , or as a 4× 2MIMO channel with inputs xuli , i = 1, . . . , 4 and outputs vul1 and vul2 . Assuming xuli ,i = 1, . . . , 4, are constructed using lattice codes, following the second interpretationand forcing the BBU pool to decode all four signals xuli separately induces the so-called MAC bottleneck [121] [95, (3.77)]. This does not happen if we follow the firstinterpretation and decode xul12 and xul34, leading to higher achievable rates as we shallsee later in this chapter.The scheme described in this toy example will be generalized in Sec. 2.4 and 2.5to allow general channel gains, number of RRHs, and users. It will also be optimizedin Sec. 2.6 subject to power constraints and fronthaul capacity constraints.Since the proposed transmission scheme relies heavily on lattice coding, somelattice preliminaries are reviewed in Appendix A.2.4 Uplink TransmissionWe start by describing the encoding at the users, followed by the processing atthe RRHs, and introducing the multi-pair computation at the BBU pool. The uplinktransmission process is summarized in Fig. 2.2.2.4.1 Encoding at the usersUsing nested-lattice coding [79], a lattice chain Λc ⊆ Λf,K ⊆ . . . ⊆ Λf,1 is gen-erated, consisting of n-dimensional lattices. The coarse lattice Λc is chosen to begood for channel coding and quantization simultaneously, whereas the fine latticesΛfk , k ∈ {1, 2, . . . , K} are chosen to be good for quantization only. User k generatesits nested lattice codebook as Culk = {Λfk∩υΛc}, where υΛc is the fundamental Voronoiregion of the coarse lattice Λc. Using a one-to-one mapping, it maps its message gkinto a lattice point sulk ∈ Culk . To make the transmitted signal independent on thelattice point, a random dither tulk , uniformly distributed over υΛc and known to allnodes in the network, is added. The result is then reduced using a modulo-latticeoperation with respect to Λc. This leads to the signaluulk = (sulk + tulk ) mod Λc, (2.12)412.4. Uplink TransmissionFigure 2.2: Uplink Transmission: (a) User k encodes its message into uulk usinglattice coding, then scales it and transmits xulk to all RRHs. (b) RRH ` compressesits dithered observed signal using lattice-based vector quantization, then maps itscompressed signal to an index eul` , and forwards it to the BBU pool via its fronthaullink. (c) The BBU pool decompresses the received signals and proceeds to decodeM integer linear combinations of the sum of user-pairs’ codewords [2, Figure 2].which is then scaled by bulk , and transmitted as xulk = bulk uulk to the RRHs. Thetransmitted signals from all users can be written as Xul = BulUul, where Bul =diag(bul1 , . . . , bulK ) is a K × K power allocation matrix and Uul = [uul1 , . . . ,uulk ]> isthe dithered codewords matrix. The uplink power constraint per user can be met byselecting a coarse lattice Λc with second moment σ2(Λc) = pul and assigning properbulk so that1nE[‖xulk ‖2] = (bulk )2pul ≤ P ulk .2.4.2 Compression at the RRHsThe received signal yul` at RRH ` is processed as follows. Given a lattice chainΛ˜c,1 ⊆ . . . ⊆ Λ˜c,L ⊆ Λ˜f,L ⊆ . . . ⊆ Λ˜f,1, RRH ` generates its compression codebook asC˜ul` = {Λ˜f,`∩υΛ˜c,`} with rate equal to its associated fronthaul capacity C`. The coarselattice Λ˜c,` is chosen to be good for channel coding and quantization simultaneously,whereas the fine lattice Λ˜f,` is chosen to be good for quantization in order to be ableto find a precise relationship between the compression rates and distortion levels[120]. Given these lattices, the `th RRH adds to its received signal yul` a randomdither t˜ul` , uniformly distributed over υΛ˜f,` . This serves to make the compressiondistortion independent of the received signal. Then, the `th RRH compresses thedithered received signal into points in Λ˜f,` using a lattice-based vector quantization,and maps the outcome into υΛ˜c,` using the modulo operation with respect to Λ˜c,` to422.4. Uplink Transmissionobtainy¨ul` = [QΛ˜f,`(yul` + t˜ul` )] mod Λ˜c,`. (2.13)Next, RRH ` maps y¨ul` to an index eul` ∈ {1, . . . , 2nRulr,`}, where Rulr,` is the rateof the nested-lattice compression code Cul` . This quantization leads to compressiondistortion given by qul` = −[yul` + t˜ul` ] mod Λ˜f ,` which is statistically independent ofyul` , uniformly distributed over υΛ˜f,` , and has power dul` equal to the second momentof Λ˜f ,`, i.e., dul` = σ2(Λ˜f ,`). We collect all distortion powers in dul = [dul1 , . . . , dulL ]>.Finally, RRH ` forwards eul` to the BBU pool via its fronthaul link.2.4.3 Decompression at the BBU poolOnce the BBU pool receives the indices eul1 , . . . , eulL , it recovers y¨ul1 , . . . , y¨ulL , thensubtracts the dithers, and reduces the result modulo Λ˜c,` asy˜ul` = [y¨ul` − t˜ul` ] mod Λ˜c,`(a)= [yul` + qul` ] mod Λ˜c,`(2.14)where (a) follows from the distributive law of the modulo-lattice operation.Based on the Integer-Forcing Source Coding (IFSC) idea proposed in [120], theBBU pool proceeds to estimate L integer linear combinations vulr,1, . . . ,vulr,L using asuccessive cancellation strategy as in [151], wherevulr,i =[L∑`=1aulr,i,`y˜ul`]mod Λ˜c,i(b)=L∑`=1aulr ,i ,`y˜ul` (2.15)for i ∈ {1, . . . , L}, where aulr,i,` ∈ Z is an integer coefficient, and (b) holds with highprobability (w.h.p.) if Λ˜c,i is good for channel coding and1nE[‖vulr,i‖2] < σ2(Λ˜c,i)[120]. We can write (2.15) in a matrix form asVulr = Aulr Y˜ul , (2.16)where Vulr = [vulr,1, . . . ,vulr,L]>, Aulr = [aulr,1, . . . ,aulr,L]> is an L × L full-rank inte-ger coefficients matrix with entries aulr,i,l and with full rank sub-matrices Aul[1:i]r fori ∈ {1, . . . , L}, and Y˜ul = [y˜ul1 , . . . , y˜ulL ]>. Note that this estimation exploits thecorrelation between the received signals at all RRHs yul1 , . . . ,yulL since each vulr,i isestimated from y˜ul1 , . . . , y˜ulL . In addition, according to the following lemma, the in-teger coefficients can be selected to minimize the compression distortion for a givencompression rate Rulr,` ≤ C`.432.4. Uplink TransmissionLemma 2.1 ([151], Theorem 3). Given an uplink power pul, channel matrix Hul,scaling matrix Bul, and full-rank integer coefficient matrix Aulr ∈ ZL×L with full ranksub-matrices Aul[1:i]r for i ∈ {1, . . . , L}, the uplink compression rate Rulr,` at the `thRRH and the compression distortion covariance matrix Dul = diag(dul) are relatedbyRulr,` =12log+(aul>r,` (pulHulBulBul>Hul> + IL + Dul)aulr,`dul`), (2.17)where Rulr,` ≤ C`.Assuming that the ratio in (2.17) is larger than 1 for all `, then the relation in(2.17) can be written asdul = Culξul, (2.18)where ξul` = aul>r,` (pulHulBulBul>Hul> + IL)aulr,` is the `th element of ξul and Cul =(diag(22Rulr,1 , . . . , 22Rulr,L)− A˜ulr)−1whereA˜ulr = (aulr,1,1)2 ... (aulr,1,L)2... ... ...(aulr,L,1)2 ... (aulr,L,L)2. (2.19)By multiplying the estimated Vulr in (2.16) by the inverse of the integer coefficientmatrix Aulr ,inv , the BBU pool obtainsYˆul = HulXul + Zul + Qul, (2.20)where Qul = [qul1 , . . . , qulL ]>.Remark 2.2. The correlation between the received signals at all RRHs yul1 , . . . ,yulLcan also be exploited using Wyner-Ziv (WZ) compression and successive decompres-sion. Assume that the BBU pool decompresses the signals in this order y¨ul1 , . . . , y¨ulL .Then, while decompressing y¨ul` , the BBU pool can use the previously decompressedsignals y˜ul1 , . . . , y˜ul`−1 as side information to reduce the distortion in y˜ul` for a givencompression rate or reduce the compression rate for a given distortion. The achiev-able compression rate using WZ compression is given by [107]:RulWZ,` =12log(pulHulτ`BulBul>Hul>τ` + Iτˆ` + Dulτˆ`(pulHulτ`−1BulBul>Hul>τ`−1 + Iτˆ`−1 + Dulτˆ`−1)dul`),where τ` and τ`−1 represent the matrix’s dimension of [1 : `,K] and [1 : ` − 1, K],respectively. Also, τˆ` and τˆ`−1 represent the matrix’s dimension of [1 : `, 1 : `] and[1 : `− 1, 1 : `− 1], respectively.442.4. Uplink TransmissionRemark 2.3. If the channel state information (CSI) is not known at the RRHs [107],a Single-User (SU) compression scheme can be used. In this case, RRH ` compressesits received signal yul` into y¨ul` , and the BBU pool decompresses y¨ul` ,∀` ∈ {1, . . . , L}independently, without exploiting the correlation between yul1 , . . . ,yulL . The achiev-able uplink compression rate using SU compression is given by [107]RulSU,` =12log(pulhul>` BulBul>hul` + 1 + dul`dul`). (2.21)Now that the compression and decompression have been described, we describethe computation that is performed at the BBU pool.2.4.4 Multi-Pair Computation at the BBU poolThe novelty of the uplink transmission in the multi-pair computation at the BBUpool. The BBU pool proceeds to decode M =K2integer linear combinations of thesum of user-pairs’ codewords (instead of decoding K integer linear combinations ofusers’ individual codewords as in [121, 149]). This reduces the required number ofcomputation steps at the BBU pool to the half, thereby reducing the number ofrate constraints and the computational complexity as well. Namely, the BBU pooldecodesvulψ,j =[M∑m=1aulψ,j,m[K∑k=1wm,ksulk]]mod Λc, (2.22)for j ∈ {1, . . . ,M}, where aulψ,j,m ∈ Z is an integer coefficient. Computing M combi-nations instead of K decreases the number of constraints on the computation rate,which improves performance. We can write (2.22) in matrix form asVulψ = [Aulψ WSul ] mod Λc, (2.23)where Aulψ is an M ×M integer coefficient matrix with entries aulψ,j,m and with rankM = K/2, and Sul = [sul1 , . . . , sulK ]>. This decoding can be done by multiplying Yˆulby an equalizer ρulj , removing the dither tulk , and reducing the result modulo Λc asµulj =[ρul>j Yˆul −K∑k=1tulk]mod Λc=[ρul>j HulBulSul + ρul>j (Zul + Qul)]mod Λc= [aul>ψ,j WSul + zuleff,j ] mod Λc, (2.24)452.4. Uplink Transmissionfrom which the BBU pool computes the desired signal [aul>ψ,j WSul] mod Λc, wherezuleff,j = (ρul>j HulBul−aul>ψ,j W)Sul+ρul>j (Zul+Qul) is the effective noise with varianceσulj2=1nE[‖zuleff,j‖2]= pul‖ρul>j HulBul − aul>ψ,j W‖2+ρul>j (IL + Dul)ρulj (2.25)In order to minimize the effective noise variance in (2.25), ρulj is chosen as theMMSE scaling equalizer given byρul>j = pulaul>ψ,j WBul>Hul>(pulHulBulBul>Hul> + IL + Dul)−1. (2.26)By substituting (2.26) into (2.25) and applying the matrix inversion lemma, theeffective noise variance σulj2can be rewritten asσulj2= ‖aul>ψ,j WFulψ ‖2 (2.27)where Fulψ is obtained from the the Cholesky decompositionFulψ Ful>ψ = (1pulIK + Bul>Hul>(IL + Dul)−1HulBul)−1. (2.28)A detailed proof of equation (2.27) is provided in Appendix B.To conclude the discussion on the uplink, we state its achievable rate in thefollowing theorem.Theorem 1. Let user k belong to pair mk, i.e., wm,k = 1. Then, the achievable uplinkcomputation rate for user k can be expressed asRulk ≤ minj∈{1,...,M}aulψ,j,mk6=012log+(pulσulj2), (2.29)where σulj2is given by (2.27).This theorem follows from the decoding of vulψ,j which has power pul from µuljin (2.24), where it is corrupted by noise with variance σulj2. The minimum findsthe bottleneck rate constraint, since vulψ,j is decoded from µulj for all j such thataulψ,j,mk = 0. Note that since σulj2depends on Dul which in turn depends on Aulr462.5. Downlink TransmissionFigure 2.3: Downlink Transmission: (a) The BBU compresses the computed combi-nations vulψ,m, maps each compressed linear combination to an index, and forwardsindices to RRHs. (b) RRH ` recovers its desired signal and broadcasts it to all users.(c) User k decodes its desired signal using its own codeword as side information [2,Figure 3].(2.18), then the achievable rate in (2.29) depends on our choice of Bul, Aulr , and Aulψwhich need to be optimized.To realize the novelty of the MPTWC downlink transmission, instead of recover-ing the original messages as in [121], the BBU compresses the computed combinationsvulψ,j (2.22) and forwards them to the RRHs through the fronthaul links as describednext. As a result, this will reduce the signal processing complexity at the BBU pool.2.5 Downlink TransmissionThe basic idea of the downlink is to employ a reverse-quantized-compute-and-forward scheme [79] in a C-RAN. This is explained next as shown in Fig. 2.3.2.5.1 Compression at the BBU poolThe goal of the BBU pool is to design signals that include two ingredients. Thefirst is beamforming using an L × M matrix Bdl = [bdl1 , . . . , bdlL ]> to enable theoptimization of the transmission from the RRHs to the users. The second involvespre-processing using an L × L matrix Adlr,inv, followed by compression, and thenmultiplication by an L×L integer coefficient matrix Adlr , to enable the optimizationof the transmission from the BBU pool to the RRHs as we shall see in Sec. 2.5.2.This process is described next.472.5. Downlink TransmissionThe BBU pool starts by constructingSdl = BdlVulψ = Bdl[Aulψ WSul ] mod Λc, (2.30)where Sdl = [sdl1 , . . . , sdlL ]> and sdl` is the signal intended to be recovered and sent(within some distortion) by the RRH `. Then, in order to enable each RRH ` toextract and recover its desired signal, the BBU pool multiplies Sdl by Adlr,inv to obtainVdlr = Adlr,invSdl (2.31)where Vdlr = [vdl1 , . . . ,vdlL ]> and Adlr,inv is the inverse of an L × L full rank integercoefficients matrix Adlr with full rank sub-matrices Adl[1:i]r for i ∈ {1, . . . , L}.For compression, the BBU pool uses a lattice chain Λˆc,1 ⊆ . . . ⊆ Λˆc,L ⊆ Λˆf,L ⊆. . . ⊆ Λˆf,1, where the coarse lattice Λˆc,` is good for channel coding and quantizationsimultaneously, whereas the fine lattice Λˆf,` is good for quantization only. Next,the BBU pool adds a random dither matrix Tˆdl = [tˆdl1 , tˆdl2 , . . . , tˆdlL ]> to Vdlr , wheretˆdl` is uniformly distributed over υΛˆf,` ,∀` ∈ {1, . . . , L}. The dithered output is thenquantized asVˆdlr =QΛˆf,1(vdl1 + tˆdl1 )...QΛˆf,L(vdlL + tˆdlL ) . (2.32)This leads to a downlink compression distortion Qdl = [qdl1 , . . . , qdlL ]> with an L× Lcovariance matrix Ddl = diag(ddl) where ddl = [ddl1 , . . . , ddlL ]> and ddl` = σ2(Λˆf ,`).Using a successive cancellation strategy as in [151], the BBU pool proceeds togenerate integer linear combinations V˜dlr = Adlr Vˆdlr and to reduce them modulo coarselattice as followsv˜dlr,i =[adl>r,i Vˆdlr]mod Λˆc,i , (2.33)for i ∈ {1, . . . , L}. Note that v˜dlr,i belongs to the nested lattice code defined byΛˆf ,i and Λˆc,i . Hence, it has a rate equal to that of this nested lattice code, whichwe denote by Rdlr,` which must satisfy Rdlr,` ≤ C`. Finally, the BBU pool maps itscompressed linear combinations v˜dlr,i to an index edli ∈ {1, . . . , 2nRdlr,`}, and forwards itto the ith RRH.2.5.2 Decompression at the RRHsThe goal at the RRHs is to recover a version of sdl` ∀ ` ∈ {1, . . . , L} within somedistortion. To this end, once the `th RRH receives the index edl` , it recovers v˜dlr,`, then482.5. Downlink Transmissionsubtracts adl>r,` Tˆdl and reduces the result modulo Λˆc,` to obtainxdl` =[v˜dlr,` − adl>r,` Tˆdl]mod Λˆc,`=[adl>r,` (Vdlr + Tˆdl + Qdl)− adl>r,` Tˆdl]mod Λˆc,`=[adl>r,` Adlr,invSdl + adl>r,` Qdl]mod Λˆc,`(c)= sdl>` + adl>r,` Qdl, (2.34)where xdl` is the recovered and transmitted signal by RRH ` and (c) holds by satisfyingthe condition in (6.11) and w.h.p. if 1nE[‖xdl` ‖2] < σ2(Λˆc,`). The following lemmarelates the downlink compression rate and distortion.Lemma 2.4 ([151], Theorem 3). Given uplink power pul, downlink channel matrixHdl, downlink beamforming matrix Bdl, downlink compression distortion covariancematrix Ddl, and a full-rank integer coefficient matrix Adlr ∈ ZL×L with full rank sub-matrices Adl[1:i]r for i ∈ {1, . . . , L}, the downlink compression rate and distortion arerelated byRdlr,` =12log+(pulbdl>` bdl` + adl>r,` Ddladlr,`ddl`), (2.35)where Rdlr,` ≤ C`.Assuming that the ratio in (2.35) is larger than 1 for all `, then the relation in(2.35) can be written asddl = Cdlξdl, (2.36)where ξdl` = pulbdl>` bdl` is the `th element of ξdl and Cdl =(diag(22Rdlr,1 , . . . , 22Rdlr,L)− A˜dlr)−1,whereA˜dlr = (adlr,1,1)2 ... (adlr,1,L)2... ... ...(adlr,L,1)2 ... (adlr,L,L)2. (2.37)Finally, after the `th RRH recovers its desired signal xdl` , it broadcasts it to theusers with power1nE[‖xdl` ‖2] = pulbdl>` bdl` + adl>r,` Ddladlr,`, pdl` ≤ P dl` . (2.38)492.5. Downlink Transmission2.5.3 Decoding at the usersThe received signals at all the users can be written in matrix form asYdl = HdlXdl + Zdl= Hdl(Sdl + Adlr Qdl) + Zdl (2.39)= Hdl(BdlVulψ + Adlr Qdl) + Zdl.The kth user scales its received signal ydlk by ρdlk and reduces the result modulo Λcto obtainµdlk = [ρdlk yulk ] mod Λc= [ρdlk hdl>k (BdlVulψ + Adlr Qdl) + ρdlk zdlk ] mod Λc= [adl>ψ,kVulψ + zdleff,k ] mod Λc, (2.40)where hdl>k is the kth row of Hdl, adl>ψ,k is the kth row of the K ×M matrix Adlψ =W>Aulψ,inv with rank M , where Aulψ,inv is the inverse of Aulψ , and zdleff,k is the effectivenoise given byzdleff,k = (ρdlk hdl>k Bdl − adl>ψ,k )Vulψ + ρdlk (hdl>k Adlr Qdl + zdlk ). (2.41)Note that [adl>ψ,kVulψ ] mod Λc is the desired signal of the kth user that includes thesum of the codewords of the user-pair k, k′ ∈ {1, 2, . . . , K}, k 6= k′ . The power ofthe effective noise zdleff,k is given byσdlk2=1nE[‖zdleff,k‖2] = pul‖ρdlk hdl>k Bdl − adl>ψ,k‖2+ρdlk2(hdl>k Adlr DdlAdl>r hdlk + 1) (2.42)This effective variance can be minimized using the MMSE coefficient as the scalingfactor asρdlk =puladl>ψ,kBdl>hdlkhdl>k (Adlr DdlAdl>r + pulBdlBdl>)hdlk + 1(2.43)By substituting (2.43) into (2.42) and applying the matrix inversion lemma, theeffective noise power σdlk2can be rewritten asσdlk2= ‖Fdlψadlψ,k‖2, (2.44)502.5. Downlink Transmissionwhere Fdlψ is obtained from the Cholesky decompositionFdl>ψ Fdlψ =(1pulIM +Bdl>hdlk hdl>k Bdl(1 + hdl>k Adlr DdlAdl>r hdlk ))−1.Finally, user k decodes [adl>ψ,kVulψ ] mod Λc from µdlk , and then uses its own codewordsulk as side information to recover sulk ′ as follows[[adl>ψ,kVulψ ] mod Λc − sulk]mod Λc= [adl>ψ,kAulψ WSul − sulk ] mod Λc= [w>k Aulψ,invAulψ WSul − sulk ] mod Λc=[M∑m=1wm,kK∑u=1wm,usulu − sulk]mod Λc(d)= [sulk + sulk′ − sulk ] mod Λc = sulk′ , (2.45)where wk is the kth column of W, and (d) follows from the structure of W.Next, we state the achievable rate of the proposed downlink scheme.Theorem 2. The achievable downlink rate for the kth user is given byRdlk =12log+(pulσdlk′2)(2.46)This theorem follows from the decoding of [adl>ψ,kVulψ ] mod Λc which has power pulfrom µdlk in (2.40), where it is corrupted by noise with variance σdlk′2.Finally, we summarize the end-to-end achievable rate in the following theorem.Theorem 3. [152] The end-to-end rate of user k achieved by the proposed scheme isgiven byRk = min{Rulk , Rdlk }, (2.47)where Rulk and Rdlk are given in (2.29) and (2.46), respectively.This statement follows since the achievable end-to-end rate is bounded by thesmallest between the uplink rate and the downlink rate [148, 152]. Next, the uplinkand downlink scheme parameters are optimized in order to maximize the achievableend-to-end sum rate.512.6. End-to-End Rate Optimization2.6 End-to-End Rate OptimizationIn this section, we propose uplink and downlink optimization algorithms to max-imize the end-to-end rate of the multi-pair two-way computation (MPTWC) schemein (2.47). The proposed optimization is carried in two main steps, where each of theuplink and downlink parameters are optimized.2.6.1 Uplink Rate OptimizationThe achievable uplink rate Rulk can be optimized by assigning appropriate scalingmatrix Bul and full rank integer coefficient matrices Aulr and Aulψ to harness inter-pair interference, and selecting the uplink compression distortion covariance matrixDul to satisfy the fronthaul capacity constraint. Given an uplink power constraintP ulk , k ∈ {1, . . . , K} and a channel matrix Hul, the uplink optimization problem canbe formulated as followsmaxBul∈RK×K , Dul∈R+L×L ,Aulr ∈ZL×L, Aulψ ∈ZM×MK∑k=1Rulk (2.48a)subject to (bulk )2pul ≤ P ulk ∀ k ∈ {1, . . . , K} (2.48b)rank(Aulr ) = L (2.48c)rank(Aulψ ) = M (2.48d)Rulr,` ≤ C` ∀ ` ∈ {1, . . . , L} (2.48e)where (2.48b) is the uplink power constraint per user, (2.48c) and (2.48d) are theinteger coefficient matrices rank constraints, and (2.48e) is the fronthaul capacityconstraint.Due to the non-linearity of the objective function and the presence of the inte-ger variables, this optimization problem is a mixed-integer non-linear programming(MINLP) problem which is difficult to solve and is considered a non-deterministicpolynomial-time (NP-hard) problem. Obviously, the calculation of the proper Aulr ,Aulψ , and Dul depends on the scaling matrix Bul. On the other hand, the selection ofBul depends on Dul, Aulr , and Aulψ . In addition, it is also clear from equations (2.17)and (2.29) that Aulr , Aulψ , and Dul are tightly coupled. Note that joint optimizationfor the four variables is difficult and remains unsolved. Therefore, one way to solvethis optimization problem is by decoupling it into two sub-problems and iteratingover them. At first, for a fixed scaling matrix Bul, we maximize the uplink sum ratewith respect to Dul, Aulr , and Aulψ . Second, under the selected Dul, Aulr , and Aulψ ,522.6. End-to-End Rate OptimizationAlgorithm 1: Selection of Dul, Aulr , and Aulψ1: Initialization: Set  small, dmin = 0 and dul` = dmax ∀ ` (large) such thatmax`Rulr,` < C`.2: for ` = 1, . . . , L do3: while (C` −Rulr,`) >  or (Rulr ,` − C`) > 0 do4: if (Rulr ,` − C`) > 0 then5: dmin = dul`6: else7: dmax = dul`8: end if9: dul` = (dmax + dmin)/210: Fulr = Chol(HulBulPulBul>Hul>+IL+Duldul`)11: Aulr = LLL(Fulr )12: Rulr,` =12log+(||Fulr aulr,l||2)13: end while14: end for15: Calculate Cul using (2.19).16: Fulψ = Chol((1pulIK + Bul>Hul>(I + Dul)−1HulBul)−1)17: Aulψ = LLL(Fulψ W>)18: return (Dul,Aulr ,Aulψ )we maximize the uplink sum-rate with respect to Bul. Then, we iterate over thetwo sub-problems until convergence. The convergence of this iterative algorithm isproved in [153]. A detailed explanation of the proposed iterative uplink optimizationalgorithm is discussed next.2.6.1.1 Selection of Dul, Aulr , and AulψFor a fixed scaling matrix Bul, the optimization problem in (2.48) can be rewrittenasmaxDul∈R+L×L ,Aulr ∈ZL×L, Aulψ ∈ZM×MK∑k=1Rulk (2.49)subject to (2.48c), (2.48d), and (2.48e).532.6. End-to-End Rate OptimizationFrom (2.17), we can see that the uplink compression rate of the `th RRH Rulr,` isdependent on the distortion levels of all RRHs dul1 , . . . , dulL .In addition, given Dul, finding the optimal L×L integer coefficient matrix Aulr isequivalent to finding the L shortest linearly independent vectors (i.e., the successiveMinima) of the L dimensional lattice spanned by the matrix Fulr , where Fulr is ob-tained from the Cholesky decomposition Fulr Ful>r =(pulHulBulBul>Hul>+IL+Duldul`). Thesame concept is applied on finding the optimal full rank M ×M integer coefficientmatrix Aulψ . This problem is known as the Shortest Independent Vector Problem(SIVP) which is NP-hard [154, 155]. However, its solution can be efficiently ap-proximated using the LLL algorithm, whose running time is polynomial [156]. See[157, 158] for further details. Thus, we propose a sub-optimal algorithm to selectthe Dul,Aulr ,Aulψ matrices as follows. We start by initializing the distortion levels ofall RRHs to a large value dul` = dmax ∀ ` ∈ {1, . . . , L}, computing the correspondingAulr using the LLL algorithm on Fulr , and then checking if max`Rulr,` < C`. If this isnot satisfied, then dmax is enlarged until it is satisfied. Once dmax is set, we iterateas follows. We update dul` ∀ ` ∈ {1, . . . , L} using bisection search until (2.48e) issatisfied with equality, each time updating Aulr as described above. Finally, we usethe obtained Dul = diag(dul1 , . . . , dulL ) to calculate Aulψ using the LLL algorithm onFulψ defined after (2.27). This is explained in detail in Algorithm 1. The results ofthis algorithm will be used as inputs to optimize the scaling matrix Bul.2.6.1.2 Updating Scaling Matrix BulGiven the matrices Dul,Aulr , and Aulψ obtained from Algorithm 1, we can de-termine the appropriate scaling matrix Bul by solving the following optimizationproblemmaxBul∈RK×KK∑k=1Rulk (2.50)subject to (2.48b) and (2.48e).The above optimization problem is a non-convex problem due to the coupled in-terference terms in (2.25). One way to solve this problem is by using a barrier method[159]. At first, the barrier method converts the optimization problem in (2.50) toa sequence of minimization problems by introducing all the inequality constraintsinto the objective function. This can be done by introducing a logarithmic barrierfunction with a given parameter θ > 0 to control the accuracy of the solution [159].542.6. End-to-End Rate OptimizationAlgorithm 2: Updating Scaling Matrix Bul1: Set θ = θ(0) > 0, and solve the barrier problem using newton method to getBul(0)= Bul∗(θ).2: For barrier parameter η > 1 and γ = 1, 2, 3, . . . , repeat3: Solve barrier problem at θ = θ(γ) using newton method initialized at θ(γ−1) toproduce Bul(γ)= Bul∗(θ).4: Stopping criteria at K + L/θ < 5: Else, increase θ := ηθ6: Calculate σulm2using (2.27) ∀ m ∈ {1, . . . ,M}.7: Calculate rul = [Rul1 , . . . , RulK ]>using (2.29).8: return (Bul,Cul, rul)Therefore, the optimization problem in (2.50) can be reformulated to the followingminimization problemminBulΨ(Bul) = −θf(Bul) + φ(Bul) (2.51)where f(Bul) =∑Kk=1 Rulk and φ(Bul) = −∑Kk=1 log(P ulk − (bulk )2pul) − L∑`=1log(C` −Rulr,`).This optimization problem can be solved by using Newton’s method, and its so-lution is called a central point in the central path which is related to the originaloptimization problem in (2.50) [159]. Particularly, as θ increases, the accuracy ofthe central point will increase to approximate the optimal solution of (2.50). Math-ematically, the barrier method is carried in two steps. The first one is called thecentering step in which the outer iteration is required to compute the central point.The second one is known as the Newton step which is the inner iteration executedwithin the centering step. In other words, given the parameter θ, the Newton step isadopted to compute the central point in each centering step of the barrier method.The Newton step at Bul denoted by ∆Bulθ is given by∇2Ψθ(Bul)∆Bulθ = −∇Ψθ(Bul), (2.52)where ∇Ψθ(Bul) and ∇2Ψθ(Bul) are the gradient and Hessian of Ψθ(Bul), respec-tively, and ∆Bulθ can be obtained from (2.52) using the conjugate direction method[160]. The details of the procedure of finding Bul are given in Algorithm 2.552.6. End-to-End Rate Optimization2.6.2 Downlink Rate OptimizationThe aim of this step is to obtain an achievable downlink user-rate greater thanor equal to the uplink user-rate, i.e., Rdlk ≥ Rulk . Given the downlink channel matrixHdl = Hul>, the downlink powers pdl` , ` = 1, . . . , L, and the outputs of the uplinkoptimization algorithm, the achievable downlink user-rate Rdlk should be tuned byselecting proper integer coefficient matrix Adlr , beamforming matrix Bdl, and down-link compression distortion covariance matrix Ddl so that Rdlk ≥ Rulk . One way toformulate this problem is as followsminAdlr ∈ZL×L,Bdl∈RL×M , Ddl∈R+L×LK∑k=1(Rdlk −Rulk )2 (2.53a)subject to pdl` ≤ P dl` ∀ ` ∈ {1, . . . , L} (2.53b)rank(Adlr ) = L (2.53c)Rdlr,` ≤ C` ∀ ` ∈ {1, . . . , L} (2.53d)The above optimization problem is a non-convex problem due to the coupled interfer-ence terms in (2.42). Since the downlink integer coefficient matrix Adlr is generated atthe BBU pool to enable each RRH ` to recover its sdl` within some distortion, we cansimplify this problem by choosing Adlr = Aul>r . Then, we obtain Bdl that minimizes(2.53) using the barrier method as in updating scaling matrix Bul optimization [159].Therefore, the optimization problem in (2.53) can be reformulated to the followingminimization problemminBdlΨ(Bdl) = θdlf(Bdl) + φ(Bdl) (2.54)where f(Bdl) =K∑k=1(Rdlk −Rulk )2, φ(Bdl) =∑L`=1 log(Pdl` −pdl` )+L∑`=1log(C`−Rdlr,`), andθdl > 0 is a given parameter to control the accuracy of the solution. After obtainingthe proper Bdl, we can calculate the downlink distortion levels ddl = [ddl1 , . . . , ddlL ]>using (2.36), where Cdl = Cul>. The details of this procedure are given in Algorithm3.Remark 2.5. Other performance criteria can also be considered such as weighted sum-rate or minimum rate [159, 161]. Similar to the sum-rate maximization problemsolved in this section, the barrier method can also be used to solve the weightedsum-rate maximization problem [162, 163] and minimum-rate maximization problem[164, 165].562.6. End-to-End Rate OptimizationAlgorithm 3: Updating Beamforming Matrix Bdl1: Initialization: Set Hdl = Hul>, Adlr = Aul>r . Cdl = Cul>,rdl = [Rdl1 , . . . , RdlK ]>= 0K×1,2: Set θdl = θdl(0)> 0, and solve the barrier problem using newton method to getBdl(0)= Bdl∗(θ).3: For barrier parameter η > 1 and γ = 1, 2, 3, . . . , repeat4: Solve barrier problem at θdl = θdl(γ)using newton method initialized at θ(γ−1)to produce Bdl(γ)= Bdl∗(θdl).5: Stopping criteria at K + L/θdl < 6: Else, increase θdl := ηθdl7: ddl = Cdl ξdl8: Calculate pdl` , ρdlk , and rdl = [Rdl1 , . . . , RdlK ]>using (2.38), (2.43), and (2.46),respectively.9: return (Bdl, rdl)2.6.3 Complexity AnalysisNow we focus on the overall computational complexity of our proposed scheme.In Algorithm 1, the worst-case number of iterations of the bisection search is boundedto log(d), where d = dmax − dmin + 1. In each iteration, we calculate Aulr using theLLL algorithm with a total computational complexity of O(L4 log(L)) [158]. Thebisection search algorithm iterates until the fronthaul capacity constraint is satisfiedfor each RRH `, i.e. Rul` ≤ C`, ∀ ` ∈ {1, . . . , L}. In Fig. (2.4) in the numericalresults, we can find that dul` ∀ ` ∈ {1, . . . , L} converges quickly within few iterations.Then, we use the optimized Dul to calculate Aulψ using the LLL algorithm with atotal computational complexity of O(M4 log(M)) [158]. As a result, the worst-casetotal computational complexity of Algorithm 1 over all RRHs is O(L5 log(L) log(d)+M4 log(M)). In Algorithm 2, Bul is optimized using the barrier method. Each mainiteration of the barrier method has a worst-case complexity which is a polynomialfunction of the problem size, specifically in the order O((K + L)3) [159]. Then, weiterate over Algorithm 1 and Algorithm 2 until convergence. As a result, the totalcomputational complexity of the uplink rate optimization is O(Iit(L5 log(L) log(d) +M4 log(M) + (K + L)3)), where Iit is the number of iterations between Algorithm 1and Algorithm 2 until convergence which can be obtained from the numerical resultsas indicated in Fig. (2.5) in the numerical results. In the downlink rate optimization(2.53), choosing Adlr = Aul>r reduces the computational complexity of (2.53). InAlgorithm 3, Bdl is optimized using the barrier method with total computational572.7. Numerical Results0 2 4 6 8 10 12 14number of iterations1.21.41.61.822.22.42.6Compression distortion per RRH (d lul ) 10-6Compression distortion per RRH 1 (d1ul)Compression distortion per RRH 2 (d2ul)Figure 2.4: Convergence of bisection search at L = 2, K = 4, transmitted power= −5 dBm, and C` = 400 Mbps [2, Figure 4].complexity in the order of O((K + L)3) as in optimizing Bul [159].Note that the optimization of multi-pair two-way communication can employvarious methods, among which machine learning algorithms are considered. However,the chosen approach is specifically adopted due to its capability to address our end-to-end transmission mathematical model comprehensively. This includes the efficientoptimization of diverse uplink and downlink transmission matrices within a minimalnumber of iterations, as demonstrated in the numerical results section. It is essentialto highlight that this approach is also applied to all optimization sections in Chapters3 to 5, ensuring a consistent and effective methodology across the entire study.Now we are ready to evaluate the proposed scheme numerically and compare itwith existing schemes in the literature. This is discussed next.2.7 Numerical ResultsIn this section, the proposed multi-pair two-way computation (MPTWC) opti-mization scheme is evaluated and compared to the following existing schemes in582.7. Numerical Results1 2 3 4 5 6 7 8 9 10number of iterations6.76.86.977.17.27.37.47.57.6Uplink Sum Rate [bits/sec/Hz]AIFSC+MPTWCFigure 2.5: Convergence of the uplink iterative algorithm at L = 2, K = 4, trans-mitted power = −5 dBm, and C` = 400 Mbps [2, Figure 5].literature:1. Asymmetric integer-forcing source coding and channel coding (AIFSC+IFCC).2. Symmetric integer-forcing source and channel coding (SIFSC+IFCC).3. Optimized Wyner-Ziv compression with integer-forcing channel coding (WZ+IFCC).4. Optimized single-user compression with integer-forcing channel coding (SU+IFCC).In addition to comparing with these schemes, we combine our MPTWC scheme withthem to show the effect of taking the message source-destination information intoaccount and pairing the communicating users together on their performance in intra-cloud C-RAN communications. All the MPTWC-related schemes are evaluated byapplying the end-to-end rate optimization proposed in section (2.6).592.7. Numerical Results-40 -30 -20 -10 0 10 20Transmitted Power [dBm]012345678910End-to-End Sum Rate [bits/sec/Hz]AIFSC+MPTWCAIFSC+IFCCSIFSC+MPTWCSIFSC+IFCCWZ+MPTWCWZ+IFCCSU+MPTWCSU+IFCCFigure 2.6: End-to-End sum rate versus transmitted power in dBm at L = 2, K = 4(M = 2), and C` = 400 Mbps [2, Figure 6].Users are randomly distributed in the network with minimum and maximumdistances between user k and RRH ` equal dmin`,k = 50 m and dmax`,k = 300 m, re-spectively. We use 5000 realizations of the L × K Rayleigh fading channel ma-trix H = Hul = Hdl>, where each element h`,k is i.i.d N (0, σ2`,k), σ2`,k = Cdα`,k ,C = 10Gt+Gr−33.9510 , d`,k is the distance between user k and RRH ` in m, α = 3.67, andGt = 5 dBi and Gr = 0 dBi are the RRH ` and user k antenna gains, respectively[166]. The noise power is set to −102+10 log10(BW )+nf , where BW = 100 MHz isthe channel bandwidth and nf = 15 dBm is the noise figure. The maximum trans-mitted power per user P ulk = 25 dBm and the maximum transmitted power per RRHP dl` = 40 dBm. We also evaluate our scheme with different numbers of RRHs L anduser-pairs M = K/2. Furthermore, we assume that the capacities of the fronthaullinks are equal, i.e., C1 = · · · = CL.In Fig. 2.4 and 2.5, we evaluate the number of iterations that the bisection searchin Algorithm 1 and the uplink iterative algorithm over Algorithm 1 and Algorithm2 need to converge, respectively. These figures demonstrate that both algorithmsconverge within a few iterations.602.7. Numerical Results-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10Transmitted Power [dBm]024681012End-to-End Sum Rate [bits/sec/Hz]AIFSC+MPTWC (L=2, K=8, M=4)AIFSC+IFCC (L=2, K=8, M=4)AIFSC+MPTWC (L=2, K=10, M=5)AIFSC+IFCC (L=2, K=10, M=5)AIFSC+MPTWC (L=3, K=12, M=6)AIFSC+IFCC (L=3, K=12, M=6)AIFSC+MPTWC (L=4, K=14, M=7)AIFSC+IFCC (L=4, K=14, M=7)Figure 2.7: End-to-End sum rate versus transmitted power in dBm at differentnumbers of RRHs and users, and C` = 400 Mbps [2, Figure 7].Fig. 2.6 shows the achievable end-to-end sum rate of our proposed scheme, theIFCC schemes in bits/sec/Hz versus different transmitted power values in dBm atL = 2, K = 4, M = 2, and C` = 400 Mbps which is considered a small-scale C-RAN.This figure demonstrates that schemes with MPTWC have superior performance.Numerically, the achievable end-to-end sum rate is approximately doubled by theMPTWC scheme compared to the achieved rates in the existing IFCC ones at certaintransmitted power values (e.g., at transmitted power = −25 dBm). This is due tothe exploitation of the multi-pair lattice-based computation strategy that reduces thenumber of decoded linear combinations at the BBU pool to 2 in the MPTWC schemesinstead of 4 as required by existing IFCC schemes. This relaxes the constraints onthe uplink, reduces the computational complexity, and increases the uplink data ratewhich in turn increases the achievable end-to-end sum rate. In addition, Fig. 2.6indicates the performance of the AIFSC scheme is nearly the same as that in theoptimized WZ scheme in both MPTWC and conventional IFCC strategies. Moreover,due to the fronthaul capacity constraint, the performance of SIFSC schemes is lowerthan the other distributed compression schemes. Further, the optimized SU schemes612.7. Numerical Results200 250 300 350 400 450 500 550Fronthaul Capacity per RRH [Mbps]2345678End-to-End Sum Rate [bits/sec/Hz]AIFSC+MPTWCAIFSC+IFCCSIFSC+MPTWCSIFSC+IFCCWZ+MPTWCWZ+IFCCSU+MPTWCSU+IFCCFigure 2.8: End-to-End sum rate versus C` in Mbps at L = 2, K = 4 (M = 2), andtransmitted power = −5 dBm [2, Figure 8].have the poorest performance because the correlation between the received signalsat RRHs is not exploited.In Fig. 2.7, we consider different numbers of RRHs and users and study theachievable end-to-end sum rate of our proposed scheme and the AIFSC+IFCC inbits/sec/Hz versus different transmitted power values in dBm at C` = 400 Mbps. Thesame conclusion as in Fig. 2.6 can be observed from this figure. Numerically, at L = 2RRHs, as k increases, we notice that the achievable end-to-end sum rate decreasesfaster for the AIFSC+IFCC scheme compared to that in MPTWC approach. Thiscan be explained by the number of users competing on the available network resourcesand causing mutual interference, which is 4, 8, and 10 users in Fig. 2.6 and 2.7,respectively, which is reduced to 2, 4, and 5 pairs by the MPTWC scheme, whichexploit interference to enable decoding codewords’ pairs. Furthermore, in Fig. 2.7,we also consider larger C-RANs, where the number of RRHs and users are increasedto L = 3 and 4 RRHs and K = 12 and 14 users, respectively. This indicatesthat even with increasing the number of RRHs and communicating users in thenetwork, the MPTWC schemes still achieve a significant improvement in terms of622.8. Chapter Summarythe achievable end-to-end sum rate compared to the existing IFCC approaches, i.e.,the achievable end-to-end sum rate in MPTWC scheme is approximately twice thatin the AIFSC+IFCC at transmitted power = −15 dBm.While having transmitted power values less than 0 dBm may not be practical inthe real deployment of the network, we intentionally introduced this range in Fig.2.6 and 2.7 to simulate scenarios where communicating users are distant from theRRHs, experiencing weak channel gains between them. It is essential to reiterate thatour MPTWC scheme still demonstrates superior performance compared to existingschemes in the literature, especially in the practical range of transmitted powervalues greater than 0 dBm. This underscores the robustness and effectiveness of ourproposed approach, showcasing its ability to outperform alternatives in more realisticdeployment scenarios.Fig. 2.8 and 2.9 show the achievable end-to-end sum rate of our proposed schemeand existing ones versus different fronthaul link capacity values in Mbps at a trans-mitted power of −5 dBm and different numbers of RRHs and users. In Fig. 2.8, wefix the number of RRHs and users to L = 2 and K = 4, respectively. In contrast,in Fig. 2.9, we increase the numbers to L = 3, 4 RRHs and K = 12, 14 users. Allof these figures show that the achievable end-to-end sum rate in MPTWC schemesoutperforms that of the existing schemes at all fronthaul capacity values.In summary, the proposed MPTWC scheme outperforms state-of-the-art IFCCschemes at different transmitted powers and fronthaul capacities for intra-cloud C-RAN communications.2.8 Chapter SummaryIn this chapter, we presented a novel approach known as the Multi-Pair Two-WayComputation (MPTWC) scheme, specifically designed for intra-cloud Cloud RadioAccess Network (C-RAN) communications, where users are grouped into communi-cating pairs. The key innovation of the MPTWC scheme lies in its utilization ofa multi-pair lattice-based computation strategy. Unlike conventional integer-forcingmethods where the Baseband Unit (BBU) pool decodes integer linear combinationsof individual codewords, our scheme takes a different approach. Here, the BBU pooldecodes integer linear combinations of paired users’ codewords. This strategic shiftsignificantly reduces the number of required computation steps at the BBU pool, con-sequently lowering the number of rate constraints. Furthermore, rather than recov-ering the original messages, which is customary in standard BBU pools, our schemecompresses the previously computed combinations directly. These compressed com-binations are then transmitted to the Remote Radio Heads (RRHs) through the632.8. Chapter Summary200 250 300 350 400 450 500 550Fronthaul Capacity per RRH [Mbps]23456789101112End-to-End Sum Rate [bits/sec/Hz]AIFSC+MPTWC (L=4, K=14, M=7)AIFSC+IFCC (L=4, K=14, M=7)AIFSC+MPTWC (L=3, K=12, M=6)AIFSC+IFCC (L=3, K=12, M=6)Figure 2.9: End-to-End sum rate versus C` in Mbps at different numbers of RRHsand users, and transmitted power = −5 dBm [2, Figure 9].fronthaul links. This alteration in the data forwarding process contributes to thescheme’s efficiency and further relaxing its complexity. To further enhance the per-formance of the MPTWC scheme, we introduced a set of iterative algorithms. Thesealgorithms are designed to fine-tune various uplink and downlink parameters and con-figurations, ensuring efficient operation and maximizing the scheme’s performance.Through comprehensive simulations and analysis, we demonstrated that the pro-posed MPTWC scheme outperforms existing methods in terms of end-to-end sumrate. This improvement showcases the scheme’s effectiveness and its potential tosignificantly enhance the overall performance of C-RAN networks.64Chapter 3Multi-Pair Computation forC-RAN With Intra-Cloud andInter-Cloud CommunicationsIn this chapter, we broaden the scope of the multi-pair computation concept fromintra-cloud C-RAN scenarios to encompass setups with concurrent intra-cloud andinter-cloud communications. By categorizing users’ traffic into these distinct groups,we aim to elevate the overall performance of the C-RAN network. This departurefrom conventional relaying schemes, which treat all user transmissions uniformly,regardless of their nature as intra-cloud or inter-cloud communications, marks asignificant advancement.This chapter’s organization is given as follows. The accomplished works andresearch contributions are summarized in Section 3.1. The C-RAN system modelis introduced in Section 3.2. The uplink and downlink transmission schemes areproposed and investigated in Section 3.3 and Section 3.4, respectively. The multi-paircomputation iterative optimization algorithm is described in Section 3.5. Numericalresults are presented in Section 3.6, and finally, the chapter is concluded in Section3.7.3.1 Accomplished Works and ResearchContributionsThe contributions of this chapter are summarized as follows. We introduce ageneralized multi-pair computation strategy tailored for C-RANs with inter-cloudand intra-cloud communications, factoring in source-destination information for mes-sage exchange. We adopt a complex-valued transmission model utilizing real-valuedvector representation, a departure from the real-valued transmission model in theintra-cloud scenario. Furthermore, we derive achievable uplink and downlink ratesfor both types of communicating users, introduce an iterative algorithm for jointoptimization of uplink and downlink transmission parameters, and conduct compre-653.2. System ModelFigure 3.1: A C-RAN with inter and intra-cloud communicating users.hensive performance assessments across varying numbers of intra- and inter-cloudcommunicating users. The results attest to notable improvements compared to thecurrent state-of-the-art approaches.3.2 System ModelWe consider a C-RAN with L single-antenna RUs, K single-antenna users, and aCU. Each RU ` ∈ {1, . . . , L}, is connected to the CU via a noiseless digital fronthaullink with limited capacity. In this network, intra-cloud and inter-cloud communica-tions may occur simultaneously as shown in Fig. 3.1. We classify users into intra-and inter-cloud communicating users. An intra-cloud communicating user pair (k, k′)exchange their messages with each other via the C-RAN, while an inter-cloud com-municating user communicates with a user served by another C-RAN.The communication is completed in uplink and downlink phases over n channeluses each.4 We assume that the CU has perfect global channel state information4Uplink and downlink transmissions are assumed to be half-duplex over the same frequency663.2. System Model(CSI) of all RUs and users, to enable the CU to coordinate the RUs’ transmission.Global CSI can be obtained in practice by estimating the channels at the RUs andforwarding quantized estimates to the CU, and perfect CSI is assumed here forsimplicity (by neglecting errors due to estimation and quantized feedback)5 [167].We assume that RUs and users only have knowledge of local transmission schemeparameters. Hence, communication overhead on the fronthaul links is relativelymodest [146].Let the transmit signal of user k over n transmissions be represented by xR,k +jxI,k, where j =√−1 and xR,k,xI,k ∈ Rn are the real and imaginary parts of thesignal, respectively.6 Define Xk = [xR,k,xI,k]> ∈ R2×n, and X = [X>1 , . . . ,X>K ]> ∈R2K×n. Then, the baseband complex channel model can be written using an equiva-lent real-valued representation as Y = HX+Z, where Y = [yR,1,yI,1, . . . ,yR,L,yI,L]> ∈R2L×n, yR,`,yI,` ∈ Rn are the real and imaginary parts of the received signal at RU`, respectively, Z ∈ R2L×n consists of independent Gaussian noises with zero meanand unit variance N (0, 1), and H is the channel gain matrix given byH =[H¯1,1 ... H¯1,K.........H¯L,1 ... H¯L,K](3.1)with H¯`,k =[hR,`,k −hI,`,khI,`,k hR,`,k]and h`,k = hR,`,k+jhI,`,k being the complex-valued channelfrom user k to RU `. We assume that H remains fixed during the transmission andchanges independently between transmissions. As a result, we can treat the complex-valued C-RAN with users k ∈ {1, . . . , K} and RUs ` ∈ {1, . . . , L} as a real-valuedone with users κ ∈ {1, . . . , 2K} and RUs λ ∈ {1, . . . , 2L}, where user k (RU `) inthe complex-valued C-RAN is represented by users 2κ− 1 and 2κ (RUs 2λ− 1 and2λ) in the real-valued one.We denote the uplink transmit power constraint of user κ normalized by noisevariance N0 by Pulκ = P¯ulκ /N0, the downlink transmit power of RU λ by Pdlλ = P¯dlλ /N0and its fronthaul capacity by Cλ. We also define Kintra , {1, . . . , Kintra} as the setof intra-cloud communicating users, and Kinter , {Kintra + 1, . . . , Kintra + Kinter} asthe set of inter-cloud communicating users, where Kintra +Kinter = 2K.Intra- and inter-cloud communications are captured by grouping indicators wm,κ ∈{0, 1}, m ∈ {1, . . . , 2M}, where wm,κ = 1 if user κ belongs to group m, and wm,κ = 0otherwise, such that∑2Mm=1wm,κ = 1 for all κ, and∑2Kκ=1 wm,κ = 2 if group m is anband.5In case of CSI errors, the performance can be analyzed similar to [143].6All vectors in this work are column vectors.673.3. Uplink TransmissionFigure 3.2: Uplink Transmission Model: (a) User κ encodes its message intouulκ using lattice coding, then scales it and transmits xulκ to all RRHs. (b) RRH λcompresses its dithered observed signal using lattice-based vector quantization, thenmaps its compressed signal to an index eulλ , and forwards it to the BBU pool via itsfronthaul link. (c) The BBU pool decompresses the received signals and proceedsto decode 2M integer linear combinations of user-pairs’ codewords for intra-cloudcommunicating users, and individual codewords for inter-cloud communicating ones.In the end, the BBU pool recovers the codeword sums Sulψ = WSul by multiplyingthe decoded equations with the inverse of the uplink integer linear coefficient matrix.intra-cloud communicating pair of users, whereas∑2Kκ=1wm,κ = 1 if ‘virtual’ groupm contains only one inter-cloud communicating user.7We discuss the transmission scheme over this network next.3.3 Uplink TransmissionThe uplink transmission process is depicted graphically in Fig. 3.2, and is de-scribed in detail next.Given an n-dimensional lattice chain Λc ⊆ Λf,2K . . . ⊆ Λf,1 ∈ Rn, user κ ∈{1, . . . , 2K} constructs its nested lattice codebook Culκ = {Λf,κ ∩ υΛc} with rateRκ, where Λc is the coarse lattice, Λf,κ is the fine lattice of user κ, and υΛc isthe fundamental Voronoi region of Λc [79]. Then, it maps its message gulκ into alattice point sulκ ∈ Culκ and adds a random dither tulκ ∼ Unif(υΛc) known to allother nodes, to make its transmitted signal and the lattice point independent from7Due to splitting a user in the original complex-valued C-RAN into two in the real-valued C-RAN, if a user κ (κ odd) is paired with user κ′ (or is an inter-cloud communicating user) in thereal-valued C-RAN, then user κ+1 is also paired with user κ′+1 (or is an inter-cloud communicatinguser).683.3. Uplink Transmissioneach other. The result is then reduced modulo Λc, scaled by bulκ , and transmitted asxulκ = bulκ((sulκ + tulκ ) mod Λc) ∈ Rn, which must satisfy 1nE[‖xulκ ‖2] = (bulκ )2pul ≤ P ulκ ,where pul = σ2(Λc) is the second moment of Λc.The observed signal at the RUs is given byYul = HulXul + Zul, (3.2)where Yul = [yul1 , . . . ,yul2L]>, yulλ ∈ Rn is the observed signal at RU λ ∈ {1, . . . , 2L},Hul ∈ R2L×2K is the uplink channel gain matrix between all users and RUs in thenetwork (following a real-valued representation as in (3.1)), Xul = [xul1 , . . . ,xul2K ]>,and Zul ∈ R2L×n consists of independent Gaussian noises with zero mean and unitvariance.Each RU λ constructs its compression codebook C˜λ = {Λ˜f,λ ∩ υΛ˜c,λ} with rateRulr,λ to compress its signal yulλ toy¨ulλ = [QΛ˜f,λ(yulλ + t˜ulλ )] mod Λ˜c,˘, (3.3)where Λ˜c,1 ⊆ . . . ⊆ Λ˜c,2L ⊆ Λ˜f,2L ⊆ . . . ⊆ Λ˜f,1∈ Rn and t˜ulλ ∼ Unif(υΛ˜f,λ) is a randomdither vector. Then, RU λ forwards the compression index eulλ ∈ {1, . . . , 2nRulr,λ} ofy¨ulλ to the CU through its fronthaul link, provided Rulr,λ ≤ Cλ.Once the CU receives the indices eul1 , . . . , eul2L, it recovers y¨ul1 , . . . , y¨ul2L and calcu-latesy˜ulλ = [y¨ulλ − t˜ulλ ] mod Λ˜c,λ= [yulλ + qulλ ] mod Λ˜c,λ, (3.4)where qulλ = −[yulλ + t˜ulλ ] mod Λ˜f,λ ∼ Unif(υΛ˜f,λ) is the quantization error which is in-dependent of yulλ , and qulλ has independent N (0, dulλ ) components where dulλ is the dis-tortion power. The CU then estimates 2L linear integer combinations vulr,1, . . . ,vulr,2Lof the recovered compressed signals as in [151]vulr,i =[2L∑λ=1aulr,i,λy˜ulλ]mod Λ˜c,i(a)=2L∑˘=1aulr,i ,˘ y˜ul˘ , (3.5)where i ∈ {1, . . . , 2L}, aulr,i,λ ∈ Z is an integer coefficient, and (a) is obtained bychoosing 1nE[‖vulr,i‖2] < σ2(Λ˜c,i) [151]. We can write (3.5) in matrix form as Vulr =Aulr Y˜ul, where Aulr ∈ Z2L×2L is an uplink integer coefficient matrix which we requireto be of full rank, and Y˜ul = [y˜ul1 , . . . , y˜ul2L]>.693.3. Uplink TransmissionThe uplink compression rate at RU λ isRulr,λ =12log+2(ξulλ + aul>r,λ Dulaulr,λdulλ), (3.6)where ξulλ = aul>r,λ (pulHulBulBul>Hul>+I2L)aulr,λ, aul>r,λ is row λ of Aulr , Bul = diag(bul1 , . . . , bul2K),I2L is an identity matrix, Dul = diag(dul) with dul = [dul1 , . . . , dul2L]>, and log+2 (x) =max(0, log2(x)). We can write the distortion power levels as dul = Cul−1ξul whereξul = [ξul1 , . . . , ξul2L] andCul = diag(22Rulr,1 , . . . , 22Rulr,2L)− aul2r,1,1 ... aul2r,1,2L... ... ...aul2r,2L,1 ... aul2r,2L,2LBy multiplying the estimated Vulr by the inverse of the uplink integer coeffi-cient matrix Aulr,inv, the CU can recover Y˜ul = HulXul + Zul + Qul, where Qul =[qul1 , . . . , qul2L]>.Finally, the CU aims to decode 2M = K linear integer combinations of user-groups’ codewords to get vulψ,u =[2M∑m=1aulψ,u,m[2K∑κ=1wm,κsulκ]]mod Λc, where u ∈{1, . . . , 2M} and aulψ,u,m ∈ Z is an integer coefficient. We can write this as vulψ,u =([aul>ψ,uWSul]>) mod Λc where aulψ,u = [aulψ,u,1, . . . , aulψ,u,2M ]>, W is the 2M×2K ‘group-ing’ matrix with components wm,u, and Sul = [sul1 , . . . , sul2K ]>. Note that this de-creases the number of required computations at the CU to K compared to 2K in[149], which enhances the overall performance. These integer combinations of user-groups’ signals can be decoded at the CU by processing Y˜ul with a linear equalizerρulu , removing dithers, and reducing the result modulo Λc to obtainµulu =[[ρul>u Y˜ul]> −2K∑κ=1tulκ]mod Λc=[[aul>ψ,uWSul]> + zuleff,u]mod Λc (3.7)from which the CU computes the desired signal vulψ,u, where zul>eff,u = (ρul>u HulBul −aul>ψ,uW)Sul+ρul>u (Zul+Qul) is the uplink effective noise with power σul2u =1nE[‖zuleff,u‖2asσul2u = pul‖(ρul>u HulBul − aul>ψ,uW)‖2+ ρul>u (I2L + Dul)ρulu (3.8)703.4. Downlink TransmissionThe uplink effective noise variance in (3.8) can be minimized by choosing ρulu asthe MMSE equalizer calculated byρul>u = aul>ψ,uWPulBul>Hul>(pulHulBulBul>Hul>+ I2L + Dul)−1 (3.9)By substituting this into (3.8) and applying the Woodbury matrix identity, weobtain σul2u = ‖FulψW>aulψ,u‖2, where Fulψ is the Cholesky decomposition satisfyingFulψFul>ψ =[I2Kpul+ Bul>Hul>(I2L + Dul)−1HulBul]−1. (3.10)The achievable uplink computation rate for user κ belonging to group mκ (i.e.,wm,κ = 1) can be written asRulκ ≤ minu∈{1,...,2M}aulψ,u,mκ 6=012log+(pulσulu2). (3.11)At this point, the CU has Vulψ = [vulψ,1, . . . ,vulψ,2M ]> = [AulψWSul] mod Λc, whereAulψ = [aulψ,1, . . . , aulψ,2M ]> ∈ Z2M×2M . It recovers the codeword sums WSul by multi-plying Vulψ by Aulψ,inv. Codeword sums corresponding to inter-cloud communication(consisting of the sum of a users’ codeword and zero since these users are not paired)are passed to another cloud, whereas codeword sums corresponding to intra-cloudcommunication are sent in the downlink, as described next.3.4 Downlink TransmissionThe downlink transmission process is depicted graphically in Fig. 3.3, and isdescribed in detail next.The CU maps the decoded codeword sums of intra-cloud communicating usersas well as the downlink inter-cloud messages from other C-RANs that need to bedelivered to users in Kinter into lattice codewords S˜dl = [s˜dl1 , . . . , s˜dl2M ]>∈ R2M×n usinga nested-lattice chain Λc ⊆ Λf,2M ⊆ . . . ⊆ Λf,1, where 1n E[‖s˜dlm‖2] = pdl = pul =σ2(Λc). Then, the CU constructs 2M integer linear combinations of the latticecodewords to obtain Vdlψ = [Adlψ S˜dl] mod Λc, where Adlψ ∈ Z2M×2M is a full-rankinteger coefficient matrix. After that, the CU uses the beamforming matrix Bdl =[bdl1 , . . . , bdl2L]> ∈ R2L×2M to produceSdl = [sdl1 , . . . , sdl2L]> = Bdl[Adlψ S˜dl] mod Λc, (3.12)713.4. Downlink TransmissionFigure 3.3: Downlink Transmission Model: (a) The CU precodes the computedequations, maps each compressed linear equation to an index, and forwards themto RUs. (b) RU λ recovers its desired signal and broadcasts it to all users. (c)Intra-cloud communicating user κ ∈ Kintra decodes its desired signal using its owncodeword as side information, whereas inter-cloud communicating user κ ∈ Kinterdecodes its desired message directly.where sdlλ is the signal to be decompressed and sent with some distortion by RUλ. Then, the CU pre-inverts Sdl using a matrix Adlr,inv which is the inverse of afull-rank downlink integer coefficient matrix Adlr = [adlr,1, . . . ,adlr,2L]> ∈ Z2L×2L to beused for the downlink compressed signals, to obtain Vdlr = [vdl1 , . . . ,vdl2L]> = Adlr,invSdl.This enables optimizing the downlink compression while ensuring that each RU canextract its intended compressed signal by multiplying by Adlr . Next, the CU generatesa lattice chain Λˆc,1 ⊆ . . . ⊆ Λˆc,2L ⊆ Λˆf,2L ⊆ . . . ⊆ Λˆf,1, adds a random dither matrixTˆdl = [tˆdl1 , . . . , tˆdl2L]> to Vdlr , where tˆdlλ ∼ Unif(υΛˆf,λ), and quantizes the result intoVˆdlr = QΛˆf,1 (vdl1 +tˆdl1 )...QΛˆf,2L(vdl2L+tˆdl2L). (3.13)This leads to a downlink quantization error Qdl = [qdl1 , . . . , qdl2L]> with covariancematrix Ddl = diag(ddl) ∈ R2L×2L+ where ddl = [ddl1 , . . . , ddl2L]> and ddlλ = σ2(Λˆf,˘).The CU proceeds to estimate integer linear combinations of the compressed sig-nals as v˜dlr,i =([adl>r,i Vˆdlr ]>)mod Λˆc,i as in [151]. Finally, it maps v˜dlr,i to an indexedli ∈ {1, . . . , 2nRdlr,λ}, and forwards it to RU λ, where Rdlr,λ is the nested-lattice com-pression code rate which is chosen to be Rdlr,λ ≤ Cλ.723.4. Downlink TransmissionOnce RU λ receives edlλ , it recovers v˜dlr,λ and computesxdlλ =[v˜dlr,λ − [adl>r,λ Tˆdl]>]mod Λˆc,˘(b)= sdl>˘ + [adl>r,˘ Qdl]>, (3.14)where (b) is obtained by choosing 1nE[‖xdlλ ‖2] < σ2(Λˆc,λ). The downlink compressionrate at RU λ can be expressed asRdlr,λ =12log+(pdlbdl>λ bdlλ + adl>r,λ Ddladlr,λddlλ)(3.15)Finally, after recovering its intended signals sdlλ with some distortion, RU λ broad-casts xdlλ to all users such that1nE[‖xdlλ ‖2] = pdlbdl>λ bdlλ + adl>r,λ Ddladlr,λ , pdl` ≤ P dlλ . (3.16)We write the received signals at the users in a matrix form asYdl = HdlXdl + Zdl (3.17)= Hdl(BdlVdlψ + Adlr Qdl) + Zdl,where Ydl = [ydl1 , . . . ,ydl2K ]>, ydlκ is the received signal at user κ, Hdl ∈ R2K×2L is thedownlink channel gain matrix between all RUs and users, Xdl = [xdl1 , . . . ,xdl2L]>, andZdl ∈ R2K×n has independent N (0, 1) components. User κ scales ydlκ using ρdlκ andreduces the result modulo Λc to obtainµdlκ = [ρdlκ ydlκ ] mod Λc = [adl>d,κVdlψ + zdleff,κ] mod Λc (3.18)where zdleff,κ is the downlink effective noise given by (ρdlκ hdl>κ Bdl−adl>d,κ )Vdlψ +ρdlκ (hdl>κ Adlr Qdl+zdlκ ), hdl>κ is row κ of Hdl, adl>d,κ is row κ of Adld = W>Adlψ,inv ∈ R2K×2M , Adlψ,inv is theinverse of Adlψ , vdlψ,κ = [adl>d,κVdlψ ] mod Λc is the intended signal of user κ that includesthe desired codeword sum. The power of zdleff,κ is given byσdlκ2=1nE[‖zdleff,κ‖2]= pdl‖(ρdlκ hdlκ Bdl − adld,κ)‖2 + ρdlκ 2(hdlκ Adlr DdlAdl>r hdl>κ + 1) (3.19)733.5. Uplink and Downlink Sum-rate OptimizationWe can minimize the downlink effective variance in (3.19) by selecting the MMSEcoefficient for the linear equalizer ρdlκρdlκ =pdladld,κBdl>hdl>κhdlκ (Adlr DdlAdl>r + pdlBdlBdl>)hdl>κ + 1(3.20)By substituting this MMSE equalizer into (3.19) and applying the Woodburymatrix identity, we can write σdlκ2= ‖Fdld,κadl>d,κ ‖2, where Fdld,k is the Cholesky decom-positionFdld,κFdl>d,κ =(I2Mpdl+ Bdl>hdl>κ (1 + hdlκAdlr DdlAdl>r hdl>κ)−1hdlκBdl)−1. (3.21)Finally, user κ decodes [adl>d,κVdlψ ] mod Λc. Users in Kintra use their own codewordas side information to recover their desired codewords, whereas users in Kinter decodetheir desired signals directly. As a result, the downlink rate isRdlκ =12log+(pdlσdlΩ2), (3.22)where Ω = κ′ if κ ∈ Kintra and user κ′ is the user paired with user κ, and Ω = κ ifκ ∈ Kinter.The end-to-end data rate of user κ ∈ Kintra is given byRκ = min{Rulκ , Rdlκ }, (3.23)where Rulκ and Rdlκ ∀ κ ∈ Kintra are given in (3.11) and (3.22), respectively, and(3.23) follows because the end-to-end rate in intra-cloud communication is boundedby the smallest between the uplink and the downlink rates [148]. In contrast, therate of inter-cloud communicating users is given by (3.11) and (3.22) in the uplinkand downlink, respectively.3.5 Uplink and Downlink Sum-rate OptimizationWe propose an iterative algorithm to optimize the achievable sum-rate, whileimposing a quality-of-service (QoS) constraint in terms of rate. The algorithm iscarried out in two main steps where the uplink and downlink sum-rates are optimized.743.5. Uplink and Downlink Sum-rate Optimization3.5.1 Uplink Rate OptimizationGiven the uplink channel matrix Hul, coding power pul, and the maximum uplinkpower per user P ulκ ∀ κ, we can optimize the achievable uplink rate by selectingproper Dul and Aulr to satisfy the limited fronthaul capacity constraint per RU, andassigning appropriate Bul and Aulψ to minimize the uplink effective noise. The uplinksum-rate maximization problem can be formulated as followsmaxBul,Dul,Aulr ,Aulψ2K∑κ=1Rulκ (3.24a)subject to (bulκ )2pul ≤ P ulκ ∀ κ ∈ {1, . . . , 2K} (3.24b)rank(Aulr ) = 2L, rank(Aulψ ) = 2M (3.24c)Rulr,λ ≤ Cλ ∀ λ ∈ {1, . . . , 2L} (3.24d)Rulκ ≥ Rulth ∀ κ ∈ {1, . . . , 2K} (3.24e)This is a mixed-integer non-linear programming (MINLP) which is NP-hard.Joint optimization for the variables in (3.24) is extremely difficult and remains un-solved. One way to obtain a suboptimal solution is to decouple it into two subprob-lems and iterate over them as in [2, Alg. 1, Alg. 2]. Firstly, we fix Bul and optimizeDul using bisection search with a number of iterations bounded by log(d) where d isthe search distance, and we optimize Aulr and Aulψ using the LLL algorithm with acomputational complexity of O((2L)4 log(2L)) and O((2M)4 log(2M)), respectively[158]. Secondly, given the obtained Dul, Aulr , and Aulψ , we optimize Bul using thebarrier method with a worst-case complexity of O((2K + 2L)3) [168].3.5.2 Downlink Rate OptimizationGiven Hdl = Hul>, P dlλ ∀ λ, and the results of the uplink iterative algorithms,the downlink sum-rate can be optimized by choosing appropriate Adlr , Adlψ , Bdl, andDdl. The downlink sum-rate maximization problem can be formulated asmaxAdlr ,Adlψ ,Bdl,Ddl2K∑κ=1Rdlκ (3.25a)subject to pdlλ ≤ P dlλ , Rdlr,λ ≤ Cλ, λ ∈ {1, . . . , 2L} (3.25b)rank(Adlr ) = 2L, rank(Adlψ ) = 2M (3.25c)Rdlκ ≥ Rulκ ∀ κ ∈ Kintra (3.25d)753.6. Numerical ResultsAlgorithm 4: Downlink Iterative Algorithm1: Iterate between the two steps until convergence2: Step 1: Optimize Bdl using barrier method as in [2, Alg. 3]3: Calculate ddl = Cdl ξdl4: Calculate pdlλ , ρdlκ , and rdl = [Rdl1 , . . . , RdlK ]>using (3.16), (3.20), and(3.22), respectively5: return (Bdl,Ddl, rdl)6: Step 2: Optimize Adlψ using LLL algorithm7: Calculate Fdld,κ using (3.21)8: Update Adlψ = LLL(Fdld,κadl>d,κ )9: repeat step 410: return (Adlψ , rdl)Rdlκ ≥ Rdlth ∀ κ ∈ Kinter (3.25e)This is also a MINLP which is NP-hard. We decouple it into two separate sub-problems and iterate over them until convergence as shown in Algorithm 4. Firstly,we optimize Bdl that maximize (3.25) using the barrier method with a worst-casecomplexity of O((2K + 2L)3) following the same steps of [2, Alg. 3].Since Adlr is constructed at the CU to enable each RU λ ∈ {1, . . . , 2L} to extractits desired quantized signal, we can simplify this optimization by selecting Adlr =Aul>r . This will reduce the overall computational complexity.At each internal iteration of the barrier method, we calculate the downlink dis-tortion power levels ddl = [ddl1 , . . . , ddl2L]>using ddl = Cdl−1ξdl, where Cdl = Cul>,ξdl = [ξdl1 , . . . , ξdl2L]>, and ξdlλ = pulbdl>λ bdlλ .Secondly, we optimize Adlψ using the LLL algorithm on Fdld in (3.21) with a totalcomputational complexity of O((2M)4 log(2M)) [158]. Note that we impose thatthe downlink rate must be larger than or equal the uplink rate for intra-cloud com-municating users in (3.25d). This ensures the achievability of the uplink rate as anend-to-end rate for intra-cloud communication [148].3.6 Numerical ResultsIn this section, we evaluate the proposed scheme and compare it to the conven-tional symmetric integer-forcing source and channel coding (IFSC+IFCC) scheme.User-groups are distributed randomly in the service area with distances dλ,κ be-763.6. Numerical Results-30 -20 -10 0 10 20Uplink Transmitted Power [dBm]02468101214161820Uplink Sum-Rate [bits/sec./Hz]MPC (L=2, K=8, M=4, Kintra=8)MPC (L=2, K=8, M=5, Kintra=6)MPC (L=2, K=8, M=6, Kintra=4)MPC (L=2, K=8, M=7, Kintra=2)IFCC (L=2, K=8)Figure 3.4: Achievable uplink sum-rate versus uplink transmitted power per user P¯ ulκat Cλ = 400 Mbps [3, Figure 1a].tween RU λ and user κ varies from 50 to 300 meters. We use 5000 channel realiza-tions of Rayleigh fading, where elements in Hul and Hdl are independent N (0, σ2λ,κ),σ2λ,κ =%dαλ,κ, % = 10Gt+Gr−33.9510 , α = 3.67, and Gr = 0 dBi and Gt = 5 dBi are userκ and RU λ antenna gains, respectively. We set N0 = −102 + 10 log10(B) + nf ,where B = 100 MHz is the bandwidth and nf = 15 dBm is the noise figure. Weevaluate our scheme with different Kintra, thereby different numbers of user-groupsM , assuming that C1 = · · · = C2L, P¯ ul1 = · · · = P¯ ul2K , and P¯ dl1 = · · · = P¯ dl2L.we solve problem (3.24) and (3.25) and present the numerical results for the uplinktransmission in figures 3.4, 3.5, and 3.6, while noting that the downlink transmissionplots achieve similar performance as indicated in figures 3.7 and 3.8.Particularly, figures 3.4 and 3.5 show the total achievable uplink sum-rate inbits/sec/Hz and the uplink outage percentage (percentage of users whose uplinkrates do not satisfy the quality of services constraint (3.24e)) of our proposed MPCscheme and the state-of-the-art IFCC scheme versus different transmitted power lev-els P¯ ulκ in dBm at threshold rate Rulth = 50 Mbps and Cλ = 400 Mbps, respectively.Additionally, fig. 3.6 shows the total achievable uplink sum-rate in bits/sec/Hz ver-773.6. Numerical Results-40 -35 -30 -25 -20 -15 -10 -5 0 5Uplink Transmitted power [dBm]0102030405060708090100Uplink Outage PercentageMPC (L=2, K=8, M=4, Kintra=8)MPC (L=2, K=8, M=5, Kintra=6)MPC (L=2, K=8, M=6, Kintra=4)MPC (L=2, K=8, M=7, Kintra=2)IFCC(L=2, K=8)Figure 3.5: Uplink outage percentage versus P¯ ulκ at Rulth = 50 Mbps and Cλ = 400Mbps [3, Figure 1b].sus different fronthaul link capacities in Mbps at transmitted power of −5 dBm. Incontrast, fig. 3.7 shows the total achievable downlink sum-rate in bits/sec/Hz of ourproposed MPC scheme and the state-of-the-art IFCC scheme versus different trans-mitted power levels P¯ ulκ in dBm at Cλ = 400 Mbps. Additionally, fig. 3.8 indicatesthe total achievable downlink sum-rate in bits/sec/Hz versus different fronthaul linkcapacities in Mbps at transmitted power of −5 dBm.These figures demonstrate that the proposed MPC scheme outperforms the state-of-the-art at different numbers of intra-cloud and inter-cloud communicating users.This is because of the MPC strategy that reduces the number of decoded linear inte-ger combinations at the CU to M = 4, 5, 6, and 7 combinations for Kintra = 8, 6, 4,and 2, respectively, instead of 8 combinations required by the IFCC scheme (regard-less the number of intra-cloud communicating users). This relaxes the constraints onthe achievable sum-rates. Fig. 3.7 also shows that the performance is saturated ina high transmit power regime due to the limited fronthaul capacity constraint andincreased inter-user interference.783.7. Chapter Summary200 250 300 350 400 450 500Fronthaul Capacity per RU (C ) [Mbps]56789101112131415Uplink Sum-Rate [bits/sec./Hz]MPC (L=2, K=8, M=4, Kintra=8)MPC (L=2, K=8, M=5, Kintra=6)MPC (L=2, K=8, M=6, Kintra=4)MPC (L=2, K=8, M=7, Kintra=2)IFCC (L=2, K=8)Figure 3.6: Achievable uplink sum-rate versus Cλ at P¯ulκ = −5 dBm [3, Figure 1c].3.7 Chapter SummaryThis chapter extends the application of multi-pair computation techniques toencompass scenarios involving both intra-cloud and inter-cloud communications inC-RAN networks. By categorizing user traffic into these distinct groups, the over-all performance of the C-RAN network is significantly enhanced. This representsa departure from conventional relaying schemes, which treat all user transmissionsuniformly, regardless of their nature as intra-cloud or inter-cloud communications.The contributions of this chapter are manifold. It introduces a generalized multi-pair computation strategy tailored specifically for C-RANs with combined inter-cloudand intra-cloud communications, integrating source-destination information for mes-sage exchange. Moreover, the chapter introduces a complex-valued transmissionmodel employing a real-valued vector representation, deviating from the real-valuedtransmission model in intra-cloud scenarios. We proposed a multi-pair computa-tion transmission scheme and its optimization for intra- and inter-cloud C-RANcommunications, where the CU decodes integer linear combinations of codewords ofuser-groups (of 1 or 2 users) instead of decoding individual codewords. This reducesthe required number of computations at the CU, leading to less stringent rate con-793.7. Chapter Summary-30 -20 -10 0 10 20Downlink Transmitted Power [dBm]02468101214161820Downlink Sum-Rate [bits/sec./Hz]MPTWC (L=2, K=8, M=4, Kintra=8)MPTWC (L=2, K=8, M=5, Kintra=6)MPTWC (L=2, K=8, M=6, Kintra=4)MPTWC (L=2, K=8, M=7, Kintra=2)IFCC (L=2, K=8)Figure 3.7: Achievable downlink sum-rate versus uplink transmitted power per userP¯ ulκ at Cλ = 400 Mbps.straints. Additionally, the chapter derives achievable uplink and downlink rates forboth types of communicating users and introduces an iterative algorithm for the jointoptimization of uplink and downlink transmission parameters. Comprehensive per-formance assessments across varying numbers of intra- and inter-cloud communicat-ing users demonstrate substantial improvements compared to current state-of-the-artapproaches. In conclusion, this chapter represents a significant advancement in opti-mizing the performance of C-RAN networks through the introduction of a multi-paircomputation transmission scheme, which effectively balances the intricacies of intra-and inter-cloud communications.803.7. Chapter Summary200 250 300 350 400 450 500Fronthaul Capacity per RU (C ) [Mbps]46810121416Downlink Sum-Rate [bits/sec./Hz]MPTWC (L=2, K=8, M=4, Kintra=8)MPTWC (L=2, K=8, M=5, Kintra=6)MPTWC (L=2, K=8, M=6, Kintra=4)MPTWC (L=2, K=8, M=7, Kintra=2)IFCC (L=2, K=8)Figure 3.8: Achievable downlink sum-rate versus Cλ at P¯ulκ = −5 dBm.81Chapter 4Energy-Efficient Multi-PairComputation for Intra Cell-FreeMassive MIMO CommunicationsIn this chapter, we address a crucial scenario within CF-mMIMO networks, fo-cusing on intra-network two-way communication between user pairs. This situationarises in instances where direct links between communicating users are impracticaldue to significant distances. Consequently, users engaged in intra-cloud communi-cation rely on access points to relay their messages, capitalizing on joint process-ing capabilities at the CPU. Expanding on the foundational principles of multi-paircomputation for intra-cloud C-RAN, we present a pioneering lattice-based end-to-endmulti-pair computation scheme meticulously designed for intra-network CF-mMIMOcommunications. This scheme is purposefully tailored to prioritize energy efficiency,recognizing its paramount importance in modern communication networks.This chapter’s organization is given as follows. The accomplished works and re-search contributions are summarized in Section 4.1. The intra-cloud CF-mMIMOsystem model is introduced in Section 4.2. The end-to-end transmission scheme isproposed and investigated in Section 4.3. The energy-efficient multi-pair computa-tion (EEMPC) optimization algorithm is described in Section 4.4. Numerical resultsare presented in Section 4.5, and finally, the chapter is concluded in Section 4.6.4.1 Accomplished Works and ResearchContributionsThe contributions of this chapter are summarized as follows. We introduce arobust end-to-end energy-efficient scheme tailored to intra-cloud CF-mMIMO com-munication in the presence of imperfect channel state information (CSI). A depar-ture from conventional communication strategies, our proposed scheme refrains fromsegregating communication into distinct uplink and downlink channels. Instead, itcapitalizes on the CPU’s ability to decode combinations of codewords, reducing the824.2. System Model and Assumptionscomputational load compared to decoding individual codewords in a classical uplinkapproach. Moreover, we harness message source-destination information for pairs ofcommunicating users, augmenting the scheme’s overall performance.In contrast to the assumption of perfect Channel State Information (CSI) oftenmade in multi-pair computation for intra-cloud C-RAN, we adopt a more realisticperspective, accounting for the presence of imperfect CSI. This consideration is par-ticularly pertinent in CF-mMIMO networks, renowned for their ’massive’ nature.Alongside this, we factor in constraints related to fronthaul capacity, spectral effi-ciency, and limitations on user, access point (AP), and fronthaul power.Throughout this chapter, we conduct a comprehensive characterization of theachievable rate of our proposed scheme, optimizing its performance with a focus onenergy efficiency. The results of our analyses unequivocally demonstrate the superiorperformance of our approach when compared to state-of-the-art schemes. This chap-ter significantly contributes to advancing the field of CF-mMIMO communications,offering a robust and efficient solution for intra-network communication scenarios.4.2 System Model and AssumptionsWe consider a CF-mMIMO system that includes a CPU, K single-antenna users(M = K/2 user-pairs), and L K single-antenna APs connected to a CPU throughfronthaul links with capacity C`, ` ∈ {1, . . . , L}. Each AP ` ∈ {1, . . . , L}, is con-nected to the CU via a noiseless digital fronthaul link with limited capacity C`. Usersin each user-pair m ∈ {1, . . . ,M} aim to communicate with each other (intra CF-mMIMO communications) in a two-way fashion.8 Specifically, users k, k′exchangemessages with each other, where k 6= k′ ∈ {1, . . . , K}. We introduce an M ×K user-pairing matrix W, with components wm,k ∈ {0, 1} representing user-pair associationindicators, where wm,k = 1 if user k belongs to user-pair m and wm,k = 0 otherwise,such that∑Mm=1 wm,k = 1 and∑Kk=1wm,k = 2 for all k and m.Following the modeling of multi-hop two-way relay networks (TWRN) [148], themessage exchange among users within each user-pair is accomplished through twophases: Phase (a) representing the users-to-CPU transmission and phase (b) rep-resenting the CPU-to-users transmission, each with n channel uses. We assumehalf-duplex transmissions over phase (a) and (b) utilizing the same frequency band.We assume that global imperfect CSI of all APs’ and users’ channels at the CPU,thereby enabling coordinated transmission by the APs. We can model the CSI as8Combined intra- and inter-CF-mMIMO communication can be treated as in [3].834.3. End-to-End Transmission SchemeHˆa = Ha + Ea, (4.1)where Hˆa and Ha ∈ RL×K are the estimated and actual channel gain matrices9between all users and APs in the network during phase (a), respectively, and Ea ∈RL×K and is the channel estimation error matrix assumed to be Gaussian distributedwith mean 0 and covariance matrix σa2e IL, i.e., N (0, σa2e IL) [169]. We further assumeRayleigh block fading channels that remain constant throughout the transmissionof an entire codeword over the two phases (a) and (b), thus Hb = Ha> ∈ RK×L.Additionally, to minimize communication overhead on the fronthaul links, we assumethat APs and users know their respective local transmission parameters (e.g., theirlocal CSI and power values) only [146].Next, we discuss the end-to-end transmission scheme over the CF-mMIMO net-work.4.3 End-to-End Transmission SchemeThe transmission scheme consists of two phases. In phase (a), the CPU computescombinations of user-pairs’ codewords received through the APs. In phase (b), theusers decode their desired codewords from the combinations transmitted by the CPUthrough the APs. Note that the transmission scheme we consider was proposed in[2] to maximize the achievable sum-rate in a C-RAN without considering CSI errorsand a fronthaul link power constraint. We extend this scheme here to propose arobust and energy-efficient CF-mMIMO network while accounting for these effects.Details are given next.4.3.1 Phase (a) ProcessingUsing nested lattice codes, user k constructs its lattice codebook as Ck = {Λf,k ∩υΛc} with coding rate Rk, where Λf,k represents the fine lattice of the kth user andυΛc denotes the Voronoi region of the coarse lattice Λc. Subsequently, it encodes itsmessage gak into a designated lattice point sak ∈ Ck, scales it by bak, and transmitsxak = baksak ∈ Rn to all APs, which must satisfypak =1nE[‖xak‖2] = (bak)2pa ≤ P ak , (4.2)9This real-valued transmission model can be extended to encompass a complex-valued frameworkthrough the utilization of the real-valued vector representation of complex numbers [3].844.3. End-to-End Transmission Schemewhere pa = σ2(Λc) represents the second moment of the coarse lattice Λc and Pak isthe power constraint for user k.The observed signal at all APs is expressed asYa = (Hˆa − Ea)Xa + Za, (4.3)where Ya = [ya1, . . . ,yaL]>, ya` ∈ Rn represents the received signal the `th AP, Xa =[xa1, . . . ,xaK ]>, and Za ∈ RL×n is an identically and independent distributed (i.i.d.)additive white Gaussian noise (AWGN) with zero mean and unit variance N (0, 1).Each AP ` constructs its compression codebook C˜` = {Λ˜f,` ∩ υΛ˜c,`} with rate Rar,`to compress its signal yaλ using lattice-based vector compression asy¨a` = [QΛ˜f,`(ya` + t˜a`)] mod Λ˜c,`, (4.4)where the lattice chain Λ˜c,1 ⊆ . . . ⊆ Λ˜c,L ⊆ Λ˜f,L ⊆ . . . ⊆ Λ˜f,1∈ Rn and t˜a` ∼ Unif(υΛ˜f,`)is a random dither vector added to make quantization error independent of the signalto be processed at the CPU.After that, AP ` forwards the quantization index ea` ∈ {1, . . . , 2nRar,`} of y¨a` tothe CPU through its fronthaul link, which requires Rar,` ≤ C`. The traffic-dependentpower per fronthaul link during phase (a) is given byP afh,` = Pfh,TRar,`C`, (4.5)where Pfh,T is the total required power for fronthaul transmission at full capacity.After receiving the indices ea1, . . . , eaL, the CPU proceeds to recover y¨a1, . . . , y¨aL andcalculatesy˜a` = [y¨a` ] mod Λ˜c,` = [ya` + qa` ] mod Λ˜c,`, (4.6)where qa` = −[ya` ] mod Λ˜f,` denotes the quantization error and qa` ∼ N (0, da`), andda` is the quantization error power.Subsequently, the CPU estimates L integer linear combinations, var,1, . . . ,var,L, ofthe recovered compressed signals at the CPU, as in [149], by exploiting the correlationbetween the received signals at all APs asvar,i =[L∑`=1aar,i,`y˜a`]mod Λ˜c,i (4.7)(a)=L∑`=1aar,i,`y˜a` ,854.3. End-to-End Transmission Schemewhere aar,i,` ∈ Z is an integer coefficient, i ∈ {1, . . . , L}, and (a) is obtained assuming1nE[‖var,i‖2] < σ2(Λ˜c,i) [151]. Equation (4.7) can be written asVar = AarY˜a, (4.8)where Aar ∈ ZL×L is a full-rank integer coefficient matrix of the recovered compressedsignals, and Y˜a = [y˜a1, . . . , y˜aL]>. The integer coefficients can be selected to reduce thevariance of the compressed signals which decreases the required compression rates.The quantization rate at AP ` in phase (a) isRar,` =12log+2(ξa` + aa>r,`Daaar,`da`), (4.9)where ξa` = aa>r,` (paHˆaBaBa>Hˆa>+ (1 + Ωa)IL)aar,`, aa>r,` is row ` of Aar , Ba =diag(ba1 , . . . , baK ), Ωa = σa2e Tr(paBaBa>), IL ∈ ZL×L represents an identity ma-trix, Da = diag(da) with da = [da1, . . . , daL]>, Tr(.) is the trace of a matrix, andlog+2 (x) = max(0, log2(x)). The quantization error power levels can be written asda = Ca−1ξa where ξa = [ξa1 , . . . , ξaL] andCa = diag(22Rar,1 , . . . , 22Rar,L)−aa2r,1,1 . . . aa2r,1,L.... . ....aa2r,L,1 . . . aa2r,L,L. (4.10)The CPU recovers Y˜a = (Hˆa − Ea)Xa + Za + Qa through the multiplication ofthe estimated Var by the inverse of the integer coefficient matrix Aar,inv, where Qa =[qa1, . . . , qaL]>. Ultimately, the CPU decodes M = K/2 integer linear combinations ofuser-pairs’ codewords, yieldingvaψ,u =[M∑m=1aaψ,u,m[K∑k=1wm,ksak]]mod Λc, (4.11)where aaψ,u,m ∈ Z is an integer coefficient and u ∈ {1, . . . ,M}. We can write this asvaψ,u = ([aa>ψ,uWSa]>) mod Λc, (4.12)where aaψ,u = [aaψ,u,1, . . . , aaψ,u,M ]> and Sa = [sa1, . . . , saK ]>. This decreases the numberof required computation steps at the CPU to the half as compared to [149], whichenhances the overall performance.The CPU can decode these combinations of user-pairs’ codewords by processingY˜a with a linear equalizer ρau, and then reducing the output using the modulo Λc to864.3. End-to-End Transmission Schemeobtainµau =[[ρa>u Y˜a]>]mod Λc=[ρa>j HaBaSa + ρa>j (Za + Qa)]mod Λc=[[aa>ψ,uWSa]> + zaeff,u]mod Λc, (4.13)from which the CPU computes the desired signal vaψ,u, where za>eff,u = (ρa>u HˆaBa −aa>ψ,uW)Sa − ρa>u EaBaSa + ρa>u (Za + Qa) is the effective noise during phase (a) withvarianceσa2u =1nE[‖zaeff,u‖2= pa‖(ρa>u HˆaBa − aa>ψ,uW)‖2+ρa>u ((1 + Ωa)IL + Da)ρau. (4.14)To minimize σa2u , the MMSE equalizer ρau can be used, i.e.,ρa>u = aa>ψ,uWPaBa>Hˆa>(paHˆaBaBa>Hˆa>+ ((1 + Ωa)IL + Da)−1 (4.15)After substituting ρa>u into (4.14) and applying the matrix inversion lemma, wecan express σau2 as σa2u = ‖FaψW>aaψ,u‖2, where Faψ is the Cholesky decompositionsatisfyingFaψFa>ψ =[IKpa+ Ba>Hˆa>((1 +Ωa)IL +Da)−1HˆaBa]−1. (4.16)Finally, the achievable computation rate for user k in user-pair mk (i.e. wm,k = 1)during phase (a) is computed asRak ≤ minu∈{1,...,M}aaψ,u,mk6=012log+(paσau2). (4.17)At this point, the CPU has Vaψ = [vaψ,1, . . . ,vaψ,M ]> = [AaψWSa] mod Λc, whereAaψ = [aaψ,1, . . . , aaψ,M ]> ∈ ZM×M . Next, the CPU directly compresses Vaψ (as opposedto recovering individual users’ messages as in [149]) and transmits them to the APsover the fronthaul links. Consequently, this further reduces the signal processingcomplexity at the CPU, as discussed next.4.3.2 Phase (b) ProcessingIn the downlink, we start by describing the signal compression and decompressionat the CPU and distributed APs, respectively, followed by the decoding at the intra-cloud communicating users.874.3. End-to-End Transmission SchemeTo optimize the transmission over phase (b), the CPU uses the beamformingmatrix Bb = [bb1, . . . , bbL]> ∈ RL×M to getSb = [sb1, . . . , sbL]> = Bb[AaψWSa] mod Λc, (4.18)where sb` is the signal to be recovered and forwarded with some distortion by the`th AP. Subsequently, the CPU executes pre-inversion on Sb using Abr,inv, resultingin Vbr = Abr,invSb. This allows each AP to extract its intended compressed signal,where Vbr = [vb1 , . . . ,vbL]> and Abr,inv is the inverse of Abr ∈ ZL×L, which is a full-rankinteger coefficient matrix of the compressed signals by the CPU. Then, the CPUcompresses Vbr into Vˆbr = [vˆbr,1, . . . , vˆbr,L]> using lattice-based quantization, wherevˆbr,i = QΛˆf,i(vbi ) and i ∈ {1, . . . , L}.Then, the CPU proceeds to construct an n-dimensional lattice chain Λˆc,1 ⊆ . . . ⊆Λˆc,L ⊆ Λˆf,L ⊆ . . . ⊆ Λˆf,1 ∈ Rn, adds a random dither matrix Tˆb = [tˆb1, . . . , tˆbL]> to Vbr ,where tˆb` ∼ Unif(υΛˆf,`), and quantizes the output into Vˆbr = [vˆbr,1, . . . , vˆbr,L]>, wherevˆbr,i = QΛˆf,i(vbi +tˆbi ) and i ∈ {1, . . . , L}. Consequently, This introduces a quantizationerror Qb = [qb1 , . . . , qbL]> with covariance matrix Db = diag(db) ∈ R+L×L , wheredb = [db1, . . . , dbL]> and db` = σ2(Λˆf,`).Next, the CPU performs an estimation of integer linear combinations of thecompressed signals as v˜br,i =([ab>r,i Vˆbr ]>)mod Λˆc,i ∀ i ∈ {1 , . . . ,L}. Ultimately, theCPU maps v˜br,i to an index ebi ∈ {1, . . . , 2nRbr,`}, which is subsequently forwarded tothe `th AP, where Rbr,` represents the quantization rate which requires Rbr,` ≤ C`.The traffic-dependent power consumption per each fronthaul link during phase(b) is given byP bfh,` = Pfh,TRbr,`C`. (4.19)After receiving its index eb` , AP ` recovers v˜br,`, then subtracts the dither Tˆb, andreduces the result using the modulo-lattice operation with respect to Λˆc,` to obtainxb` =[[v˜br,`]>] mod Λˆc,`=[adl>r,` (Vbr + Tˆb + Qb)− adl>r,` Tˆb]mod Λˆc,`(b)= sb>` + [ab>r,` Qb]>. (4.20)where (b) is obtained assuming 1nE[‖xb`‖2] < σ2(Λˆc,`).The quantization rate at AP ` in phase (b) is computed as884.3. End-to-End Transmission SchemeRbr,` =12log+((pbbb>` bb` + ab>r,` Dbabr,`)/db`)(4.21)Finally, AP ` broadcasts xb` ∈ Rn to all users, adhering to a per-AP transmittedpower constraint given bypb` =1nE[‖xb`‖2] = pbbb>` bb` + ab>r,` Dbabr,` ≤ P b` . (4.22)The received signals by the users can be expressed asYb = (Hˆb − Eb)Xb + Zb= Hˆb(Sb + AbrQb)− Eb(Sb + AbrQb) + Zb= Hˆb(BbVaψ + Abr Qb)− Eb(BbVaψ + Abr Qb) + Zb, (4.23)where Yb = [yb1 , . . . ,ybK ]>, ybk represents the received signal at user k, Xb =[xb1, . . . ,xbL]>, Eb ∈ RK×L and is a Gaussian distributed channel estimation errormatrix in phase (b) with N (0, σb2e IK), and Zb ∈ RK×n is i.i.d AWGN with N (0, 1)components.User k multiplies ybk by a linear scaling parameter ρbk, and then reduces the outputusing mod Λc asµbk = [ρbkybk ] mod Λc= [ab>ψ,kVaψ + zbeff,k ] mod Λc, (4.24)where zbeff,k is the effective noise in phase (b) given by (ρbkhˆb>k Bb − ab>ψ,k)Vaψ +ρbk(hˆb>k Abr Qb − eb>k (BbVaψ + Abr Qb) + zbk), hˆb>k and eb>k are the kth row of Hˆb andEb, respectively, ab>ψ,k is row k of Abψ = W>Aaψ,inv ∈ RK×M , Aaψ,inv is the inverse ofAaψ, vbψ,k = [ab>ψ,kVaψ] mod Λc is the signal to be recovered at user k that includes thedesired codeword sum. The variance of zbeff,k is computed asσbk2=1nE[‖zbeff,k‖2]= pb‖(ρbkhˆbkBb − abψ,k)‖2+ ρbk2(hˆbkAbr DbAb>r hˆb>k + Ωb + 1), (4.25)where Ωb = σ2be Tr(paBdlBb>+ Abr DbAb>r ).The MMSE equalizer for ρbk is given byρbk =pbabψ,kBb>hˆb>khˆbk(Abr DbAb>r + pbBbBb>)hˆb>k + Ωb + 1(4.26)894.4. Total Energy Efficiency OptimizationUpon substituting the MMSE equalizer into (4.25) and applying the matrix in-version lemma, we can writeσbk2= ‖Fbd,kab>ψ,k‖2, (4.27)where Fdld,k is the Cholesky decomposition satisfyingFbd,kFb>d,k = (IMpa+ Bb>hˆb>k (1 + Ωb + hˆbkAbr DbAb>r hˆbk)−1hˆbkBb)−1. (4.28)Finally, user k decodes [ab>ψ,kVaψ] mod Λc using its own codeword as side informa-tion to recover its desired codewords. As a result, the achievable user rate in phase(b) isRbk =12log+(pbσbk′2). (4.29)Note that similar to the multi-hop two-way relay network (TWRN) [148], theCPU does not decode the users’ messages gak and send them to users. Instead, thedecoding of message gak is only done at the user k′at the end of phase (b), withthe CPU serving as a facilitator of cooperation through the computation of integerlinear combinations of user-pairs’ codewords. Consequently, the end-to-end rate Rkfor user k is achievable if it satisfies a constraint Rk ≤ Rak in phase (a), and aconstraint Rk ≤ Rbk in phase (b). Hence the maximum achievable Rk isRk = min{Rak, Rbk}, (4.30)where Rak and Rbk are given in (4.17) and (4.29), respectively.Next, we focus on optimizing the energy efficiency of this scheme.4.4 Total Energy Efficiency OptimizationThe energy efficiency is characterized as the ratio of the end-to-end sum-rateachieved by the K users to the total consumed power over the transmissions of bothphases (a) and (b) asη =∑Kk=1 RkL(pcir. + pfh,0) +∑Kk=1 pak +∑L`=1 pb` + pafh,` + pbfh,`(4.31)where pcir. and pfh,0 are constant circuit power per AP and fronthaul link, respectively,and pak, pafh,`, pbfh,`, and pb` are given in (4.2), (4.5), (4.19), and (4.22), respectively.904.4. Total Energy Efficiency OptimizationWe propose an iterative algorithm to maximize (4.31) while imposing a minimumper-user data-rate constraint.The total energy efficiency optimization problem is formulated as followsmaxBa,Da,Aar ,Aaψ ,Abr ,Bb,Dbη (4.32a)subject to pak ≤ P ak ∀ k ∈ {1, . . . , K} (4.32b)pb` ≤ P b` ∀ ` ∈ {1, . . . , L} (4.32c)rank(Aar ) = L, rank(Aa ) = M (4.32d)rank(Abr ) = L, rank(Ab ) = M (4.32e)Rar,` ≤ C` ∀ ` ∈ {1, . . . , L} (4.32f)Rbr,` ≤ C` ∀ ` ∈ {1, . . . , L} (4.32g)Rak ≥ Rth,k ∀ k ∈ {1, . . . , K} (4.32h)Rbk ≥ Rak ∀ k ∈ {1, . . . , K}. (4.32i)where the optimization is over the phase (a) and phase (b) transmission parameters.The optimization problem in (4.32) is non-convex and NP-hard. Typically, thejoint optimization of the parameters in (4.32) is extremely difficult and unsolved.To tackle this issue, we propose an iterative energy-efficient multi-pair computation(EEMPC) optimization algorithm as indicated in Algorithm 5. The algorithm it-erates between optimizing the parameters of phases (a) and (b) until the objectivefunction converges.4.4.1 Optimizing Transmission Parameters for Phase (a)Under fixed phase (b) transmission parameters and given Hˆa, Ea, P ak ∀ k, andsecond moment of Λc, the energy efficiency can be optimized by choosing appropriateDa and Aar ∈ ZL×L that achieve Rar,` ≤ C` and assigning proper Ba and Aaψ ∈ ZM×Mthat minimize the variance of the effective noise in phase (a). As a result, problem(4.32) is formulated as followsmaxBa,Da,Aar ,Aaψη (4.33a)subject to (4.32b), (4.32d), (4.32f), (4.32h)The optimization in (4.33) is non-convex, rendering it intricate to achieve an optimalsolution. One approach to solve this optimization is to decompose the problem intotwo distinct subproblems and iterate over them.914.4. Total Energy Efficiency OptimizationAlgorithm 5: Energy-Efficient Multi-Pair ComputationrepeatStep A: Optimize phase (a) transmission parameters:repeatOptimize Da using bisection search.Optimize Aar using LLL.Calculate Ca and Faψ using (4.10) and (4.16), respectively.Optimize Aaψ = LLL(FaψW>).Optimize Bul using barrier method.Calculate pak and pafh,` and using (4.2) and (4.5).until Until convergence occurs ;Step B: Optimize phase (b) transmission parameters:Optimize Bb using barrier method.Compute db = Cb ξb.Calculate P bfh,` and pb` using (4.19) and (4.22), respectively.until Until convergence occurs ;The first subproblem involves fixing Ba and determining the suitable Da,Aar andAaψ to optimize the consumed fronthaul power during phase (a). Selecting optimalfull-rank Aar and Aaψ matrices is related to the Shortest Independent Vector Prob-lem (SIVP), which is recognized as NP-hard. Nonetheless, it is feasible to obtainsuboptimal full-rank solutions using the LLL algorithm [158]. To optimize Da, weemploy the bisection search, aiming at achieving asymmetric distortion power levels.In particular, we initialize da` = dmax ∀ ` ∈ {1, . . . , L} and subsequently optimizethe corresponding Aar using the LLL algorithm on Far , which is the Cholesky decom-position satisfying FarFa>r =1dapaHˆaBaBa>Hˆa>+ IL(1+Ωada+ 1) and has a worst-caserun-time complexity of O(L4 log(L)) [158]. We then update da` ∀ ` ∈ {1, . . . , L} usingbisection search until (4.32f) is satisfied. It is noteworthy that the bisection searchiterations aimed at optimizing Da are bounded by log(d), where d = dmax− dmin + 1denotes the total search distance. Following this, the optimized Da is employed tocompute Aaψ using the LLL algorithm on Faψ with a worst-case run-time complexityof O(M4 log(M)) [158].In the second subproblem, once the matrices Da, Aar , and Aaψ have been selected,we can use the barrier method to determine the appropriate Ba matrix that maxi-mizes (4.33), while satisfying (4.32b) and (4.32h) with a total run-time complexityof O((K + L)3) [170]. We then iterate over the two subproblems until convergenceis achieved.924.4. Total Energy Efficiency Optimization2 4 6 8 10 12 14Number of iterations121416182022242628Energy Efficiency [bits/Joul./Hz]Imperfect EEMPC ( 2e=0.2, K=4, L=24)Imperfect EEMPC ( 2e=0.2, K=4, L=64)Figure 4.1: Total energy efficiency versus the number of iterations.4.4.1.0.1 Optimizing Transmission Parameters for Phase (b) Given Hˆb =Hˆa>, P b` ∀ `, and the outcomes of the phase (a) transmission parameters optimizationproblem, we can optimize the energy efficiency by choosing appropriate Abr , Bb, andDb. One approach to formulating this problem is asmaxAbr ,Bb,Dbη (4.34a)subject to (4.32c), (4.32e), (4.32g), (4.32i)Since the CPU constructs Abr to enable AP ` ∀ ` ∈ {1, . . . , L} to extract its intendedquantized signal, we can choose Abr = Aa>r to simplify the optimization process andfurther reduce its computational complexity. Then, the barrier method is utilized toobtain Bb that maximizes (4.34), while satisfying (4.32c) and (4.32i) with a total run-time complexity of O((K + L)3) [170]. Following this, we calculate the quantizationerror power levels db = [db1, . . . , dbL]>in phase (b) using db = Cb ξb, where Cb = Ca>,ξb = [ξb1 , . . . , ξbL]>, and ξb` = pabb>` bb` .The proof of the convergence of the iterative EEMPC algorithm is demonstratedin [171].934.5. Numerical ResultsFigure 4.2: Total energy efficiency versus number of APs atK = 4 users and C` = 400Mbps.4.5 Numerical ResultsIn this section, we conduct a performance evaluation of the proposed EEMPCscheme under both perfect CSI and imperfect CSI scenarios and compare it with otherlattice-based transmission schemes, including compute-and-forward (CoF) (CoF inthe uplink and reverse CoF in the downlink) and the integer-forcing channel coding(IFCC) scheme with perfect CSI. The deployment scenario involves randomly dis-tributed APs and users within a service area of 500 meters × 500 meters. For ourevaluation, 4000 instances of the L×K channel matrix with Rayleigh fading, whereelements in Ha and Hb are independent N (0, σ2`,k), σ2`,k = %dα`,k , % = 10Gt+Gr−33.9510 ,α = 3.67, Gt = 5 dBi and Gr = 0 dBi represent the antenna gains of AP ` anduser k, respectively. We set N0 = −102 + 10 log10(B) + nf , where B = 100 MHzis the bandwidth and nf = 15 dBm corresponds to the noise figure. The proposedscheme is evaluated under different numbers of users and APs, where pcir. = 0.2 Wand pfh,0 = 0.825 W, Pfh,T = 0.25 W/(Gbps), Pa1 = · · · = P aK = 100 mW, andP b1 = · · · = P bL = 200 mW.944.5. Numerical ResultsFigure 4.3: Total energy efficiency versus number of K at L = 32 APs and C` = 400Mbps.First, we investigate the number of iterations required by our proposed EEMPCoptimization to converge at different numbers of APs, at C` = 400 Mbps ∀ `, K = 4,and σ2e = σa2e = σb2e = 0.2. Fig. 4.1 demonstrates that our proposed algorithmconverges within a few iterations (e.g., 7 and 14 iterations at L = 24 and 64, respec-tively).Additionally, figures 4.2 and 4.3 show the total energy efficiency in bits/Joule/Hzof our proposed EEMPC optimization and the state-of-the-art CoF and IFCC schemeswith perfect CSI versus different numbers of APs and users at K = 4 users andL = 32 APs, respectively, as well as at C` = 400 Mbps and threshold rate Rth = 50Mbps. Furthermore, fig. 4.4 shows the total energy efficiency in bits/Joule/Hz versusdifferent capacity values of fronthaul link in Mbps, assuming C1 = · · · = CL and atK = 4 users and L = 64 APs. The results indicate that the EEMPC optimization inthe CF-mMIMO with imperfect CSI outperforms the IFCC and CoF schemes withperfect CSI. This improvement is attributed to the multi-pair computation strat-egy that reduces the number of decoded linear integer combinations at the CPU tothe half compared to other lattice-based schemes, relaxes the constraints on (4.32),954.5. Numerical ResultsFigure 4.4: Total energy efficiency versus C` at K = 4 users and L = 64 APs.minimizes noise variance and system complexity.In the preceding analysis, σ2e has been treated as a constant. However, in morepractical models, it is regarded as a function dependent on various other systemparameters and variables. Hereafter, we adopt a model as proposed in [169], whereinthe channel is characterized by block fading, and estimation is executed throughthe process of averaging over N noisy pilot symbols. Additionally, we address thescenario where the power allocation designated for pilot symbols, denoted as (ps),may not necessarily equate to the power allocated for data transmission. Assumingperfect orthogonality among the pilot sequences, σ2e is computed as followsσ2e =p−4(γ+1)(2βNp2(γ+1) + 1)β2N2, (4.35)where γ and β are system parameters that relate the power of the pilots and datasymbols as ps = βp(1−γ). We used N = L, as this represents the smallest possiblepilot length size that maintains orthogonality among pilot sequences. In figures4.5 and 4.6, we re-evaluate the performance of the EEMPC scheme and the otherconventional schemes with σ2e calculated as (4.35) at different values of γ and β.964.6. Chapter Summary20 30 40 50 60 70 80 90 100 110 120Number of APs16182022242628Energy Efficiency [bits/Hz/Joul.]Perfect EEMPCImperfect EEMPC ( = 0.5, =0.5)Imperfect EEMPC ( = 1, =2)Perfect IFCCPerfect CoFFigure 4.5: Total energy efficiency versus number of APs atK = 4 users and C` = 400Mbps [4, Figure 1b].Fig. 4.5 demonstrates that at a lower number of APs (e.g., typically below 28APs, which is not indicative of massive MIMO networks), the energy efficiency ofthe lattice-based schemes with perfect CSI surpasses that of the imperfect EEMPCscheme with modeled CSI error. Notably, as the value of σ2e diminishes with anincrease in L, the EEMPC optimization in CF-mMIMO with imperfect CSI exhibitssuperior performance compared to the IFCC and CoF schemes in massive MIMOnetworks. This same conclusion is supported by the findings in Fig. 4.6.4.6 Chapter SummaryThis chapter addresses a critical scenario within CF-mMIMO networks, focus-ing on intra-network two-way communication between user pairs. This becomesessential when direct links between communicating users are impractical due to sub-stantial distances. In such instances, users engaged in intra-cloud communicationrely on access points to relay their messages, utilizing joint processing capabilitiesat the CPU. Building upon the foundational principles of multi-pair computation974.6. Chapter Summary0.5 1 1.5 2 2.5 3 3.5 4Fronthaul Capacity per AP [bits/sec./Hz]2020.52121.52222.52323.5Energy Efficiency [bits/Hz/Joul.]Perfect EEMPCImperfect EEMPC ( = 0.5, =0.5)Imperfect EEMPC ( = 1, =2)Perfect IFCCPerfect CoFFigure 4.6: Total energy efficiency versus C` at K = 4 users and L = 64 APs [4,Figure 1d].for intra-cloud C-RAN, this chapter introduces a pioneering lattice-based end-to-endmulti-pair computation scheme designed meticulously for intra-network CF-mMIMOcommunications. A key emphasis is placed on prioritizing energy efficiency, recog-nizing its paramount importance in modern communication networks.We introduced a robust end-to-end energy-efficient scheme, tailored to intra-cloudCF-mMIMO communication in the presence of imperfect channel state information(CSI). Departing from conventional communication strategies, this proposed schemerefrains from segregating communication into distinct uplink and downlink channels.Instead, it leverages the CPU’s ability to decode combinations of codewords, therebyreducing the computational load compared to decoding individual codewords in aclassical uplink approach. Additionally, message source-destination information forpairs of communicating users is harnessed, further enhancing the scheme’s overallperformance.In contrast to the assumption of perfect Channel State Information (CSI) oftenmade in multi-pair computation for intra-cloud C-RAN, a more realistic perspec-tive is adopted, accounting for the presence of imperfect CSI. This consideration984.6. Chapter Summaryis particularly pertinent in CF-mMIMO networks, distinguished for their ’massive’nature. Alongside this, constraints related to fronthaul capacity, spectral efficiency,and limitations on user, access point (AP), and fronthaul power are factored in.Throughout this chapter, a comprehensive characterization of the achievable rateof the proposed scheme is conducted, optimizing its performance with a primaryfocus on energy efficiency. The results of the analyses unequivocally demonstrate thesuperior performance of this approach when compared to state-of-the-art schemes.Overall, this chapter makes a substantial contribution to advancing the field of CF-mMIMO communications, offering a robust and efficient solution for intra-networkcommunication scenarios.99Chapter 5Distributed Multi-PairComputation for Intra C-RANBidirectional CommunicationsIn this chapter, we embark on a comprehensive investigation of a groundbreak-ing concept known as the Distributed Multi-Pair Computation (DMPC) scheme,uniquely tailored for bidirectional communication networks within Cloud Radio Ac-cess Networks (C-RANs). The essence of this approach lies in its departure fromtraditional paradigms, advocating for the delegation of specific computational tasksfrom the Central Processing Unit (CPU) to the distributed Radio Units (RUs). Thistask offloading is facilitated through the implementation of an advanced lattice-basedquantization strategy.This chapter’s organization is given as follows. The accomplished works andresearch contributions are summarized in Section 5.1. The system model is intro-duced in Section 5.2. The uplink and downlink transmission schemes are proposedand investigated in Section 5.3 and Section 5.4, respectively. The end-to-end dis-tributed multi-pair computation optimization algorithm is described in Section 5.5.Numerical results are presented in Section 5.6, and finally, the chapter is concludedin Section 5.7.5.1 Accomplished Works and ResearchContributionsThe contributions of this chapter are summarized as follows. We build upon themulti-pair computation framework introduced in [2] by considering a scenario wherethe computation of certain user-pair codewords can be offloaded from the CentralProcessing Unit (CPU) to the distributed Radio Units (RUs). This strategic offload-ing serves to diminish the communication overhead over the constrained-capacityfronthaul links. In pursuit of this goal, we put forth a Distributed Multi-Pair Com-putation (DMPC) scheme within a Cloud Radio Access Network (C-RAN), that aims1005.2. System Modelto maximize the achievable end-to-end sum-rate.The primary objective of this scheme is twofold. Firstly, it seeks to substan-tially reduce the volume of data transmitted over the fronthaul links, which serveas the critical conduits between the RUs and the Central Processing Unit (CPU),thereby alleviating potential congestion and delays in data processing. Secondly, theDMPC scheme introduces a dynamic processing allocation strategy, wherein specificuser pairs are processed locally by an RU, while others are processed centrally by theCPU. This dynamic allocation is carefully optimized to maximize the achievable end-to-end rates for each pair, considering factors such as signal strength, interference,and network load. The chapter meticulously details derivations and optimizations toensure the effectiveness of this approach. Additionally, the chapter conducts thor-ough numerical evaluations, taking into account real-world constraints like limitedfronthaul capacity and power availability. These evaluations serve to validate theperformance of the proposed DMPC scheme, providing tangible evidence of its po-tential to revolutionize the operation and efficiency of C-RAN networks. In summary,this chapter represents a pivotal advancement in the design and operation of C-RANnetworks, offering a more flexible, adaptive, and efficient approach to distributingcomputation tasks across the network infrastructure.5.2 System ModelWe consider a C-RAN set-up that includes a CPU, M single-antenna user-pairs,and L single-antenna distributed RUs10, where the capacity of the digital fronthaullink between the CPU and each RU ` ∈ {1, . . . , L} is limited to C`. Each RU` ∈ {1, . . . , L}, is connected to the CU via a noiseless digital fronthaul link withlimited capacity C`. Using intra C-RAN communications, users in each user-pairm ∈ {1, . . . ,M} aim to communicate with each other. In other words, users km, k′m,exchange messages with each other, where k 6= k′ ∈ {1, 2} and m ∈ {1, . . . ,M}. As aresult, we can consider the uplink and downlink transmissions in the C-RAN networkas a multi-hop two-way relay network (TWRN) [95]. In this context, the uplinktransmission corresponds to the signal flow from the users to the CPU, whereas thedownlink transmission refers to the signal path from the CPU to the users. Therefore,we introduce a M×K user-pairing matrix W, where K = 2M is the total number ofusers in the network. Each element wkm ∈ {0, 1} in the matrix W represents a user-pair association indicator, i.e., wkm = 1 if user km belongs to user-pair m, wkm = 0otherwise. Furthermore,∑Mm=1wkm = 1 and∑2k=1wkm = 2 for k ∈ {1, 2} and10This approach can be extended to Cell-Free Massive MIMO networks.1015.3. Uplink TransmissionFigure 5.1: Uplink Transmission.m ∈ {1, . . . ,M}. The end-to-end message exchange among users in each user-pairm is completed in uplink and downlink phases over n channel uses.11Next, we describe the uplink and downlink transmissions.5.3 Uplink TransmissionThe uplink transmission process is depicted graphically in Fig. 5.1, and is de-scribed in detail next.5.3.1 Lattice encoding at usersThrough using nested lattice coding [172], an n-dimensional lattice chain Λc ⊆Λf,m ⊆ . . . ⊆ Λf,1∈ Rn is constructed, where Λc is the coarse lattice, Λf,m is thefine lattice of the mth user-pair, and m ∈ {1, . . . ,M}. Each user km in user-pairm generates its nested-lattice codebook as Culkm = {Λf,m ∩ υΛc} with coding rateRkm , where k ∈ {1, 2} and υΛc is the fundamental Voronoi region of Λc. Then, itmaps its message gulkm into a lattice point sulkm∈ Culkm and adds a random dither vectortulkm ∼ Unif(υΛc), which is known to all other nodes in the network, to make the lattice11Note that we assume half-duplex uplink and downlink transmissions over the same frequencyband.1025.3. Uplink Transmissionpoint and its transmitted signal independent on each other. The resulting ditheredsignal is then reduced using modulo Λc as uulkm= (sulkm + tulkm) mod Λc, scaled by bulkm,and transmitted as xulkm = bulkmuulkm ∈ Rn to all distributed RUs. The uplink powerconstraint of the transmitted signal xulkm is1nE[‖xulkm‖2] = (bulkm)2pul ≤ P ulkm , wherepul = σ2(Λc) is the second moment of Λc and Pulkmis the uplink power constraint foruser km.5.3.2 Low-Level and High-level Compression at thedistributed RUsThe received signal at the `th distributed RU is given byyul` =M∑m=12∑k=1hul`,kmxulkm + zul` , (5.1)where yul` ∈ Rn is the received signal at the `th distributed RU, hul`,km is the uplinkchannel gain12 between user km and RU `, and zul` ∈ Rn is an identically and inde-pendent distributed (i.i.d.) additive white Gaussian noise (AWGN) with zero meanand unit variance N (0, 1). We assume Rayleigh block fading channels that remainconstant over the transmission of a complete codeword.The observed signal at the `th distributed RU is processed as follows. At first, RU` performs a low-level quantization process to obtain its locally processed user-paircodewords asyp` =M∑m=1rp`,m[QΛf,m(yul` )] mod Λc=M∑m=1rp`,m(2∑k=1hul`,kmbulkmuulkm + [QΛf,m(∑j∈M/m2∑k=1hul`,kjxulkj+ zul` )] mod Λc)=M∑m=1rp`,m(2∑k=1hul`,kmbulkjuulkm + qp`,m), (5.2)where rp`,m ∈ {0, 1} is a user-pair local processing indicator, i.e., rp`,m = 1 if themth user-pair is processed locally at RU `, rp`,m = 0 if it is processed in the CPU,12We can extend this real-valued transmission model to a complex-valued model using the real-valued vector representation of complex numbers [3].1035.3. Uplink Transmission∑Mm=1 rp`,m = {0, 1} for ` ∈ {1, . . . , L} and∑L`=1 rp`,m ∈ {0, 1} for m ∈ {1, . . . ,M},and qp`,m is the low-level quantization error.If rp`,m = 1, this means that user-pair m is processed at RU ` only. In this case,bul1m and bul2m can be optimized to achieve user-pair signals alignment at RU `, i.e.hul`,1mbul1m = hul`,2mbul2m = hˆul`,m = 1. As a result, we can write the output of the low-levelquantization process asyp` =M∑m=1rp`,m(2∑k=1hˆul`,m(uulkm − tulkm) + qp`,m)=M∑m=1rp`,m(2∑k=1hˆul`,m(sulkm) + qp`,m) (5.3)Assuming 1nE[‖qp`,m‖2] ≤ σ2(Λf,m) ∀ m ∈ {1, . . . ,M} [151], the low-level quanti-zation rate at RU ` is calculated asRp` =12log+2 (pulhul` BulRp`Bul>hul>`dulm), (5.4)where hul` = [hul`,11, hul`,21 , . . . , hul`,1M, hul`,2M ]>, Bul = diag(bul11 , bul21, . . . , bul1M , bul2M), Rp` =diag(rp`W), rp` = [rp`,1, . . . rp`,M ]>, Rp = [rp1, . . . , rpL]> is the L ×M local processingmatrix, and dulm = σ2(Λf,m) is the second moment of the fine lattice Λf,m,m ∈{1, . . . ,M}.Then, RU ` subtracts the result of the low-level quantization process from itsoriginal observed signal to obtain the remaining signal to be centralized processed atthe CPU as followsyc` = yul` − yp` = h˜ul` Xul + zul` , (5.5)where yc` is the signal to be compressed and forwarded to the CPU, h˜ul` = hul` (IK −Rp`), IK ∈ ZK×K is an identity matrix, and Xul = [xul11 ,xul21 , . . . ,xul1M ,xul2M ]>.After that, RU ` generates its quantization codebook as C˜` = {Λ˜f,` ∩ υΛ˜c,`} withuplink quantization rate Rulr,` using lattice-based vector quantization to compress yc`toy¨ul` = [QΛ˜f,`(yc` + t˜ul` )] mod Λ˜c,`, (5.6)where the lattice chain Λ˜c,1 ⊆ . . . ⊆ Λ˜c,L ⊆ Λ˜f,L ⊆ . . . ⊆ Λ˜f,1∈ Rn and t˜ul` is arandom dither vector t˜ul` ∼ Unif(υΛ˜f,`) to make quantization error independent ofthe signal to be processed at the CPU.1045.3. Uplink TransmissionFinally, RU ` forwards the quantization index eul` ∈ {1, . . . , 2nRulr,`} of y¨ul` to theCPU via its fronthaul link, which requires Rulr,` ≤ C`.5.3.3 Decompression and computations at the CPUAfter receiving the indices eul1 , . . . , eulL from all the distributed RUs, the CPUproceeds to recover y¨ul1 , . . . , y¨Lul. Following this, it subtracts the dithers and reducesthe output using the modulo Λ˜c, ` asy˜ul` = [y¨ul` − t˜ul` ] mod Λ˜c,`= [yc` + qul` ] mod Λ˜c,` (5.7)where qul` = −[yc` + t˜ul` ] mod Λ˜f ,` ∼ Unif(ÆΛ˜f,`) is the quantization error and qul` ∼N (0, dul` ) where dul` is the quantization error power.Subsequently, the CPU estimates L integer linear combinations, vr, 1ul, . . . ,vr, Lul,of the recovered compressed signals using the correlation between the signals receivedfrom all distributed RUs, as in [151]vulr,i =[L∑`=1aulr,i,`y˜ul`]mod Λ˜c,i(b)=L∑`=1aulr ,i ,`y˜ul` , (5.8)where aulr,i,` ∈ Z is an integer coefficient, i ∈ {1, . . . , L}, and (b) is obtained assuming1nE[‖vulr,i‖2] ≤ σ2(Λ˜c,i) [151]. The matrix equation of (5.8) can be expressed asVulr = Aulr Y˜ul , where Aulr ∈ ZL×L is an uplink integer coefficient matrix of thecompressed signals required to be a full-rank matrix, and Y˜ul = [y˜ul1 , . . . , y˜ulL ]>. Theinteger coefficients can be selected to reduce the variance of the compressed signalswhich decreases the required quantization rates.The uplink quantization rate at the `th RU isRulr,` =12log+2 (aul>r,` (pulH˜ulBulBul>H˜ul>+ IL + Dul)aulr,`dul`) (5.9)where aul>r,` is the `th row of Aulr , H˜ul = [h˜ul1 , . . . , h˜ulL ]>, IL ∈ ZL×L is an iden-tity matrix, Dul = diag(dul) ∈ R+L×L is the uplink quantization error covari-ance matrix with dul = [dul1 , . . . , dulL ]>, and log+2 (·) = max(0, log2(·)). The distor-1055.3. Uplink Transmissiontion power levels dul can be written as dul = Cul ξul, where ξul = [ξul1 , . . . , ξulL ]>,ξul` = aul>r,` (H˜ulBulPulBul>H˜ul>+ IL)aulr,` is the `th row of ξul, andCul =22Rulr,1 − (aulr,1,1)2 . . . −(aulr,1,L)2.... . ....−(aulr,L,1)2 . . . 22Rulr,L − (aulr,L,L)2−1(5.10)The CPU can recover Y˜ul = H˜ulXul + Zul + Qul by multiplying the estimatedVulr by the inverse of the uplink integer coefficient matrix Aulr ,inv , where Qul =[qul1 , . . . , qulL ]> and Zul ∈ RL×n.5.3.4 Multi-Pair Computation at the CPUAfter that, the CPU constructs M × K centralized processing user-pair matrixWc, where wckm ∈ {0, 1} is a user pair centralized processing indicator, i.e., wckm = 1if∑L`=1 rp`,m = 0, wcm,km= 0 otherwise for all k ∈ {1, 2} and m ∈ {1, . . . ,M}.Then, the CPU decodes M = K/2 integer linear combinations of user-pairs’codewords to obtainvulψ,j =[M∑m=1aulψ,j,m[K∑k=1wcm,κsulk]]mod Λc, (5.11)where aulψ,j,m ∈ Z is an integer coefficient and j ∈ {1, . . . ,M}. This decreases thenumber of required computation steps at the CPU to the half as compared to [149],which enhances the overall performance. The matrix equation of (5.11) can beexpressed asVulψ = [Aulψ WcSul ] mod Λc, (5.12)where Aulψ ∈ ZM×M is an integer coefficient matrix with rank equal to M and Sul =[sul1 , . . . , sulK ]>. It should be noted that if∑L`=1 rp`,m = 1, the mth row aul>ψ,m of Aulψmust be a zero vector, except its element aul>ψ,m,m = 1.The CPU can decode these integer linear combinations of user-pair codewordsby processing Y˜ul with a linear equalizer ρulj , eliminating dithers, and then reducingthe output using the modulo Λc, as follows1065.3. Uplink Transmissionµulj =[ρul>j Y˜ul −K∑k=1tulk]mod Λc=[ρul>j H˜ulBulSul + ρul>j (Zul + Qul)]mod Λc= [aul>ψ,j WcSul︸ ︷︷ ︸desired signal+zuleff,j ] mod Λc (5.13)from which the CPU computes [aul>ψ,j WcSul] mod Λc,K , where zuleff,j = (ρul>j H˜ulBul−aul>ψ,j Wc)Sul + ρul>j (Zul + Qul) is the uplink effective noise with varianceσulj2=1nE[‖zuleff,j‖2= pul‖(ρul>j H˜ulBul − aul>ψ,j Wc)‖2+ ρul>j (IL + Dul)ρulj . (5.14)To minimize the uplink effective noise variance in (5.14), the MMSE equalizerρulj can be computed asρul>j = aul>ψ,j WcPulBul>H˜ul>(pulH˜ulBulBul>H˜ul> + IL + Dul)−1(5.15)After substituting the MMSE equalizer into (5.14) and applying the matrix in-version lemma, we can express σulj2asσulj2= aul>ψ,j Wc[Fulψ Ful>ψ ]Wc>aulψ,j= ‖Fulψ Wc>aulψ,j‖2, (5.16)where Fulψ is the Cholesky decomposition satisfyingFulψ Ful>ψ = (1pulIK + Bul>H˜ul>(IL + Dul)−1H˜ulBul)−1. (5.17)Finally, the achievable uplink computation rate for user km for k ∈ {1, 2} andm ∈ {1, . . . ,M} can be expressed asRculkm ≤ minj∈{1,...,M}aulψ,j,km 6=012log+(pulσulj2). (5.18)For locally processed user-pairs, the achievable uplink rate is calculated as followsRpulkm≤ min{Rculkm , min`∈{1,...,L}rp`,m 6=0Rp`}. (5.19)1075.4. Downlink TransmissionFigure 5.2: Downlink Transmission.The CPU directly compresses the integer linear combinations of the user pairs’codewords previously computed (as opposed to recovering the original messages ofindividual users as in [149]) and transmits them to the distributed RUs through thefronthaul links, as detailed in the following section. Consequently, this approachfurther reduces the signal processing complexity at the CPU, as discussed next.5.4 Downlink TransmissionThe downlink transmission process is depicted graphically in Fig. 5.2, and isdescribed in detail next.5.4.1 Compression at the CPUIn order to enable the optimization of the downlink transmission from the dis-tributed RUs to the users, the CPU uses the beamforming matrix Bdl ∈ RL×M togetSdl = Bdl Vulψ = Bdl[Aulψ WcSul ] mod Λc (5.20)where Sdl = [sdl1 , . . . , sdlL ]>, sdl` is the signal to be recovered and forwarded with somedistortion by the `th RU, Bdl = [bdl1 , . . . , bdlL ]> and bdl` = [bdl`,1, . . . , bdl`,M ]>, i.e. ifrp`,m = 1, bdl`,m = 1, if rp`,m = 0 and∑L`=1 rp`,m = 1, bdl`,m = 0, and if∑L`=1 rp`,m = 0,bdl`,m ∈ R for all ` ∈ {1, . . . , L}.Next, the CPU performs pre-inversion of Sdl using Adlr,inv, resulting in Vdlr =Adlr,invSdl , which allows each distributed RU to extract its intended compressed signal,where Vdlr = [vdl1 , . . . ,vdlL ]> and Adlr,inv is the inverse of the downlink full-rank integercoefficient matrix of the compressed signals Adlr ∈ ZL×L. Then, the CPU proceeds to1085.4. Downlink Transmissionconstruct an n-dimensional lattice chain Λˆc,1 ⊆ . . . ⊆ Λˆc,L ⊆ Λˆf,L ⊆ . . . ⊆ Λˆf,1 ∈ Rn,adds a random dither matrix Tˆdl = [tˆdl1 , . . . , tˆdlL ]> to Vdlr , where tˆdl` ∼ Unif(υΛˆf,`),∀ ` ∈{1, . . . , L}, and quantizes the output as followsVˆdlr = QΛˆf,1 (vdl1 +tˆdl1 )...QΛˆf,L(vdlL +tˆdlL ). (5.21)This results in a downlink quantization error Qdl = [qdl1 , . . . , qdlL ]> with covariancematrix Ddl = diag(ddl) ∈ R+L×L where ddl = [ddl1 , . . . , ddlL ]> and ddl` = σ2(Λˆf ,`).Hereafter, the CPU performs an estimation of integer linear combinations ofthe compressed signals, donated by V˜dlr = Adlr Vˆdlr and reduces them using moduloΛˆc,i ∀ i ∈ {1, . . . , L} as v˜dlr,i =[adl>r,i Vˆdlr]mod Λˆc,i as in [151]. Finally, the CPUmaps v˜dlr,i to an index edli ∈ {1, . . . , 2nRdlr,`} ∀ i ∈ {1, . . . , L}, and sends it to the ithRU, where Rdlr,` is the downlink quantization rate which requires Rdlr,` ≤ C`.5.4.2 Decompression at the distributed RUsAfter receiving its index edl` , the RU ` recovers v˜dlr,`, then subtracts the ditherTˆdl, and reduces the result using the modulo-lattice operation with respect to Λˆc,`to obtainxdlc,` =[v˜dlr,` − adl>r,` Tˆdl]mod Λˆc,`=[adl>r,` (Vdlr + Tˆdl + Qdl)− adl>r,` Tˆdl]mod Λˆc,`(b)= sdl>` + adl>r,` Qdl, (5.22)where (b) is obtained assuming 1nE[‖xdlc,`‖2] < σ2(Λˆc,`).The downlink quantization rate at RU ` can be expressed asRdlr,` =12log+(bdl>` P˜dl` bdl` + adl>r,` Ddladlr,`ddl`), (5.23)where P˜dl = diag([p˜dl1 , . . . , p˜dlM ]), p˜dlm = σ2(Λc) = pul if∑L`=1 rp`,m = 0, otherwisep˜dlm = 0.After the recovery of its intended signals sdl` , RU ` combines its local processedsignal to its xdlc,` to obtain1095.4. Downlink Transmissionxdl` = xdlc,` + yp` (5.24)= sdl>` + adl>r,` Qdl + rp`WSul,= bdl` Vˆulψ,` + adl>r,` Qdlwhere Vˆulψ,` = [Aulψ WSul ] mod Λc.RU ` broadcasts xdl` ∈ Rn to all users with transmitted power satisfying thefollowing constraintpdl` =1nE[‖xdl` ‖2]= pulbdl>` bdl` + adl>r,` Ddladlr,` ≤ P dl` . (5.25)The received signals at the intra-cloud communicating users can be expressed inmatrix form asYdl = HdlXdl + Zdl (5.26)= Hdl(BdlVˆulψ + Adlr Qdl) + Zdl,where Ydl = [ydl11 ,ydl21, . . . ,ydl1M ,ydl2M]>, ydlkm is the received signal at user km ∀ k ∈{1, 2} and m ∈ {1, . . . ,M}, Hdl = Hul> ∈ RK×L is the downlink channel gainmatrix between all RUs and intra-cloud communicating users assuming having chan-nel reciprocity, Xdl = [xdl1 , . . . ,xdlL ]>, and Zdl ∈ RK×n is i.i.d AWGN with N (0, 1)components.User km multiplies ydlkmby a linear scaling parameter ρdlkm and reduces the outputusing modulo Λc to getµdlkm = [ρdlkmyulkm ] mod Λc (5.27)= [ adlψ,kmVˆulψ︸ ︷︷ ︸intended signal+zdleff,km ] mod Λc,where zdleff,km is the downlink effective noise given by (ρdlk hdlkmBdl − adlψ,km)Vˆulψ +ρdlkm(hdlkmAdlr Qdl + zdlkm), adlψ,kmis the kmth row of Adlψ , Adlψ = W>Aulψ,inv ∈ RK×M ,Aulψ,inv is the inverse of Aulψ matrix, hdlkmis the kmth row of Hdl ∈ RK×L, vdlψ,km =[adlψ,kmVulψ ] mod Λc is the signal to be recovered at user km which includes the sum ofthe codewords of the user pair km, k′m ∈ {1m, 2m}, km 6= k′m. The downlink effectivenoise variance σdlkm2= 1nE[‖zdleff,km‖2] isσdlkm2= pul‖(ρdlkmhdlkmBdl − adlψ,km)‖2(5.28)+ ρdlkm2(hdlkmAdlr DdlAdl>r hdl>km + 1).1105.5. Distributed Multi-Pair Computation OptimizationBy selecting ρdlkm as the MMSE scaling parameter, we can minimize σdlkm2in (5.28)as followsρdlkm =puladlψ,kmBdl>hdl>kmhdlkm(Adlr DdlAdl>r + BdlPulψ Bdl>)hdl>km + 1(5.29)Finally, user km utilizes its own codeword [sulkm] mod Λc as side information to de-code [adlψ,kmVulψ ] mod Λc which enables it to recover its desired codeword [sulk ′m ] mod Λc(the codeword belonging to user k′m) as follows[[adlψ,kmVulψ ] mod Λc − sulkm]mod Λc= [adlψ,kmAulψ WSul − sulkm ] mod Λc= [sulkm + sulk′m− sulkm ] mod Λc = [sulk′m ] mod Λc (5.30)The achievable downlink rate of user km is given byRdlkm =12log+2 (pulσdlkm2 ) (5.31)Theorem 4 ([2]). The achievable end-to-end data-rate of user km is calculated byRkm = min{Rulkm , Rdlkm}, (5.32)where Rulkm is given by (5.18) if user km is processed at the CPU and is given by(5.19) if it is processed locally at the `th RU and Rdlkm is given in (5.31).Proof: This statement is justified because the achievable end-to-end rate is boundedby the minimum of the uplink and downlink rates.5.5 Distributed Multi-Pair ComputationOptimizationIn this section, we introduce an iterative distributed multi-pair computation(DMPC) optimization algorithm for optimizing the end-to-end rate in (5.32), whichconsists of two steps, where the end-to-end user rates and the distributed user-pairprocessing assignment are optimized iteratively.The end-to-end sum-rate optimization problem can be formulated as follows1115.5. Distributed Multi-Pair Computation OptimizationmaxRp,Bul,Dul,Aulr ,Aulψ ,Adlr ,Bdl,DdlM∑m=12∑k=1Rkmsubject toM∑m=1rp`,m = 1 ∀ ` ∈ {1, . . . , L} (5.33a)L∑`=1rp`,m ∈ {0, 1} ∀ m ∈ {1, . . . ,M} (5.33b)hul`,1mbul1m = hul`,2mbul2m = hˆul`,m ∀ rp`,m = 1 (5.33c)(bulkm)2pul ≤ P ulkm ∀ k ∈ {1, 2},m ∈ {1, . . . ,M} (5.33d)pdl` ≤ P dl` ∀ ` ∈ {1, . . . , L} (5.33e)rank(Aulr ) = L, rank(Aul ) = M (5.33f)rank(Adlr ) = L, rank(Ad ) = M (5.33g)Rulr,` ≤ C` ∀ ` ∈ {1, . . . , L} (5.33h)Rdlr,` ≤ C` ∀ ` ∈ {1, . . . , L}, (5.33i)where the optimization is over the local user-pair processing matrix and the uplinkand downlink parameters.The optimization problem defined in (5.33) is a mixed-integer non-linear pro-gramming (MINLP) problem, which is an NP-hard problem. Generally, optimizingthe parameters in (5.33) jointly is an extremely difficult and unsolved problem. Toaddress this problem, we propose an iterative distributed multi-pair computation(DMPC) rate optimization algorithm to optimize the achievable end-to-end sum-rate, which is carried out in two main steps as shown in Algorithm 6. First, for afixed local user-pair processing matrix, the achievable uplink and downlink sum-ratesare optimized. Second, under the uplink and downlink transmission parameters solu-tion, the algorithm optimizes the local user-pair processing matrix. We iterate overthe two steps until convergence is achieved.5.5.1 Uplink and Downlink Rate OptimizationIn this subsection, we introduce the first step of the algorithm, where the uplinkand downlink parameters are optimized under a fixed user-pair processing matrixRp.1125.5. Distributed Multi-Pair Computation Optimization5.5.1.1 Uplink Sum-Rate OptimizationGiven the uplink channel matrix between all users and RUs Hul = [hul1 , . . . ,hulL ]>,the maximum uplink power per user P ulkm ∀ km, and second moment of Λc, theachievable uplink sum-rate can be optimized by choosing the appropriate Dul andAulr ∈ ZL×L that achieve Rulr,` ≤ C`, and assigning proper Bul and Aulψ ∈ ZM×M thatminimize the variance of the uplink effective noise. As a result, the uplink sum-rateoptimization problem can be formulated as followsmaxBul,Dul,Aulr ,AulψM∑m=12∑k=1Rulkm (5.34a)subject to (5.33d), (5.33c), (5.33f), (5.33h)The optimization of (5.34) is a MINLP problem, which is hard to solve. Therefore,one possible approach to solving this optimization problem is to break it down intotwo separate subproblems and iterate over them.The first subproblem involves fixing Bul and selecting the proper Dul,Aulr andAulψ . The selection of optimal full-rank Aulr and Aulψ matrices is related to the Short-est Independent Vector Problem (SIVP), which is known to be NP-hard. How-ever, it is possible to obtain suboptimal full-rank solutions using the LLL algorithm[158]. Dul can be optimized using the bisection search. Instead of having symmet-ric dul` ∀ ` ∈ {1, . . . , L} as in [138], we optimize Dul to have asymmetric distortionpower levels. To solve this problem, we initialize dul` = dmax ∀ ` ∈ {1, . . . , L} andthen optimize the corresponding Aulr using the LLL algorithm on Fulr which is theCholesky decomposition that satisfies Fulr Ful>r =1dulpulHulBulBul>Hul>+ IL(1dul+ 1)and has a worst case run-time complexity of O(L4 log(L)) [158]. We then updatedul` ∀ ` ∈ {1, . . . , L} using bisection search until (5.33h) is achieved with equality.Note that the bisection search iterations to optimize Dul are bounded by log(d),where d = dmax − dmin + 1 represents the total search distance. Following this, weuse the optimized Dul to compute Aulψ using the LLL algorithm on Fulψ with a totalrun-time complexity of O(M4 log(M)) [158]. In the second subproblem, once thematrices Dul, Aulr, and Aulψ have been selected, we can use the barrier method todetermine the appropriate Bul matrix with a total complexity of O((K +L)3) [168].We then iterate over the two subproblems until convergence is achieved. The resultsof the uplink sum-rate maximization problem are subsequently utilized as inputs tothe downlink sum-rate optimization problem, which we discuss afterward.1135.5. Distributed Multi-Pair Computation OptimizationAlgorithm 6: Distributed Multi-Pair Computation AlgorithmrepeatStep A: Optimize the uplink and downlink transmission parametersrepeatOptimize Dul using bisection search and Aulr using LLL.Calculate Cul and Fulψ using (5.10) and (5.17), respectively.Obtain Aulψ = LLL(Fulψ W>).Optimize Bul using barrier method.until Until convergence occurs ;Optimize Bdl using barrier method.Compute ddl = Cdl ξdl.Calculate pdl` , ρdlkm, and rdl = [Rdl11 , Rdl21, . . . , Rdl2M ]>using (5.25), (5.29),and (5.31), respectively.Step B: Optimize Rp using Hungarian algorithm as in [172, Alg. 1].until Until convergence occurs ;5.5.1.2 Downlink Sum-Rate OptimizationThe objective of this stage is to achieve a downlink user-rate that is equal to orgreater than the achievable uplink rate, i.e., Rdlkm ≥ Rulkm . This guarantees that theuplink rate can be achieved as an end-to-end rate for intra-cloud communications[148]. Given Hdl = Hul>, P dl` ∀ `, and the outcomes of the uplink sum-rate opti-mization problem, we can optimize the downlink sum-rate by selecting proper Adlr ,Bdl, and Ddl. One approach to formulating this problem is as followsminAdlr ,Bdl,DdlM∑m=12∑k=1(Rdlkm −Rulkm)2 (5.35a)subject to (5.33e), (5.33f), (5.33i)Since the CPU constructs Adlr to allow RU ` ∀ ` ∈ {1, . . . , L} to extract its intendedquantized signal, we can select Adlr = Aul>r to simplify the optimization process andfurther reduce its computational complexity. Afterward, through utilizing the barriermethod, we can obtain Bdl that maximizes (5.35) with a worst-case complexity ofO((K+L)3) [168]. Following this, we calculate the downlink quantization error powerlevels ddl = [ddl1 , . . . , ddlL ]>using ddl = Cdl ξdl, where Cdl = Cul>, ξdl = [ξdl1 , . . . , ξdlL ]>,and ξdl` = bdl>` P˜dlbdl` .1145.6. Numerical Results5.5.2 Local User-Pair Processing AssignmentAfter obtaining the uplink and downlink transmission parameters in the previousstep of the DMPC algorithm, we proceed to find the optimal assignment of localuser-pair processing. The formulation of this optimization problem is as followsminRp−M∑m=12∑k=1Rkm (5.36a)subject to (5.33a), (5.33b), (5.33h), (5.33i)The solution to this assignment problem is equivalent to finding the best one-to-oneprocessing location for each user-pair that can maximize the achievable end-to-endsum-rate. An algorithm solving such a problem has been proposed in [173, 174]by using the Hungarian algorithm with backtracking with a worst-case run-timecomplexity of O((M + L)3).5.6 Numerical ResultsIn this section, the proposed DMPC scheme is evaluated and compared to the con-ventional multi-pair two-way computation (MPTWC) scheme and symmetric integer-forcing channel coding (IFCC) scheme. Our network consists of L = 3 distributedRUs, K = 4 intra-cloud communicating users (M = 2 user-pairs), assuming thatP ul11 = Pul21= P ul12 = Pul22, P dl1 = Pdl2 = Pdl3 , and C1 = C2 = C3. To conduct the evalu-ation, 3000 instances of the L ×K channel matrix H = Hul = Hdl> are generated,where each element h`,km is i.i.d N (0, 1).Figures 5.3 and 5.4 indicate the total achievable end-to-end sum-rate, measuredin bits per second per hertz (bits/sec/Hz), of the proposed DMPC scheme alongsidethe conventional fully-centralized MPTWC and IFCC schemes. Fig. 5.3 shows theachievable rates as SNR at a fixed fronthaul link capacity of C` = 4 bits/sec/Hz, whileFig. 5.4 depicts the rates at an SNR of 40 dB and varying fronthaul link capacityvalues. The results demonstrate that the DMPC scheme outperforms the otherconventional approaches. This improvement is attributed to the utilization of a low-level lattice-based quantization that enables each distributed RU to extract its locallyprocessed user-pair codeword and subtract it from the original observed signal. Thisallows for achieving user-pair signals alignment for the locally processed user-pairs,reducing the communication overhead over the limited-capacity fronthaul links andthe effective noise variance in the CPU, which in turn maximizes the achievable end-to-end sum-rate compared to the fully-centralized MPTWC and IFCC schemes. In1155.7. Chapter Summary-10 0 10 20 30 40 50 60 70SNR [dB]024681012141618End-to-End Sum Rate [bits/sec/Hz]DMPCMPTWCIFCCFigure 5.3: End-to-End sum-rate versus SNR in dB at C` = 4 bits/transmission [5,Figure 1].addition, using a multi-pair computation strategy at the CPU reduces the number ofdecoded linear combinations at the CPU from 4 equations (as required in the IFCC)to 2 equations (similar to the MPTWC). As a result, the constraints on the uplinkcomputational rates are relaxed, the computational complexity is reduced, and theachievable end-to-end sum-rate is increased.5.7 Chapter SummaryThe chapter introduces a novel approach called the Distributed Multi-Pair Com-putation (DMPC) scheme, specifically tailored for bidirectional communication net-works within Cloud Radio Access Networks (C-RANs). The goal of this scheme is toefficiently distribute computational tasks among different network components to op-timize performance. In traditional C-RAN setups, computation tasks are primarilyhandled by the Central Processing Unit (CPU) pool. However, this chapter proposesa paradigm shift, suggesting that certain computational tasks, particularly those re-lated to multi-pair computations, can be offloaded from the CPU pool to the Radio1165.7. Chapter Summary1.5 2 2.5 3 3.5 4 4.5 5 5.5Fronthaul Capacity per RRH [bits/sec/Hz]2468101214End-to-End Sum Rate [bits/sec/Hz]DMPTWCMPTWCIFCCFigure 5.4: End-to-End sum-rate versus C` in bits/transmission at SNR = 40 dB [5,Figure 2].Units (RUs) in the network, facilitated by an advanced lattice-based quantizationstrategy. The chapter aims to achieve two primary objectives: reduction of fronthaultraffic and optimization of user-pair processing. By offloading specific computationsto the RUs, there is a significant reduction in the volume of data transmitted overthe fronthaul links, alleviating potential congestion and enhancing network efficiency.The DMPC scheme introduces dynamic processing allocation for user pairs, maxi-mizing the achievable end-to-end rates. The chapter conducts extensive numericalevaluations, considering real-world constraints such as limited fronthaul capacityand power availability, to validate the performance of the proposed DMPC scheme.In summary, the DMPC scheme provides a flexible and efficient way to distributecomputation tasks within C-RANs, effectively addressing fronthaul congestion andmaximizing achievable end-to-end rates for user pairs. This approach represents asignificant advancement in the design and operation of C-RAN networks.117Chapter 6Conclusions and Future WorksIn this chapter, we provide the concluding remarks on the accomplished works inthis thesis. In the preceding chapters, we embarked on a comprehensive explorationof critical research gaps within the domain of distributed antenna systems. Ourinvestigation primarily focused on the significant tendency in prior works to concen-trate either exclusively on uplink or downlink transmissions, potentially leading toan inadvertent decline in the overall system performance. This issue is particularlyacute in scenarios characterized by a substantial exchange of messages within a sin-gle cloud or network, a circumstance frequently encountered in local area networkcommunications within venues like shopping centers, stadiums, and university cam-puses, especially when numerous distributed antenna terminals are deployed over awide geographic expanse. To address this challenge, we advocated for a paradigmshift towards a more inclusive optimization strategy, called ”multi-pair computa-tion”. This involves jointly optimizing the uplink and downlink transmissions whileconsidering message source-destination information.Furthermore, we identified another critical challenge in the prevailing relianceon fully centralized processing for both uplink and downlink transmissions. Thiscentralized processing paradigm has the potential to strain the fronthaul links, asthe volume of data exchanged between the central processing unit (CPU) and thedistributed radio units (RUs) may surpass the capacity of these links. In response,we proposed a transition towards distributed processing, allowing communicationbetween the CPU and RUs to be processed in a distributed manner. This shift holdsthe potential to significantly alleviate the communication overhead over the fronthaullinks, a facet that has been inadequately addressed in existing research endeavors. Byincorporating this adjustment into our optimization strategy, we aimed to cultivate amore efficient and balanced system, capitalizing on the benefits of jointly optimizingthe uplink and downlink transmission parameters while mitigating the constraintsimposed by fronthaul communication.Through these concerted efforts, we endeavored to formulate a comprehensive ap-proach that not only amplifies communication efficiency within the cloud but also el-evates the end-to-end performance of the system holistically. This research endeavorstands as a pivotal advancement in the realm of wireless communication networks,1186.1. Concluding Remarksholding the potential to yield substantial enhancements in system performance andresource utilization, particularly in densely populated and geographically expansiveenvironments.The concluding remarks on these developed schemes in each chapter are providedin the next section.6.1 Concluding RemarksSome concluding remarks on the accomplished works of this thesis are presentedas follows.− In Chapter 2, we introduced a groundbreaking end-to-end transmission schemedesigned for intra-cloud C-RAN communications. The conventional approachoften emphasizes either uplink or downlink transmissions, potentially leadingto suboptimal system performance, particularly in scenarios involving substan-tial message exchange within the same cloud or network. We took a differentapproach by jointly addressing uplink and downlink transmissions, consideringthe specific source-destination attributes of messages. The focus was on pair-wise message exchanges within a C-RAN framework. We proposed a multi-pair two-way transmission scheme, which employs a lattice-based computationstrategy. In this chapter, the Baseband Processing Unit (BBU) pool decodesinteger linear combinations of paired users codewords, reducing computationalload compared to decoding individual codewords. The BBU pool subsequentlyprecodes and compresses the signals, transmitting them to the Remote RadioHeads (RRHs). The RRHs decompress and relay the signals to users, who thendecode their intended messages. We rigorously derived the achievable end-to-end user data rate for this scheme, optimizing it while considering constraintson power and fronthaul capacity. Extensive numerical evaluations were car-ried out to validate the proposed approach, demonstrating an approximately1.3-fold improvement in end-to-end data rate compared to existing methods.− In Chapter 3, we expanded the scope of multi-pair computation from intra-cloud C-RAN scenarios to encompass C-RAN setups involving both intra-cloudand inter-cloud communications. This is a pivotal advancement, as it addressesa notable gap in the existing literature, which often focuses solely on either up-link or downlink transmissions. By categorizing users’ traffic into these distinctgroups, the chapter aims to enhance the overall performance of the C-RANnetwork. This departure from conventional relaying schemes allows for the1196.1. Concluding Remarksdevelopment of a tailored multi-pair computation strategy. We introduced acomplex-valued transmission model utilizing real-valued vector representation,a crucial distinction from the real-valued representations in the intra-cloudscenario. We established achievable uplink and downlink rates for both typesof communicating users, introducing an iterative algorithm for joint optimiza-tion of uplink and downlink transmission parameters. Performance evaluationsare conducted across varying numbers of intra- and inter-cloud communicatingusers, illustrating significant enhancements compared to current state-of-the-art approaches.− In Chapter 4, we addressed a scenario involving intra-network two-way com-munication within CF-mMIMO networks. This becomes particularly relevantwhen direct links between communicating users are impractical due to sub-stantial distances. Users engaged in intra-cloud communication rely on accesspoints to relay their messages, capitalizing on joint processing capabilities at theCPU. We introduced a robust end-to-end lattice-based multi-pair computationscheme tailored for intra-network CF-mMIMO communications. This schemedeviates from the traditional uplink-downlink segmentation, instead focusingon decoding codeword combinations at the CPU. Additionally, it leverages mes-sage source-destination information for communicating user-pairs, augmentingperformance. We adopted the more realistic assumption of imperfect Chan-nel State Information (CSI), particularly pertinent in CF-mMIMO networksdue to their ’massive’ nature. Constraints related to fronthaul capacity, spec-tral efficiency, and limitations on user, access point (AP), and fronthaul powerare carefully considered. We conducted a comprehensive characterization of theachievable rate of this scheme and optimized its performance in terms of energyefficiency, demonstrating its superior performance compared to state-of-the-artschemes.− In Chapter 5, we embarked on a comprehensive investigation of a distributedmulti-pair computation framework tailored specifically for intra C-RAN bidi-rectional networks. This innovative approach involves task delegation fromthe CPU to distributed Remote Units (RUs), effectively reducing essentialfronthaul traffic. The proposed Distributed Multi-Pair Computation (DMPC)scheme is intricately tailored for C-RAN setups featuring intra-cloud bidirec-tional communication. Within this framework, certain user-pairs are attendedto either locally by an RU or centrally by the CPU, introducing a dynamicway of processing user pairs. Rigorous derivations are conducted to ascer-tain the achievable end-to-end rates for both locally and centrally processed1206.2. Current Limitationsuser pairs. We strategically optimized processing locations to maximize theserates, considering constraints related to limited fronthaul capacity and power.Extensive numerical evaluations are conducted, affirming that the proposedscheme adeptly overcomes fronthaul capacity limitations. This leads to a no-table enhancement in the achievable end-to-end sum-rate when compared toconventional centralized approaches. This chapter represents a significant ad-vancement in the design and operation of C-RAN networks, providing a moreflexible and efficient way to distribute computation tasks within the network.6.2 Current LimitationsDespite the significant advancements achieved in this thesis regarding fronthaulutilization in Distributed Antenna Systems (DAS), several challenges persist, war-ranting further research and innovation. In this section, we delineate the existinglimitations for future exploration.One of the primary constraints in efficient fronthaul utilization arises from thepractical limitations of fronthaul links. The capacity of these links serves as a crit-ical bottleneck, restricting the amount of data that can be exchanged between thedistributed radio units (RU) and the central processing unit (CPU). This limitation,while mitigated to some extent through the strategies proposed in this thesis, stillpresents a practical barrier. Especially, in ultra-dense wireless networks, where alarge number of RUs are deployed in close proximity to serve a high density of users,the demand on fronthaul links can be substantial. This is because each RU may needto communicate with the CPU for tasks such as signal processing, coordination, andresource allocation. As a result, the capacity of fronthaul links can become a criticalbottleneck, potentially leading to congestion and delays in data transmission.Additionally, there are many challenges associated with data collection within theService Management and Orchestration (SMO) platform used in Open Radio AccessNetwork (O-RAN) architectures. This platform plays a pivotal role in the efficientmanagement and optimization of various facets of the Open RAN system, relyingheavily on a unified data collection mechanism from all network elements to builda comprehensive network overview. However, this process of gathering substantialdata from a diverse array of network elements introduces a set of significant hurdles.Firstly, the transmission of large data volumes introduces additional communicationoverhead over the fronthaul and midhaul links, which can congest the network andimpede the efficiency of data transmission. Secondly, it leads to heightened powerconsumption, potentially straining the energy resources of the network infrastructure.Not only does increased data usage lead to higher energy consumption during data1216.3. Suggested Future Workcollection, but it also translates into elevated operational costs, impacting the eco-nomic viability of the network. Moreover, the process can introduce latency, affectingreal-time decision-making, a critical aspect in dynamic network environments. Fi-nally, inefficiencies in data collection and processing may lead to delays in obtainingcritical information, potentially compromising the effectiveness of network opera-tions. Addressing this limitation necessitates the development of innovative datacollection mechanisms that balance performance and cost, involving optimization ofdata acquisition processes, implementation of efficient data compression techniques,and minimization of communication overhead for the efficient operation of the SMOplatform and, by extension, the overall effectiveness of the Open RAN architecture.Furthermore, the optimization of receivers for Quadrature Amplitude Modula-tion (QAM) symbol detection within the context of intra-cloud Cloud Radio AccessNetwork (C-RAN) communications remains an area of unmet need. The existingtechnology and methodologies may not be fully equipped to handle the intricacies ofsymbol detection in this specific scenario. This signifies a potential area for futureresearch and innovation to enhance the efficiency of symbol detection processes inintra-cloud C-RAN communications.6.3 Suggested Future WorkThis thesis delves into the exploration of multi-pair computation (MPC) schemesto optimize fronthaul utilization in distributed antenna systems. However, thereremain intriguing research avenues pertaining to the efficient allocation of resourcesthrough MPC that warrant further investigation. Below, we outline potential futureextensions for the research undertaken in this thesis.6.3.1 Integrating Device-to-Device Communications withDMPC for Further Relaxing FronthaulCommunications OverheadAn exciting avenue for future research lies in the integration of device-to-device(D2D) communications with the existing distributed multi-pair computation (DMPC)scheme. This integration holds the potential to alleviate the communications over-head over the Distributed Antenna System (DAS) interfaces, further optimizing theoverall network performance.By introducing D2D communications, some of the data exchange tasks that typi-cally occur over fronthaul links can be offloaded and handled directly between neigh-1226.3. Suggested Future Workboring user devices. This means that certain communications, which would otherwisetraverse the constrained fronthaul links, can now occur locally. As a result, the bur-den on the fronthaul links is significantly reduced.By incorporating D2D communications into the DMPC framework, we can ex-plore a dynamic approach to selecting the most suitable communication mode -whether centralized, distributed, or D2D - based on the current network conditionsand traffic patterns. Reinforcement learning, a powerful machine learning technique,presents itself as a promising methodology for automating this decision-making pro-cess. Through reinforcement learning algorithms, the network can learn and adaptits communication mode selection strategy over time, ultimately leading to a moreefficient and responsive network. Specifically, in scenarios where fronthaul links areapproaching their capacity limits, the intelligent decision-making mechanism can optto utilize D2D communications for certain tasks. This enables more data to be pro-cessed directly at the edge of the network, bypassing the potential bottleneck of thefronthaul links.This future endeavor will entail a comprehensive investigation into the interac-tions between DMPC and D2D communications, focusing on how they can mutuallybenefit each other in terms of reducing communication overhead and enhancing over-all network performance. The proposed reinforcement learning framework will serveas the intelligent decision-making mechanism, dynamically adapting to changing net-work conditions and traffic demands.Moreover, this research will involve extensive simulations and real-world exper-iments to validate the effectiveness and efficiency of the integrated DMPC-D2Dapproach. The results obtained from these evaluations will provide valuable in-sights into the practical implications and benefits of this combined communicationparadigm, potentially paving the way for significant advancements in the design andoperation of future wireless networks.6.3.2 Designing Efficient Data Collection Models for OpenRadio Access Network Service ManagementOrchestrationMobile operators must efficiently allocate limited resources in complex environ-ments and deploy cutting-edge capabilities like closed-loop assurance and networkslicing, which have increased the network management complexity. This underscoresthe importance of intelligent automation in managing Radio Access Network (RAN)operations. Self-optimization of 5G Open RAN service management orchestrationis now critical to ensure high-quality and dependable network services. The Open1236.3. Suggested Future WorkRAN Alliance’s introduction of the Service Management and Orchestration (SMO)unit promises enhanced network performance and customer experience. The SMOplatform relies on unified data collection to monitor the multi-vendor Open RANarchitecture, handle RAN data, support policy control, and foster innovation. How-ever, collecting substantial data from all network elements introduces high powerconsumption, communication overhead, and latency across O-RAN interfaces, re-quiring an innovative data collection mechanism that balances performance and cost.This surge in data usage results in substantial energy consumption costs, highlight-ing the urgency for adept data handling. Current data accumulation practices leadto excessive energy consumption per bit transmission. Furthermore, these practicesmay lead to protracted delays and significant overhead over the network interfaces,potentially resulting in decisions based on outdated information.To tackle these challenges, we can propose comprehensive data modeling and uti-lization strategies, incorporating numerical simulations and practical experiments.The key objectives of these strategies include reducing the amount of statisticalinformation required for training AI models in the near real-time RAN intelligentcontroller (RIC) while ensuring highly accurate decision-making and meeting qual-ity of service (QoS) requirements. By discerning AI models intentions, goals, andpreferences, the solution seeks to enhance learning efficiency, reduce training timeand costs, and minimize operational power consumption, communication overheadand latency across O-RAN interfaces. In the training process, emphasis is placed onthe selection of the most relevant data, even if it originates from locations outside oftheir immediate control. This results in more effective learning, as only informationdirectly applicable to the task at hand is utilized, which facilitates a swifter learn-ing curve, as the reduced need to transmit extensive data across the network leadsto shorter network delays, often translating into cost savings. The development ofa versatile pre-trained model tailored for the Open RAN architecture is a pivotalinitial step. This model, designed for scalability and adaptability, is complementedby the attention mechanism, ensuring focused analysis of data sets. The subsequentphase involves optimizing data compression for user inputs, with a focus on accu-rately estimating specific output parameters. This process streamlines informationflow without compromising accuracy. This approach will promise a more intelli-gent, reliable, and cost-effective SMO platform. The successful implementation ofthe proposed solution can enable mobile operators to meet the ever-changing users’demands, improve network performance, and reduce power consumption. This, inturn, contributes to the industry-wide goal of achieving net-zero emissions in thetelecommunications sector by the year 2050.1246.3. Suggested Future Work6.3.3 Multi-Pair Computation Linear Receiver for QAMSymbol DetectionAs an intriguing avenue for future research, we propose the exploration of amulti-pair two-way computation linear receiver for QAM symbol detection, drawinginspiration from the recent advances in the field, particularly the integer-forcing (IF)linear receiver tailored for multiple-input multiple-output (MIMO) fading channels[151]. This endeavor aims to design a specialized receiver optimized for QAM symboldetection within the context of intra-cloud C-RAN communications. The objectiveof this future work is to meticulously craft a multi-pair two-way computation linearreceiver, wherein the key focus lies in identifying and optimizing the appropriate inte-ger linear combinations of paired symbols crucial to the end-to-end decoding process.This process will entail a thorough investigation to ensure the receiver’s effectivenessin enhancing symbol detection efficiency. In the subsequent stages, the performanceof this proposed receiver will undergo a comprehensive evaluation, primarily in termsof symbol error rate. Furthermore, a comparative analysis will be conducted againstconventional linear receivers, including zero-forcing (ZF) and minimum mean squarederror (MMSE) receivers [175]. This comparative assessment aims to highlight thepotential advantages and contributions of the proposed receiver in further enhancingthe efficiency of symbol detection processes within C-RAN communications.125Bibliography[1] 3GPP TR 38.801 V2.0.0 (R14), Technical Specification Group Radio AccessNetwork; Study on New Radio Access Technology; Radio Access Architectureand Interfaces, 2017. → pages xiii, 17[2] M. A. Hasabelnaby and A. Chaaban, “Multi-pair computation for two-way in-tra cloud radio-access network communications,” IEEE Transactions on Wire-less Communications, vol. 21, no. 7, pp. 5586–5599, 2022. → pages xiv, xv, 37,42, 47, 58, 59, 60, 61, 62, 64, 75, 76, 84, 100, 111[3] ——, “Multi-pair computation for c-ran with intra-cloud and inter-cloud com-munications,” IEEE Wireless Communications Letters, vol. 11, no. 12, pp.2537–2541, 2022. → pages xv, 33, 77, 78, 79, 83, 84, 103[4] ——, “Energy-efficient multi-pair computation for intra cell-free massive mimocommunications,” IEEE Wireless Communications Letters, pp. 1–1, 2023. →pages xvi, 33, 97, 98[5] ——, “Distributed multi-pair computation for intra c-ran bidirectional com-munications,” in 2023 Biennial Symposium on Communications (BSC), 2023,pp. 42–47. → pages xvi, 33, 116, 117[6] Ericsson, Ericsson Mobility Report, November 2022. → pages 2[7] ——, Ericsson Breaking the Energy Curve Report 2022, October 2022.→ pages2[8] A. Ghosh, A. Maeder, M. Baker, and D. Chandramouli, “5g evolution: A viewon 5g cellular technology beyond 3gpp release 15,” IEEE Access, vol. 7, pp.127 639–127 651, 2019. → pages 2[9] J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. K. Soong,and J. C. Zhang, “What will 5g be?” IEEE Journal on Selected Areas inCommunications, vol. 32, no. 6, pp. 1065–1082, 2014. → pages 5, 6126Bibliography[10] H. Yanikomerog lu, “Multi-antenna systems and interconnection strategies forcdma wireless access networks.” Ph.D. dissertation, Citeseer, 2000. → pages 7[11] A. Obaid and H. Yanikomeroglu, “Reverse-link power control in cdma dis-tributed antenna systems,” in 2000 IEEE Wireless Communications and Net-working Conference, vol. 2, 2000, pp. 608–612 vol.2. → pages 7[12] C. M. R. Institute, “The 1st c-ran international workshop,” China MobileResearch Institute, 2010. [Online]. Available: http://labs.chinamobile.com/focus/C-RAN → pages 7[13] A. Checko, H. L. Christiansen, Y. Yan, L. Scolari, G. Kardaras, M. S. Berger,and L. Dittmann, “Cloud ran for mobile networks a technology overview,”IEEE Communications Surveys and Tutorials, vol. 17, no. 1, pp. 405–426,2015. → pages 7, 8, 10, 17[14] M. A. Hasabelnaby, H. A. I. Selmy, M. Dessoky, and A. Srivastava, “Perfor-mance enhancement of relayed hybrid fso/mmw fronthaul network in c-ranarchitecture,” in 2018 20th International Conference on Transparent OpticalNetworks (ICTON), 2018, pp. 1–4. → pages 7[15] M. A. Hasabelnaby, H. A. I. Selmy, and M. I. Dessouky, “C-ran availabilityimprovement using parallel hybrid fso/mmw 5g fronthaul network,” in 2018International Japan-Africa Conference on Electronics, Communications andComputations (JAC-ECC), 2018, pp. 130–133. → pages 7[16] R. Irmer, H. Droste, P. Marsch, M. Grieger, G. Fettweis, S. Brueck, H. Mayer,L. Thiele, and V. Jungnickel, “Coordinated multipoint: Concepts, perfor-mance, and field trial results,” IEEE Communications Magazine, vol. 49, no. 2,pp. 102–111, 2011. → pages 7[17] M. A. Hasabelnaby, H. A. I. Selmy, and M. I. Dessouky, “Optimal resourceallocation for cooperative hybrid fso/mmw 5g fronthaul networks,” in 2019IEEE Photonics Conference (IPC), 2019, pp. 1–2. → pages 7[18] M. Peng, Y. Sun, X. Li, Z. Mao, and C. Wang, “Recent advances in cloudradio access networks: System architectures, key techniques, and open issues,”IEEE Communications Surveys Tutorials, vol. 18, no. 3, pp. 2282–2308, 2016.→ pages 8127Bibliography[19] Y. Shi, J. Zhang, and K. B. Letaief, “Group sparse beamforming for greencloud-ran,” IEEE Transactions on Wireless Communications, vol. 13, no. 5,pp. 2809–2823, 2014. → pages 8[20] B. Dai and W. Yu, “Sparse beamforming for limited-backhaul network mimosystem via reweighted power minimization,” in 2013 IEEE Global Communi-cations Conference (GLOBECOM), 2013, pp. 1962–1967. → pages 8[21] M. S. Al-Abiad, A. Douik, S. Sorour, and M. J. Hossain, “Throughput max-imization in cloud-radio access networks using cross-layer network coding,”IEEE Transactions on Mobile Computing, vol. 21, no. 2, pp. 696–711, 2022. →pages 8[22] M. S. Al-Abiad, A. Douik, S. Sorour, and M. D. J. Hossain, “Throughput max-imization in cloud radio access networks using network coding,” in 2018 IEEEInternational Conference on Communications Workshops (ICC Workshops),2018, pp. 1–6. → pages 8[23] H. Dahrouj, W. Yu, T. Tang, J. Chow, and R. Selea, “Coordinated schedulingfor wireless backhaul networks with soft frequency reuse,” in 21st EuropeanSignal Processing Conference (EUSIPCO 2013), 2013, pp. 1–5. → pages 8[24] A. Douik, H. Dahrouj, T. Y. Al-Naffouri, and M.-S. Alouini, “Low-complexityscheduling and power adaptation for coordinated cloud-radio access networks,”IEEE Communications Letters, vol. 21, no. 10, pp. 2298–2301, 2017. → pages8[25] ——, “Coordinated scheduling and power control in cloud-radio access net-works,” IEEE Transactions on Wireless Communications, vol. 15, no. 4, pp.2523–2536, 2016. → pages 8[26] S. Park, O. Simeone, O. Sahin, and S. Shamai, “Joint Precoding and Multivari-ate Backhaul Compression for the Downlink of Cloud Radio Access Networks,”IEEE Transactions on Signal Processing, vol. 61, no. 22, 2013. → pages 8, 19,25, 26, 27[27] H. Q. Ngo, A. Ashikhmin, H. Yang, E. G. Larsson, and T. L. Marzetta, “Cell-free massive mimo: Uniformly great service for everyone,” in 2015 IEEE 16thInternational Workshop on Signal Processing Advances in Wireless Communi-cations (SPAWC), 2015, pp. 201–205. → pages 9128Bibliography[28] E. Nayebi, A. Ashikhmin, T. L. Marzetta, and H. Yang, “Cell-free massivemimo systems,” in 2015 49th Asilomar Conference on Signals, Systems andComputers, 2015, pp. 695–699. → pages 9, 10[29] G. Femenias and F. Riera-Palou, “Cell-free millimeter-wave massive mimo sys-tems with limited fronthaul capacity,” IEEE Access, vol. 7, pp. 44 596–44 612,2019. → pages 9[30] G. Interdonato, E. Bjo¨rnson, H. Q. Ngo, P. Frenger, and E. G. Larsson, “Ubiq-uitous cell-free massive mimo communications,” EURASIP Journal on Wire-less Communications and Networking, vol. 2019, no. 1, p. 197, 2019. → pages9[31] H. Q. Ngo, A. Ashikhmin, H. Yang, E. G. Larsson, and T. L. Marzetta, “Cell-free massive mimo versus small cells,” IEEE Transactions on Wireless Com-munications, vol. 16, no. 3, pp. 1834–1850, 2017. → pages 9, 10[32] A. A. M. Saleh, A. Rustako, and R. Roman, “Distributed antennas for in-door radio communications,” IEEE Transactions on Communications, vol. 35,no. 12, pp. 1245–1251, 1987. → pages 9[33] J. Zhang, S. Chen, Y. Lin, J. Zheng, B. Ai, and L. Hanzo, “Cell-free massivemimo: A new next-generation paradigm,” IEEE Access, vol. 7, pp. 99 878–99 888, 2019. → pages 10[34] H. Q. Ngo, L. Tran, T. Q. Duong, M. Matthaiou, and E. G. Larsson, “On thetotal energy efficiency of cell-free massive mimo,” IEEE Transactions on GreenCommunications and Networking, vol. 2, no. 1, pp. 25–39, 2018. → pages 10[35] E. Bjo¨rnson, J. Hoydis, and L. Sanguinetti, “Massive mimo networks: Spectral,energy, and hardware efficiency,” Foundations and Trends in Signal Processing,vol. 11, no. 3-4, pp. 154–655, 2017. → pages 10[36] L. D. Nguyen, T. Q. Duong, H. Q. Ngo, and K. Tourki, “Energy efficiency incell-free massive mimo with zero-forcing precoding design,” IEEE Communi-cations Letters, vol. 21, no. 8, pp. 1871–1874, 2017. → pages 10[37] Z. Liu and L. Dai, “A comparative study of downlink mimo cellular networkswith co-located and distributed base-station antennas,” IEEE Transactions onWireless Communications, vol. 13, no. 11, pp. 6259–6274, 2014. → pages 10129Bibliography[38] K. Shanmugam, N. Golrezaei, A. G. Dimakis, A. F. Molisch, and G. Caire,“Femtocaching: Wireless content delivery through distributed cachinghelpers,” IEEE Transactions on Information Theory, vol. 59, no. 12, pp. 8402–8413, 2013. → pages 10[39] T. Wang, Y. Sun, L. Song, and Z. Han, “Social data offloading in d2d-enhancedcellular networks by network formation games,” IEEE Transactions on Wire-less Communications, vol. 14, no. 12, pp. 7004–7015, 2015. → pages 10[40] L. Li, G. Zhao, and R. S. Blum, “A survey of caching techniques in cellularnetworks: Research issues and challenges in content placement and deliverystrategies,” IEEE Communications Surveys and Tutorials, vol. 20, no. 3, pp.1710–1732, 2018. → pages 10, 11[41] I. Parvez, A. Rahmati, I. Guvenc, A. I. Sarwat, and H. Dai, “A survey on lowlatency towards 5g: Ran, core network and caching solutions,” IEEE Commu-nications Surveys Tutorials, vol. 20, no. 4, pp. 3098–3130, 2018. → pages 11,18[42] M. Peng and K. Zhang, “Recent advances in fog radio access networks: Per-formance analysis and radio resource allocation,” IEEE Access, vol. 4, pp.5003–5009, 2016. → pages 11[43] S.-H. Park, O. Simeone, and S. Shamai Shitz, “Joint optimization of cloud andedge processing for fog radio access networks,” IEEE Transactions on WirelessCommunications, vol. 15, no. 11, pp. 7621–7632, 2016. → pages 11[44] R. Tandon and O. Simeone, “Harnessing cloud and edge synergies: towardan information theory of fog radio access networks,” IEEE CommunicationsMagazine, vol. 54, no. 8, pp. 44–50, 2016. → pages 11[45] C. Fang, F. R. Yu, T. Huang, J. Liu, and Y. Liu, “Energy-efficient distributedin-network caching for content-centric networks,” in 2014 IEEE Conferenceon Computer Communications Workshops (INFOCOM WKSHPS), 2014, pp.91–96. → pages 11[46] L. Lei, Z. Zhong, C. Lin, and X. Shen, “Operator controlled device-to-devicecommunications in lte-advanced networks,” IEEE Wireless Communications,vol. 19, no. 3, pp. 96–104, 2012. → pages 11130Bibliography[47] F. Jameel, Z. Hamid, F. Jabeen, S. Zeadally, and M. A. Javed, “A surveyof device-to-device communications: Research issues and challenges,” IEEECommunications Surveys and Tutorials, vol. 20, no. 3, pp. 2133–2168, 2018.→ pages 11[48] M. Ji, G. Caire, and A. F. Molisch, “Fundamental limits of caching in wirelessd2d networks,” IEEE Transactions on Information Theory, vol. 62, no. 2, pp.849–869, 2016. → pages 11[49] R. Karasik, O. Simeone, and S. Shamai Shitz, “How much can d2d commu-nication reduce content delivery latency in fog networks with edge caching?”IEEE Transactions on Communications, vol. 68, no. 4, pp. 2308–2323, 2020.→ pages 11[50] F. Boccardi, R. W. Heath, A. Lozano, T. L. Marzetta, and P. Popovski,“Five disruptive technology directions for 5g,” IEEE Communications Mag-azine, vol. 52, no. 2, pp. 74–80, 2014. → pages 11[51] B. Bangerter, S. Talwar, R. Arefi, and K. Stewart, “Networks and devices forthe 5g era,” IEEE Communications Magazine, vol. 52, no. 2, pp. 90–96, 2014.→ pages 11[52] A. Asadi, Q. Wang, and V. Mancuso, “A survey on device-to-device commu-nication in cellular networks,” IEEE Communications Surveys and Tutorials,vol. 16, no. 4, pp. 1801–1819, 2014. → pages 11[53] M. Polese, L. Bonati, S. D’Oro, S. Basagni, and T. Melodia, “Understandingo-ran: Architecture, interfaces, algorithms, security, and research challenges,”IEEE Communications Surveys and Tutorials, vol. 25, no. 2, pp. 1376–1411,2023. → pages 12[54] F. Kavehmadavani, V.-D. Nguyen, T. X. Vu, and S. Chatzinotas, “Intelligenttraffic steering in beyond 5g open ran based on lstm traffic prediction,” IEEETransactions on Wireless Communications, pp. 1–1, 2023. → pages 13[55] J. K. Chaudhary, J. Zou, and G. Fettweis, “Cost saving analysis in capacity-constrained c-ran fronthaul,” in 2018 IEEE Globecom Workshops, 2018, pp.1–7. → pages 13[56] S. E. Ghoreishi, D. Karamshuk, V. Friderikos, N. Sastry, M. Dohler, and A. H.Aghvami, “A cost-driven approach to caching-as-a-service in cloud-based 5g131Bibliographymobile networks,” IEEE Transactions on Mobile Computing, vol. 19, no. 5,pp. 997–1009, 2020. → pages 13[57] O. Arouk, T. Turletti, N. Nikaein, and K. Obraczka, “Cost optimization ofcloud-ran planning and provisioning for 5g networks,” in 2018 IEEE Interna-tional Conference on Communications (ICC), 2018, pp. 1–6. → pages 13[58] D. Chitimalla, K. Kondepu, L. Valcarenghi, M. Tornatore, and B. Mukherjee,“5g fronthaul-latency and jitter studies of cpri over ethernet,” Journal of Opti-cal Communications and Networking, vol. 9, no. 2, pp. 172–182, 2017. → pages14, 15, 16[59] A. Pizzinat, P. Chanclou, F. Saliou, and T. Diallo, “Things you should knowabout fronthaul,” Journal of Lightwave Technology, vol. 33, no. 5, pp. 1077–1083, 2015. → pages 14, 15, 16, 17[60] M. Peng, C. Wang, V. Lau, and H. V. Poor, “Fronthaul-constrained cloud radioaccess networks: insights and challenges,” IEEE Wireless Communications,vol. 22, no. 2, pp. 152–160, 2015. → pages 15[61] T. Pfeiffer, “Next generation mobile fronthaul and midhaul architectures [in-vited],” Journal of Optical Communications and Networking, vol. 7, no. 11, pp.B38–B45, 2015. → pages 15[62] CPRI, CPRI Interface Specification, V. 7.0, October 2015. → pages 15, 16, 18[63] W. Hu, Y. Zhu, L. Li, K. Zhang, H. Xin, Y. Fu, and X. Miao, “Enablingtechnologies for comprehensive optical mobile fronthaul access network,” in2021 Optical Fiber Communications Conference and Exhibition (OFC), 2021,pp. 1–3. → pages 15[64] A. de la Oliva, J. A. Hernandez, D. Larrabeiti, and A. Azcorra, “An overviewof the cpri specification and its application to c-ran-based lte scenarios,” IEEECommunications Magazine, vol. 54, no. 2, pp. 152–159, 2016. → pages 15, 16[65] M. Paolini, “C-ran and 5g take transport to new capacity and latency levels:Trends in backhaul, fronthaul, xhaul and mmw,” Senza Fili, Sammamish, WA,USA, Tech. Rep., March 2016. → pages 15[66] A. Kukushkin, Annex: BaseStation Site Solutions, 2018, pp. 367–375. → pages15132Bibliography[67] C.-L. I., J. Huang, Y. Yuan, and S. Ma, 5G RAN architecture: C-RAN withNGFI, 10 2017, pp. 431–455. → pages 15[68] European Telecommunications Standards Initiative, Open Radio Interface, In-dustrial Standardization Group (ORI ISG), 2014. → pages 15[69] I. Chih-Lin, J. Huang, Y. Yuan, S. Ma, and R. Duan, “Ngfi, the xhaul,” in2015 IEEE Globecom Workshops (GC Wkshps), 2015, pp. 1–6. → pages 16, 18[70] TELECOMMUNICATION STANDARDIZATION SECTOR OF ITU, 5Gwireless fronthaul requirements in a passive optical network context. ITU-TG-series Recommendations Supplement 66, 2020. → pages 16[71] M. A. Hasabelnaby, H. A. I. Selmy, and M. I. Dessouky, “Joint optimaltransceiver placement and resource allocation schemes for redirected coopera-tive hybrid fso/mmw 5g fronthaul networks,” IEEE/OSA Journal of OpticalCommunications and Networking, vol. 10, no. 12, pp. 975–990, 2018. → pages16[72] T. Pfeiffer, “Next generation mobile fronthaul architectures,” in Optical FiberCommunication Conference. Optica Publishing Group, 2015, p. M2J.7. [On-line]. Available: http://opg.optica.org/abstract.cfm?URI=OFC-2015-M2J.7→ pages 16[73] P. Chanclou, A. Pizzinat, F. L. Clech, T.-L. Reedeker, Y. Lagadec, F. Saliou,B. L. Guyader, L. Guillo, Q. Deniel, S. Gosselin, S. D. Le, T. A. Diallo,R. Brenot, F. Lelarge, L. Marazzi, P. Parolari, M. Martinelli, S. P. O’Duill,S. A. Gebrewold, D. Hillerkuss, J. Leuthold, G. Gavioli, and P. Galli, “Opticalfiber solution for mobile fronthaul to achieve cloud radio access network,” 2013Future Network & Mobile Summit, pp. 1–11, 2013. → pages 17[74] R. S. Oliveira, C. R. L. FRANceˆs, J. C. W. A. Costa, D. Viana, M. Lima, andA. L. J. Teixeira, “Analysis of the cost-effective digital radio over fiber systemin the ng-pon2 context,” 2014 16th International Telecommunications NetworkStrategy and Planning Symposium (Networks), pp. 1–6, 2014. → pages 17[75] H. Holma and A. Toskala, LTE Advanced: 3GPP Solution for IMT-Advanced.Hoboken, NJ, USA: Wiley, 2012, vol. 2012. → pages 17[76] CPRI, Common Public Radio Interface: eCPRI Interface Specification V1.2,June 2016. → pages 18133Bibliography[77] T. Quek, M. Peng, O. Simeone, and W. Yu, Cloud Radio Access Networks:Principles, Technologies, and Applications. Cambridge University Press, 2017.→ pages 19, 20, 22, 23, 24, 25, 26, 27[78] S. Park, O. Simeone, O. Sahin, and S. Shamai, “Robust and Efficient Dis-tributed Compression for Cloud Radio Access Networks,” IEEE Trans. Veh.Technol., vol. 62, no. 2, pp. 692–703, 2013. → pages 19, 22, 25[79] S. Hong and G. Caire, “Compute-and-forward strategies for cooperative dis-tributed antenna systems,” IEEE Transactions on Information Theory, vol. 59,2013. → pages 19, 20, 25, 26, 27, 41, 47, 68, 145[80] S. H. Lim, Y.-H. Kim, A. El Gamal, and S.-Y. Chung, “Noisy network coding,”IEEE Transactions on Information Theory, vol. 57, no. 5, pp. 3132–3152, 2011.→ pages 19[81] B. Dai and W. Yu, “Sparse Beamforming and User-Centric Clustering forDownlink Cloud Radio Access Network,” IEEE Access, vol. 2, 2014. → pages19, 25, 27[82] S. Hong and G. Caire, “Reverse compute and forward: A low-complexity ar-chitecture for downlink distributed antenna systems,” in IEEE InternationalSymposium on Information Theory, 2012, pp. 1147–1151. → pages 19, 26, 27[83] H. Cheng, X. Yuan, and Y. Tan, “Generalized compute-compress-and-forward,” IEEE Transactions on Information Theory, vol. 65, no. 1, pp. 462–481, 2019. → pages 19[84] Y. Li, T. Jiang, K. Luo, and S. Mao, “Green heterogeneous cloud radio accessnetworks: Potential techniques, performance trade-offs, and challenges,” IEEECommunications Magazine, vol. 55, no. 11, pp. 33–39, 2017. → pages 20[85] G. Kramer, M. Gastpar, and P. Gupta, “Cooperative strategies and capac-ity theorems for relay networks,” IEEE Transactions on Information Theory,vol. 51, no. 9, pp. 3037–3063, 2005. → pages 20[86] S. Park, K. Lee, C. Song, and I. Lee, “Joint design of fronthaul and access linksfor c-ran with wireless fronthauling,” IEEE Signal Processing Letters, vol. 23,no. 11, pp. 1657–1661, 2016. → pages 20, 25134Bibliography[87] A. El Gamal, N. Hassanpour, and J. Mammen, “Relay networks with delays,”IEEE Transactions on Information Theory, vol. 53, no. 10, pp. 3413–3431,2007. → pages 20[88] M. Raceala-Motoc, P. Jung, Z. Utkovski, and S. Staczak, “C-ran-assisted non-coherent grant-free random access based on compute-and-forward,” in 2018IEEE Globecom Workshops (GC Wkshps), 2018, pp. 1–7. → pages 20, 25[89] S. Gelincik and G. R.-B. Othman, “Lattice codes for c-ran based sectored cel-lular networks,” in ICC 2020 - 2020 IEEE International Conference on Com-munications (ICC), 2020, pp. 1–7. → pages 20[90] Q. Huang and A. Burr, “Compute-and-forward in cell-free massive mimo:Great performance with low backhaul load,” in 2017 IEEE International Con-ference on Communications Workshops (ICC Workshops), 2017, pp. 601–606.→ pages 20, 25[91] H. Jiang, L. Kong, and S. Du, “Compute-and-forward transmission scheme incell-free massive mimo systems,” ICT Express, 2023. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2405959523000255 → pages 20[92] A. L. P. Fernandes, D. D. Souza, D. B. da Costa, A. M. Cavalcante, and J. C.W. A. Costa, “Cell-free massive mimo with segmented fronthaul: Reliabilityand protection aspects,” IEEE Wireless Communications Letters, vol. 11, no. 8,pp. 1580–1584, 2022. → pages 20[93] B. Nazer and M. Gastpar, “Compute-and-forward: Harnessing interferencethrough structured codes,” IEEE Transactions on Information Theory, vol. 57,no. 10, pp. 6463–6486, 2011. → pages 20, 21, 25, 36, 38, 40[94] J. Sykora and A. Burr, Wireless Physical Layer Network Coding. CambridgeUniversity Press, 2018. → pages 20, 25[95] A. Chaaban and A. Sezgin, “Multi-way communications: An information the-oretic perspective,” Foundations and Trends in Communications and Informa-tion Theory, vol. 12, no. 3-4, pp. 185–371, 2015. → pages 20, 36, 37, 40, 41,101[96] B. Nazer, A. Sanderovich, M. Gastpar, and S. Shamai, “Structured superpo-sition for backhaul constrained cellular uplink,” in 2009 IEEE InternationalSymposium on Information Theory, 2009, pp. 1530–1534. → pages 20, 25135Bibliography[97] Y. Tan, X. Yuan, S. C. Liew, and A. Kavcic, “Asymmetric compute-and-forward: Going beyond one hop,” in 2014 52nd Annual Allerton Conferenceon Communication, Control, and Computing (Allerton), 2014, pp. 667–674. →pages 20, 25[98] V. NTranos, V. R. Cadambe, B. Nazer, and G. Caire, “Asymmetric compute-and-forward,” in 2013 51st Annual Allerton Conference on Communication,Control, and Computing (Allerton), 2013, pp. 1174–1181. → pages 20[99] J. Zhu and M. Gastpar, “Lattice codes for many-to-one interference channelswith and without cognitive messages,” IEEE Transactions on Information The-ory, vol. 61, no. 3, pp. 1309–1324, 2015. → pages 21[100] B. Nazer, V. R. Cadambe, V. NTranos, and G. Caire, “Expanding the compute-and-forward framework: Unequal powers, signal levels, and multiple linearcombinations,” IEEE Transactions on Information Theory, vol. 62, no. 9, pp.4879–4909, 2016. → pages 21, 25[101] J. Zhang, J. Zhang, J. Zheng, S. Jin, and B. Ai, “Expanded compute-and-forward for backhaul-limited cell-free massive mimo,” in 2019 IEEE Interna-tional Conference on Communications Workshops (ICC Workshops), 2019, pp.1–6. → pages 21[102] O. Ordentlich, U. Erez, and B. Nazer, “Successive integer-forcing and its sum-rate optimality,” in 2013 51st Annual Allerton Conference on Communication,Control, and Computing (Allerton), 2013, pp. 282–292. → pages 21, 25, 39[103] M. Hejazi, S. M. Azimi-Abarghouyi, B. Makki, M. Nasiri-Kenari, and T. Svens-son, “Robust successive compute-and-forward over multiuser multirelay net-works,” IEEE Transactions on Vehicular Technology, vol. 65, no. 10, pp. 8112–8129, 2016. → pages 21[104] J. Zhang, J. Zhang, D. W. K. Ng, S. Jin, and B. Ai, “Improving sum-rate of cell-free massive mimo with expanded compute-and-forward,” IEEE Transactionson Signal Processing, vol. 70, pp. 202–215, 2022. → pages 21, 25[105] Y. Tan and X. Yuan, “Compute-compress-and-forward: Exploiting asymmetryof wireless relay networks,” IEEE Transactions on Signal Processing, vol. 64,no. 2, pp. 511–524, 2016. → pages 21, 25136Bibliography[106] I. E. Aguerri and A. Zaidi, “Lossy compression for compute-and-forward inlimited backhaul uplink multicell processing,” IEEE Transactions on Commu-nications, vol. 64, no. 12, pp. 5227–5238, 2016. → pages 21, 25[107] Y. Zhou and W. Yu, “Fronthaul compression and transmit beamforming opti-mization for multi-antenna uplink c-ran,” IEEE Transactions on Signal Pro-cessing, vol. 64, no. 16, pp. 4138–4151, 2016. → pages 21, 22, 25, 44, 45[108] S. Borade, L. Zheng, and R. Gallager, “Amplify-and-forward in wireless relaynetworks: Rate, diversity, and network size,” IEEE Transactions on Informa-tion Theory, vol. 53, no. 10, pp. 3302–3318, 2007. → pages 21[109] B. Liu and N. Cai, “Analog network coding in the generalized high-snr regime,”in 2011 IEEE International Symposium on Information Theory Proceedings,2011, pp. 74–78. → pages 21, 25[110] Y. Zhou and W. Yu, “Optimized backhaul compression for uplink cloud radioaccess network,” IEEE Journal on Selected Areas in Communications, vol. 32,no. 6, pp. 1295–1307, 2014. → pages 22, 25[111] A. S. Avestimehr, S. N. Diggavi, and D. N. C. Tse, “Wireless network infor-mation flow: A deterministic approach,” IEEE Transactions on InformationTheory, vol. 57, no. 4, pp. 1872–1905, 2011. → pages 22[112] D. Gesbert, S. Hanly, H. Huang, S. Shamai Shitz, O. Simeone, and W. Yu,“Multi-cell mimo cooperative networks: A new look at interference,” IEEEJournal on Selected Areas in Communications, vol. 28, no. 9, pp. 1380–1408,2010. → pages 22[113] S.-H. Park, O. Simeone, O. Sahin, and S. Shamai Shitz, “Fronthaul compressionfor cloud radio access networks: Signal processing advances inspired by networkinformation theory,” IEEE Signal Processing Magazine, vol. 31, no. 6, pp. 69–79, 2014. → pages 22, 25[114] Y. Zhou, Y. Xu, W. Yu, and J. Chen, “On the optimal fronthaul compressionand decoding strategies for uplink cloud radio access networks,” IEEE Trans-actions on Information Theory, vol. 62, no. 12, pp. 7402–7418, 2016. → pages22, 25, 39[115] A. Wyner and J. Ziv, “The rate-distortion function for source coding withside information at the decoder,” IEEE Transactions on Information Theory,vol. 22, no. 1, pp. 1–10, 1976. → pages 22, 25137Bibliography[116] L. Zhou and W. Yu, “Uplink multicell processing with limited backhaul via per-base-station successive interference cancellation,” IEEE Journal on SelectedAreas in Communications, vol. 31, no. 10, pp. 1981–1993, 2013. → pages 22[117] R. Zamir and S. Shamai, “Nested linear/lattice codes for wyner-ziv encoding,”in 1998 Information Theory Workshop (Cat. No.98EX131), 1998, pp. 92–93.→ pages 22[118] Y. Song and N. Devroye, “A lattice compress-and-forward strategy for cancel-ing known interference in gaussian multi-hop channels,” in 2011 45th AnnualConference on Information Sciences and Systems, 2011, pp. 1–5. → pages 22[119] ——, “A lattice compress-and-forward scheme,” in 2011 IEEE InformationTheory Workshop, 2011, pp. 110–114. → pages 22, 25[120] O. Ordentlich and U. Erez, “Integer-forcing source coding,” IEEE Transactionson Information Theory, vol. 63, pp. 1253–1269, 2017. → pages 23, 25, 42, 43[121] I. El Bakoury and B. Nazer, “Integer-forcing architectures for uplink cloudradio access networks,” in Annual Allerton Conference on Communication,Control, and Computing, 2017, pp. 67–75. → pages 23, 24, 25, 41, 45, 47[122] M. Bashar, A. Akbari, K. Cumanan, H. Quoc Ngo, A. Burr, P. Xiao, andM. Debbah, “Deep learning-aided finite-capacity fronthaul cell-free massivemimo with zero forcing,” IEEE International Conferece on Communications,p. 16, 2020. → pages 23, 25[123] G. Femenias and F. Riera-Palou, “Fronthaul-constrained cell-free massivemimo with low resolution adcs,” IEEE Access, vol. 8, pp. 116 195–116 215,2020. → pages 23, 25[124] M. Bashar, K. Cumanan, A. G. Burr, H. Q. Ngo, and M. Debbah, “Cell-freemassive mimo with limited backhaul,” in IEEE International Conference onCommunications, 2018, pp. 1–7. → pages 23, 25[125] M. Bashar, H. Q. Ngo, A. G. Burr, D. Maryopi, K. Cumanan, and E. G.Larsson, “On the performance of backhaul constrained cell-free massive mimowith linear receivers,” in 2018 52nd Asilomar Conference on Signals, Systems,and Computers, 2018, pp. 624–628. → pages 23138Bibliography[126] M. Bashar, A. Akbari, K. Cumanan, H. Q. Ngo, A. G. Burr, P. Xiao, M. Deb-bah, and J. Kittler, “Exploiting deep learning in limited-fronthaul cell-freemassive mimo uplink,” IEEE Journal on Selected Areas in Communications,vol. 38, no. 8, pp. 1678–1697, 2020. → pages 23[127] H. Masoumi and M. J. Emadi, “Performance analysis of cell-free massive mimosystem with limited fronthaul capacity and hardware impairments,” IEEETransactions on Wireless Communications, vol. 19, no. 2, pp. 1038–1053, 2020.→ pages 23, 25[128] M. Bashar, K. Cumanan, A. G. Burr, H. Q. Ngo, E. G. Larsson, and P. Xiao,“On the energy efficiency of limited-backhaul cell-free massive mimo,” in IEEEInternational Conference on Communications, 2019, pp. 1–7. → pages 23, 25[129] M. Bashar, K. Cumanan, A. G. Burr, H. Q. Ngo, M. Debbah, and P. Xiao,“Maxmin rate of cell-free massive mimo uplink with optimal uniform quantiza-tion,” IEEE Transactions on Communications, vol. 67, no. 10, pp. 6796–6815,2019. → pages 24[130] C. Wang, M. Wigger, and A. Zaidi, “On achievability for downlink cloud radioaccess networks with base station cooperation,” IEEE Transactions on Infor-mation Theory, vol. 64, no. 8, pp. 5726–5742, 2018. → pages 25, 27[131] R. Zakhour and D. Gesbert, “Optimized data sharing in mimo with finitebackhaul capacity,” IEEE Transactions on Signal Processing, vol. 59, no. 12,pp. 6102–6111, 2011. → pages 25[132] A. Alameer Ahmad, H. Dahrouj, A. Chaaban, A. Sezgin, and M. Alouini,“Interference mitigation via rate-splitting and common message decoding incloud radio access networks,” IEEE Access, vol. 7, pp. 80 350–80 365, 2019. →pages 25, 27[133] P. Parida, H. S. Dhillon, and A. F. Molisch, “Downlink performance analysisof cell-free massive mimo with finite fronthaul capacity,” in IEEE VehicularTech. Conf., 2018, pp. 1–6. → pages 26, 27[134] G. Femenias and F. Riera-Palou, “Cell-free millimeter-wave massive mimo sys-tems with limited fronthaul capacity,” IEEE Access, vol. 7, pp. 44 596–44 612,2019. → pages 26139Bibliography[135] ——, “Reduced-complexity downlink cell-free mmwave massive mimo systemswith fronthaul constraints,” in 2019 27th European Signal Processing Confer-ence (EUSIPCO), 2019, pp. 1–5. → pages 26, 27[136] M. N. Boroujerdi, A. Abbasfar, and M. Ghanbari, “Cell free massive mimowith limited capacity fronthaul,” Wireless Personal Communications, vol. 104,no. 2, p. 633648, 2019. → pages 26, 27[137] P. Patil, B. Dai, and W. Yu, “Performance comparison of data-sharing andcompression strategies for cloud radio access networks,” in 2015 23rd EuropeanSignal Processing Conference (EUSIPCO), 2015, pp. 2456–2460. → pages 26[138] M. Hasabelnaby and A. Chaaban, “End-To-End rate enhancement in C-RANusing Multi-Pair Two-Way computation,” in 2021 Joint European Conferenceon Networks and Communications & 5G Summit (EuCNC/5G Summit), Jun.2021. → pages 33, 113[139] M. A. Hasabelnaby and A. Chaaban, “Intra c-ran two-way multi-pair com-putation under total power and fronthaul capacity constraints,” in 2022 17thCanadian Workshop on Information Theory (CWIT), 2022, pp. 109–114. →pages 33[140] C. M. R. Institute, “C-ran the road towards green ran.” China Mobile Re-search Institute, 2010. → pages 36[141] E. Domanovitz and U. Erez, “Outage behavior of integer forcing with randomunitary pre-processing,” IEEE Transactions on Information Theory, vol. 64,no. 4, pp. 2774–2790, 2018. → pages 38[142] X. Liu, Y. Shi, J. Zhang, and K. B. Letaief, “Massive csi acquisition for densecloud-rans with spatial-temporal dynamics,” IEEE Transactions on WirelessCommunications, vol. 17, no. 4, pp. 2557–2570, 2018. → pages 39[143] A. S. Guerreiro, G. Fraidenraich, and L. L. Mendes, “Approximate SumRate for Integer-Forcing Receiver With Imperfect Channel Estimation,” IEEETrans. Veh. Technol., vol. 67, no. 12, pp. 11 767–11 775, 2018. → pages 39, 67[144] Y. Shi, J. Zhang, and K. B. Letaief, “Robust group sparse beamforming formulticast green cloud-ran with imperfect csi,” IEEE Transactions on SignalProcessing, vol. 63, no. 17, pp. 4647–4659, 2015. → pages 39140Bibliography[145] C. I. Ionita, B. Nazer, C. Feng, and B. Aazhang, “An experimental study onthe robustness of integer-forcing linear receivers,” in 2017 IEEE InternationalConference on Communications (ICC), 2017, pp. 1–7. → pages 39[146] L. Yang and W. Zhang, “Interference Coordination for 5G Cellular Networks,”Springer, 2015. → pages 39, 67, 84[147] T. Cover and J. A. Thomas, Elements of Information Theory. John Wiley &Sons, 1991. → pages 39[148] W. Nam, S. Chung, and Y. H. Lee, “Capacity of the Gaussian Two-Way RelayChannel to Within 12Bit,” IEEE Transactions on Information Theory, vol. 56,2010. → pages 39, 51, 74, 76, 83, 90, 114[149] I. E. Bakoury and B. Nazer, “Uplink-Downlink Duality For Integer-Forcingin Cloud Radio Access Networks,” in 56th Annual Allerton Conference onCommunication, Control, and Computing, 2018, pp. 39–47. → pages 39, 45,70, 85, 86, 87, 106, 108[150] J. Guo, A. A. I. Ibrahim, A. Agaskar, D. J. Love, and N. Yazdani, “Imple-mentation of rate-adaptive integer forcing compression in distributed wirelessrelay networking,” in 2018 52nd Annual Conference on Information Sciencesand Systems (CISS), 2018, pp. 1–6. → pages 39[151] W. He and B. Nazer, “Integer-forcing source coding: Successive cancellationand source-channel duality,” in IEEE International Symposium on InformationTheory, 2016, pp. 155–159. → pages 43, 44, 48, 49, 69, 72, 86, 104, 105, 109,125[152] W. Nam, S.-Y. Chung, and Y. H. Lee, “Capacity bounds for two-way relaychannels,” in 2008 IEEE International Zurich Seminar on Communications,2008, pp. 144–147. → pages 51[153] L. Grippo and M. Sciandrone, “On the convergence of the blocknonlinear gaussseidel method under convex constraints,” Operations ResearchLetters, vol. 26, no. 3, pp. 127–136, 2000. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0167637799000747 → pages 53[154] D. Micciancio and S. Goldwasser, “Complexity of lattice problems - a cryp-tograhic perspective,” in Kluwer International Series in Engineering and Com-puter Science, 2002. → pages 54141Bibliography[155] O. Regev, “On lattices, learning with errors, random linear codes, and cryp-tography,” J. ACM, vol. 56, 2009. → pages 54[156] A. K. Lenstra, H. W. Lenstra, and L. Lovasz, “Factoring polynomials withrational coefficients,” MATH. ANN, vol. 261, pp. 515–534, 1982. → pages 54[157] E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, “Closest point search in lat-tices,” IEEE Transactions on Information Theory, vol. 48, no. 8, pp. 2201–2214, 2002. → pages 54[158] M. Bremner, Lattice Basis Reduction: An Introduction to the LLL Algorithmand Its Applications. CRC Press, 2011. → pages 54, 57, 75, 76, 92, 113[159] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge UniversityPress, 2004. → pages 54, 55, 56, 57, 58[160] R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed. Cambridge UniversityPress, 2012. → pages 55[161] L. Qi and W. Sun, An Iterative Method for the Minimax Problem. Boston,MA: Springer US, 1995, pp. 55–67. → pages 56[162] P. C. Weeraddana, M. Codreanu, M. Latva-aho, A. Ephremides, and C. Fis-chione, Weighted Sum-Rate Maximization in Wireless Networks: A Review.Now Foundations and Trends, 2012. → pages 56[163] L.-N. Tran, M. Juntti, M. Bengtsson, and B. Ottersten, “Weighted sum ratemaximization for mimo broadcast channels using dirty paper coding and zero-forcing methods,” IEEE Transactions on Communications, vol. 61, no. 6, 2013.→ pages 56[164] E. Polak, J. Higgins, and D. Mayne, “A barrier function method for minimaxproblems,” Mathematical Programming, pp. 155–176, 1992. → pages 56[165] C. Hellings, Y. Yang, and W. Utschick, “Minimax solution to the partialdecode-and-forward rate maximization in the mimo relay channel,” in WSA2020; 24th International ITG Workshop on Smart Antennas, 2020, pp. 1–6.→ pages 56[166] Q.-U.-A. Nadeem, A. Kammoun, A. Chaaban, M. Debbah, and M.-S. Alouini,“Asymptotic max-min sinr analysis of reconfigurable intelligent surface as-sisted miso systems,” IEEE Transactions on Wireless Communications, vol. 19,no. 12, pp. 7748–7764, 2020. → pages 60142Bibliography[167] A. Alameer Ahmad, H. Dahrouj, A. Chaaban, T. Y. Al-Naffouri, A. Sezgin,J. S. Shamma, and M.-S. Alouini, “Power Minimization Using Rate SplittingWith Statistical CSI in Cloud-Radio Access Networks,” Frontiers in Commu-nications and Networks, vol. 2, p. 33, 2021. → pages 67[168] R. Fletcher, Practical methods of optimization. Wiley, 1987. → pages 75, 113,114[169] D. S. Michalopoulos, N. D. Chatzidiamantis, R. Schober, and G. K. Kara-giannidis, “The diversity potential of relay selection with practical channelestimation,” IEEE Transactions on Wireless Communications, vol. 12, no. 2,pp. 481–493, 2013. → pages 84, 96[170] S. D’Oro, A. Zappone, S. Palazzo, and M. Lops, “A learning approach for low-complexity optimization of energy efficiency in multicarrier wireless networks,”IEEE Transactions on Wireless Communications, vol. 17, no. 5, pp. 3226–3241,2018. → pages 92, 93[171] L. Grippo and M. Sciandrone, “On the convergence of the block nonlinearGauss-Seidel method under convex constraints,” Operations Research Letters,vol. 26, pp. 127–136, 2000. → pages 93[172] O. Ordentlich and U. Erez, “A simple proof for the existence of good pairs ofnested lattices,” IEEE Transactions on Information Theory, vol. 62, no. 8, pp.4439–4453, 2016. → pages 102[173] H. Zhu, D. Liu, S. Zhang, Y. Zhu, L. Teng, and S. Teng, “Solving the manyto many assignment problem by improving the kuhnmunkres algorithm withbacktracking,” Theoretical Computer Science, vol. 618, pp. 30–41, 2016. →pages 115[174] I. RANdrianantenaina, M. Kaneko, H. Dahrouj, H. ElSawy, and M.-S. Alouini,“Joint scheduling and power adaptation in noma-based fog-radio access net-works,” in 2018 IEEE Global Communications Conference (GLOBECOM),2018, pp. 1–6. → pages 115[175] K. A. Alnajjar, S. Abdallah, M. Saad, and A. A. ElMoursy, “Low complexityreceivers for massive mimo cloud radio access systems,” in 2018 InternationalConference on Signal Processing and Information Security (ICSPIS), 2018, pp.1–4. → pages 125143Bibliography[176] R. Zamir, B. Nazer, Y. Kochman, and I. Bistritz, Lattice Coding for Signalsand Networks: A Structured Coding Approach to Quantization, Modulation andMultiuser Information Theory. Cambridge University Press, 2014. → pages146144AppendicesAppendix A: Lattice PreliminariesIn this Appendix, we review the main preliminaries of lattice codes that will benecessary in the dissertation. For further details, interested readers are referred to[79] and references therein.Lattices DefinitionsAn n-dimensional lattice Λ is defined as a discrete subgroup of Rn that is closedunder reflection and real addition and can be expressed byΛ = {λ = Ga | a ∈ Zn}, (6.1)where G ∈ Rn×n is the generator matrix that is used to describe the lattice and Zis the set of integers.A lattice quantizer with respect to Λ is a function QΛ : Rn → Λ that maps apoint x ∈ Rn to the nearest lattice point λ ∈ Λ in terms of Euclidean distance, withties broken symmetrically, i.e.,QΛ(x) = argminλ∈Λ‖x− λ‖2. (6.2)This can be used to define the fundamental Voronoi region υΛ of Λ as the set of allpoints in Rn quantized to the zero vector, i.e, {x ∈ Rn | QΛ(x) = 0}. The volume ofυΛ is denoted by Vol(υΛ). In addition, the modulo operator with respect to Λ returnsthe lattice quantization error, i.e,[x] mod Λ = x−QΛ(x). (6.3)The second moment of a lattice Λ can be calculated asσ2(Λ) =1n1Vol(υΛ)∫x∈υΛ‖x‖2dx = 1nE[‖x‖2], (6.4)145where x is uniformly distributed over υΛ. The normalized second moment of Λ isgiven byG(Λ) = σ2(Λ)/(Vol(υΛ))2n . (6.5)The following lemma will be useful for characterizing the distributions of ditheredlattice codewords.Lemma 6.1. (Crypto Lemma)[[176], Ch. 4]: Let x is a random vector with an arbi-trary distribution over Rn and d is a random vector, independent of x and uniformlydistributed over υΛ. It follows that the random vector [x + d] mod Λ is independentof x and uniformly distributed over υΛ.Nested Lattice CodesWe can construct a nested-lattice code by nesting layers of lattices in each other.For simplicity, consider two lattices, a fine lattice Λf and a coarse lattice Λc nestedin Λf , i.e., Λc ⊆ Λf . A nested-lattice code, denoted by a pair of {Λc,Λf}, is definedas the set of all points of a fine lattice (λ ∈ Λf ) that lie in υΛc , i.e, C = Λf ∩υΛc . Thepower of the nested-lattice codewords is given by the second moment of the coarselattice σ2(Λc). In addition, the coding rate of this code is defined as the number offine lattice points within υΛc given byR =1nlog(C) = 1nlog(Vol(υΛc)Vol(υΛf ))(6.6)where(Vol(υΛc )Vol(υΛf )) 1nis the nesting ratio of the nested-lattice code. Further, the nested-lattice pair Λc ⊆ Λf satisfies the modulo distributive law as[a[x] mod Λc + b[y] mod Λc] mod Λf = [ax + by] mod Λf , (6.7)where a, b ∈ Z and x,y ∈ Rn.As an extension of nested-lattice codes, a nested-lattice chain involves a sequenceof lattices Λ1, . . . ,Λ satisfying Λ1 ⊆ · · · ⊆ Λ. A sequence of lattices Λ(n) ⊂ Rn isgood for mean-squared error (MSE) quantization (MSE Goodness) iflimn→∞G(Λ(n)) =12pie. (6.8)Let z be a length-n i.i.d. Gaussian vector, z ∼ N (0, σ2zIn) and γ ∈ (0, 1). Thevolume to noise ratio of a lattice is defined as146µ(Λ, γ) =(Vol(υΛ))2nσ2z, (6.9)where σ2z is selected so that Pr{z /∈ υΛ} = γ.A sequence of lattices Λ(n) is good for channel coding (AWGN Goodness) iflimn→∞µ(Λ(n), γ) = 2pie. (6.10)It should be noted that if µ(Λn, γ) > 2pie, then Pr{z /∈ υΛ} decays exponentially inn.Finally, for a prime number p, an algebraic inverse of an integer square matrixA ∈ ZK×K over Zp denoted by Ainv ∈ ZK×Kp must satisfy[AinvA] mod p = IK . (6.11)These definitions are used extensively in the dissertation.147Appendix B: Proof of Equation (2.27)Starting from equation (2.24), the effective noise variance can be computed asσulj2=1nE[‖zuleff,j‖2]= pul‖ρul>j HulBul − aul>ψ,j W‖2+ρul>j (IL + Dul)ρulj= pul(ρul>j HulBul − aul>ψ,j W)(Bul>Hul>ρulj −W>aulψ,j) + ρul>j (IL + Dul)ρulj= pul(ρul>j HulBulBul>Hul>ρulj + aul>ψ,j WW>aulψ,j − ρul>j HulBulW>aulψ,j−aul>ψ,j WBul>Hul>ρulj ) + ρul>j (IL + Dul)ρulj= pul(ρul>j HulBulBul>Hul>ρulj + aul>ψ,j WW>aulψ,j − 2ρul>j HulBulW>aulψ,j)+ρul>j (IL + Dul)ρulj= ρul>j (pulHulBulBul>Hul> + IL + Dul)ρulj + pulaul>ψ,j WW>aulψ,j−2pulρul>j HulBulW>aulψ,j (6.12)In order to minimize the effective noise variance in (6.12), ρulj is chosen as theMMSE scaling equalizer given byρul>j = pulaul>ψ,j WBul>Hul>(pulHulBulBul>Hul> + IL + Dul)−1. (6.13)By substituting (6.13) into (6.12), we obtainσulj2= pul2aul>ψ,j WBul>Hul>(pulHulBulBul>Hul> + IL + Dul)−1HulBulW>aulψ,j+pulaul>ψ,j WW>aulψ,j−2pul2aul>ψ,j WBul>Hul>(pulHulBulBul>Hul> + IL + Dul)−1HulBulW>aulψ,j= pulaul>ψ,j WW>aulψ,j−pul2aul>ψ,j WBul>Hul>(pulHulBulBul>Hul> + IL + Dul)−1HulBulW>aulψ,j= aul>ψ,j W[pulIK − pulIKBul>Hul>(pulHulBulBul>Hul> + IL + Dul)−1HulBulpulIK]W>aulψ,j (6.14)The Woodbury matrix identity (referred also as matrix inversion lemma) is amathematical formula that provides an expression for the inverse of a matrix of theform A + UCV, where A and C are square matrices and U and V are rectangularmatrices. The identity is as follows(A + UCV)−1 = A−1 −A−1U(C−1 + VA−1U)−1VA−1 (6.15)148Consider thatA−1 = pulIK , (6.16)U = Bul>Hul>, (6.17)C = (pulHulBulBul>Hul> + IL + Dul), (6.18)andV = HulBul. (6.19)By substituting (6.16), (6.17), (6.18), and (6.19) into (6.15), we obtain(1pulIK+Bul>Hul>(pulHulBulBul>Hul> + IL + Dul)HulBul)−1 =[pulIK − pulIKBul>Hul>(pulHulBulBul>Hul> + IL + Dul)−1HulBulpulIK](6.20)By substituting (6.20) into (6.14), the effective noise variance σulj2can be rewrit-ten asσulj2= aul>ψ,j W(1pulIK + Bul>Hul>(pulHulBulBul>Hul> + IL + Dul)HulBul)−1W>aulψ,j= aul>ψ,j W[Fulψ Ful>ψ ]W>aulψ,j= ‖aul>ψ,j WFulψ ‖2, (6.21)where Fulψ is obtained from the the Cholesky decomposition satisfyingFulψ Ful>ψ = (1pulIK + Bul>Hul>(IL + Dul)−1HulBul)−1. (6.22)149
Thesis/Dissertation
eng
Electrical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Chaaban, Anas
Improving the performance of distributed antenna systems using multi-pair computation schemes
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