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Coordinated transmission for visible light communication systems Ma, Hao 2017

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Coordinated Transmission for Visible Light Communication SystemsbyHao MaM.A.Sc., King Abdullah University of Science and Technology, 2012B.Eng., Xi’an Jiaotong University, 2010A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)October 2017c© Hao Ma, 2017AbstractVisible light communication (VLC) is an emerging optical wireless communicationtechnology that employs the light-emitting diode (LED) as the data transmitter. Ithas great potential to alleviate the strain on the radio-frequency (RF) spectrum in theindoor environment. The integration of VLC into indoor communication networksestablishes optical attocells, responsible for the downlink traffic from the network touser terminals. These attocells could be easily deployed wherever LEDs are adoptedfor general illumination, including in electromagnetic interference sensitive areas likehospitals and airplanes. Although opaque bounds effectively contain light signals,VLC attocells would generally not operate free of interference. Illumination designersaim to have a uniform illumination at a certain height in the indoor environment,which mandates a rich overlap between the emissions of luminaires and results inunavoidable inter-attocell interference (IAI) from a communications perspective.This reality encourages us to propose the coordination of multiple VLC attocells(i.e., VLC-enabled LED luminaires) to turn the problem of overlap and thus inter-ference into an advantage. In this thesis, we study how the coordination of VLCattocells can be employed to improve the user performance. Two coordinated VLCarchitectures, both of which utilize single-carrier transmission but differ at the co-ordination level, are investigated first. The analysis primarily focuses on the beam-forming design subjected to the limited dynamic range of LED transmitters. Thedesign of robust beamformers is also considered to combat the uncertainty of channeliiAbstractinformation at the transmitter. Finally, we propose a multi-carrier coordinated VLCarchitecture that uses power lines as the backbone network for the VLC front-end.Several subcarrier allocation schemes with varying degrees of tradeoff among hard-ware, computational complexity and performance for meaningful variations of thishybrid system are proposed. The system designs developed throughout the thesisenable the collaboration among multiple LED transmitters in VLC systems, and ourresults indicate that these collaborative designs can significantly improve the perfor-mance of indoor VLC systems.iiiLay SummaryVisible light communication (VLC) employs the light-emitting diode (LED) as thewireless data transmitter. Data is transmitted by varying the instantaneous powerof LEDs in time. VLC has the potential to provide high-speed communication toindoor users at low cost via re-using LED illumination devices. On the other hand,illumination uniformity of indoor environment generally requires the installation ofmultiple wide-beam LED luminaires at the ceiling, which leads to the rich overlapof illumination footprints, and thus strong interference from a communications per-spective. In this thesis, we propose the coordination of multiple LED transmitters toturn interference into an advantage. Several signal processing designs are developedby employing the inherent multi-transmitter nature of indoor VLC system. Our re-sults demonstrate the significant enhancement of user performance with the proposedcoordinated VLC architectures.ivPrefaceThis thesis is formatted in accordance with the regulations of the University of BritishColumbia and submitted in partial fulfillment of the requirements for the Ph.D. degreeat the University of British Columbia, Vancouver, Canada. The materials presentedin this thesis are based on research performed by myself under the supervision ofProf. Lutz Lampe in the Department of Electrical and Computer Engineering atthe University of British Columbia, Vancouver, Canada. Prof. Steve Hranilovicfrom McMaster University has assisted me towards the problem formulation and theediting of all related publications, and Dr. Ayman Mostafa from the University ofBritish Columbia has helped with the editing of the publication related to Chapter3. Below is a list of publications related to the work presented in this thesis.The content of Chapter 2 has been published in the following papers:• H. Ma, L. Lampe, and S. Hranilovic, “Coordinated Broadcasting for MultiuserIndoor Visible Light Communication Systems," IEEE Transaction on Commu-nications, vol. 63, no. 9, pp. 3313-3324, Sept. 2015.• H. Ma, L. Lampe, and S. Hranilovic, “Robust MMSE Linear Precoding for Vis-ible Light Communication Broadcasting Systems," IEEE Globecom Workshops,Dec. 2013.The content of Chapter 3 has been submitted for publication.• H. Ma, A. Mostafa, L. Lampe, and S. Hranilovic, “Coordinated BeamformingvPrefacefor Visible Light Communication," submitted.The content of Chapter 4 has been published in the following papers:• H. Ma, L. Lampe, and S. Hranilovic, “Hybrid Visible Light and Power LineCommunication for Indoor Multiuser Downlink," IEEE/OSA Journal of OpticalCommunications and Networking, vol. 9, no. 8, Aug. 2017.• H. Ma, L. Lampe, and S. Hranilovic. “Subcarrier Allocation in Hybrid VisibleLight and Power Line Communication System," IEEE International Symposiumon Circuits and Systems(ISCAS), May 2016.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvNotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Visible Light Communication Development and Applications . . . . 31.1.1 Visible Light Communication Development . . . . . . . . . . 31.1.2 Visible Light Communication Applications . . . . . . . . . . 41.2 Visible Light Communication Background . . . . . . . . . . . . . . . 61.2.1 VLC Transceivers . . . . . . . . . . . . . . . . . . . . . . . . 6viiTable of Contents1.2.2 Channel Modeling . . . . . . . . . . . . . . . . . . . . . . . . 91.2.3 Standards and Constraints . . . . . . . . . . . . . . . . . . . 111.2.4 Modulation Techniques . . . . . . . . . . . . . . . . . . . . . 131.3 Motivation and Contributions of the Thesis . . . . . . . . . . . . . . 171.4 Remark on Alternating Optimization . . . . . . . . . . . . . . . . . . 221.5 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . 232 Joint Transmission in VLC Systems . . . . . . . . . . . . . . . . . . 242.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2 System Model and Transmission Scheme . . . . . . . . . . . . . . . . 252.2.1 VLC Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.2.2 Broadcast Transmission . . . . . . . . . . . . . . . . . . . . . 282.2.3 Constraints on Precoding from VLC . . . . . . . . . . . . . . 292.2.4 Design Objectives . . . . . . . . . . . . . . . . . . . . . . . . 312.3 Transmitter Design with Perfect Channel Information . . . . . . . . 312.3.1 Sum-MSE Minimization Problem . . . . . . . . . . . . . . . . 322.3.2 Minimal Illumination Level Problem . . . . . . . . . . . . . . 352.4 Robust Transmitter Design with Channel Uncertainty . . . . . . . . 362.4.1 Uncertainty Models . . . . . . . . . . . . . . . . . . . . . . . 372.4.2 Sum-MSE Minimization Problem . . . . . . . . . . . . . . . . 402.4.3 Minimal Illumination Level Problem . . . . . . . . . . . . . . 432.5 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . 452.5.1 User Position with Joint Transmission Setup . . . . . . . . . 482.5.2 Sum-MSE Minimization with Channel Uncertainty . . . . . . 552.5.3 Minimal Illumination Level Problem . . . . . . . . . . . . . . 562.5.4 Comparison between Robust and Non-Robust Design . . . . . 57viiiTable of Contents2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603 Coordinated Beamforming in VLC Systems . . . . . . . . . . . . . 623.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.2 System Model and Transmission Scheme . . . . . . . . . . . . . . . . 633.2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . 633.2.2 Transmission Scheme . . . . . . . . . . . . . . . . . . . . . . 643.2.3 Design Constraints . . . . . . . . . . . . . . . . . . . . . . . . 663.3 Transmitter Design with Perfect Channel Information . . . . . . . . 673.4 Robust Transmitter Design with Channel Uncertainty . . . . . . . . 723.4.1 Robust Design with the Deterministic Model . . . . . . . . . 733.4.2 Robust Design with the Stochastic Model . . . . . . . . . . . 763.5 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . 773.5.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . 773.5.2 Comparison of Different Coordination Levels . . . . . . . . . 803.5.3 Importance of Weight . . . . . . . . . . . . . . . . . . . . . . 833.5.4 Comparison between Robust and Non-Robust Design . . . . . 853.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864 The Hybrid VLC-PLC System . . . . . . . . . . . . . . . . . . . . . . 914.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.2.1 Problem Scenario . . . . . . . . . . . . . . . . . . . . . . . . 944.2.2 Transmitter and Receiver Model . . . . . . . . . . . . . . . . 954.2.3 Channel and Noise Model . . . . . . . . . . . . . . . . . . . . 964.3 Rate Analysis of the HVP System . . . . . . . . . . . . . . . . . . . 994.3.1 Signal at the PLC Hop . . . . . . . . . . . . . . . . . . . . . 99ixTable of Contents4.3.2 Signal at the VLC Hop . . . . . . . . . . . . . . . . . . . . . 1004.3.3 Achievable Rate Expression for Each Subcarrier Pair . . . . . 1014.4 Subcarrier Allocation in HVP Systems . . . . . . . . . . . . . . . . . 1054.4.1 OFDM-TDMA . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.4.2 OFDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104.5 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . 1144.5.1 Single-User System . . . . . . . . . . . . . . . . . . . . . . . . 1154.5.2 Multi-User System . . . . . . . . . . . . . . . . . . . . . . . . 1184.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131AppendicesA Proof of Outdated CSI Bound . . . . . . . . . . . . . . . . . . . . . . 144xList of Tables1.1 Required illuminance level for different activities specified by the Eu-ropean Norm (EN) 12464-1 Standard . . . . . . . . . . . . . . . . . . 122.1 Simulation parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . 463.1 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 783.2 Luminaire coordinates of LS-I and LS-II . . . . . . . . . . . . . . . . 803.3 Illumination performance of LS-I and LS-II . . . . . . . . . . . . . . . 803.4 User coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.1 Simulation parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . 116xiList of Figures2.1 Illustration of indoor coordinated VLC broadcast system. . . . . . . . 262.2 Illustration of outdated CSI resulting from terminal mobility in a VLCsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.3 Error bounds obtained from simulation for (a)L = 0.25 m, (b)L =0.5 m. Illumination and VLC setup for these results are described inSection 2.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.4 The distribution of indoor illuminance when IDC = 500 mA. . . . . . 472.5 User-configurations for MU-MISO VLC are considered for numericalresults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.6 Comparison of system performance with different user positions (asshown in Figure 2.5) as a function of illumination level. Sum-MSEminimization with perfect CSI. . . . . . . . . . . . . . . . . . . . . . 502.7 Comparison of the SER calculation using Equation (2.53) with MonteCarlo simulation result. . . . . . . . . . . . . . . . . . . . . . . . . . . 522.8 Different transmitter coordination levels in an MU-MISO VLC system. 532.9 Comparison of system performance with different transmitter coordi-nation. Sum-MSE minimization problem with perfect CSI. . . . . . . 542.10 SINR as a function of user location in one quadrant of the room andIDC = (IL + IU)/2. Sum-MSE minimization problem with perfect CSI. 55xiiList of Figures2.11 Robust sum-MSE minimization with outdated CSI. Setup II with x =1.25 and y = 1.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.12 Robust sum-MSE minimization with noisy CSI. Setup II with x = 1.25and y = 1.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.13 Robust illuminance minimization with perfect (L = 0) and outdated(L > 0) CSI. Setup II with x = 1.25 and y = 1.25. . . . . . . . . . . . 592.14 Comparison between robust and non-robust design for sum-MSE min-imization problem with outdated CSI. . . . . . . . . . . . . . . . . . . 613.1 Illustration of the CB structure. . . . . . . . . . . . . . . . . . . . . . 643.3 The distribution of indoor illuminance for two lighting setups whenIDC = 500 mA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823.4 SINR of User I as a function of its x-axis coordinate x1. . . . . . . . . 843.5 Comparison of system performance with different coordination levelsfor UD-II, UD-III and UD-IV. . . . . . . . . . . . . . . . . . . . . . . 873.6 (a) Left : w = [1, 1, 1, 1]T . (b) Right: w = [50, 10−7, 1.4, 2.2]T . . . . . 883.7 Comparison between robust and non-robust design with the determin-istic model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.8 Comparison between robust and non-robust design with the stochasticmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 904.1 Block diagram of the HVP system. . . . . . . . . . . . . . . . . . . . 954.2 Detailed block diagram of the SO-OFDM HVP downlink system forone luminaire and one user. Blocks with dashed lines are not presentin LED luminaires operating in amplify-and-forward mode. . . . . . . 974.3 The setup of HVP system. . . . . . . . . . . . . . . . . . . . . . . . . 121xiiiList of Figures4.4 Achievable rate as a function of user location. Nc = 16, α =√10,β = 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1224.5 Achievable rate versus relay gain (α or β). Nc = 16. User location isx = −0.5 m, y = 1.5 m, z = 0.8 m. . . . . . . . . . . . . . . . . . . . 1234.6 Comparison of different SA schemes with different chunk size Ns. α =√10, β = 10. User location is x = −0.5 m, y = 1.5 m, z = 0.8 m. . . 1244.7 NVLC_BL as a function of user location. Nc = 16. NVLC_BL is thenumber of subcarrier pairs for which the VLC hop is the bottlenecklink when the maximum achievable rate is attained. . . . . . . . . . . 1254.8 Achievable rate versus the number of users NU. SA with SP and AF-ACO are applied. β = 10, Nc = 16. . . . . . . . . . . . . . . . . . . . 1264.9 Comparison of multi-access schemes with and without PF for NU = 4.The example locations are (x = −1.25, y = 1.25, z = 0.8) m, (x =−1.25, y = −1.25, z = 0.8) m, (x = 1.25, y = 1.25, z = 0.8) m and(x = 2.5, y = 2.5, z = 0.8) m for User 1, User 2, User 3 and User 4,respectively. SA with SP and AF-ACO are applied. Nc = 16, β = 10. 127xivList of AbbreviationsAC Alternating CurrentACO-OFDM Asymmetrically Clipped Optical Orthogonal Frequency Division MultiplexingAF Amplify–and–ForwardAFE Analog Front–endAP Access PointASE Area Spectral EfficiencyAWGN Additive White Gaussian NoiseCB Coordinated BeamformingCoMP Coordinated MultipointC-RAN Cloud/Centralized Radio Access NetworkCS Coordinated SchedulingCSI Channel State InformationCSK Color Shift KeyingC-VAN Cloud/Centralized VLC Access NetworkDC Direct CurrentDCO-OFDM Direct Current–biased Optical Orthogonal Frequency Division MultiplexingDD Direct DetectionDF Decode–and–ForwardDMT Discrete MultitoneDSL Digital Subscriber LinexvList of AbbreviationsFFT Fast Fourier TransformFoV Field of ViewGPS Global Positioning SystemHVP Hybrid VLC-PLCIAI Inter–Attocell InterferenceIFFT Inverse Fast Fourier TransformIM Intensity ModulationIoT Internet–of–ThingsISI Inter–Symbol InterferenceJT Joint TransmissionLaaS Light–as–a–ServiceLBS Location–Based ServiceLED Light–Emitting DiodeLoS Line–of–SightLPTV Linear Periodically Time VaryingMHz MegaHertzMIMO Multiple–Input Multiple–OutputMISO Multiple–Input Single–OutputMMSE Minimum Mean Squared ErrorMSE Mean Squared ErrorMU Multi-UserNLoS Non–Line–of–SightNRZ Non–Return–to–ZeroOFDM Orthogonal Frequency Division MultiplexingOFDMA Orthogonal Frequency Division Multiple AccessxviList of AbbreviationsOOK On-Off KeyingOW Optical WirelessPAM Pulse Amplitude ModulationPAPR Peak–to–Average Power RatioPC Partial CoordinationPD PhotodiodePLC Power Line CommunicationPSD Power Spectral Density (PSD)PWM Pulse Width ModulationRF Radio FrequencyRGB Red–Green–BlueSA Subcarrier AllocationSDP Semidefinite ProgrammingSISO Single–Input Single–OutputSINR Signal–to–Interference–plus–Noise RatioSNR Signal–to–Noise RatioSO-OFDM Spatial Optical Orthogonal Frequency Division MultiplexingSP Subcarrier Permutation/PairingTHz TeraHertzUT Uncoordinated TransmissionVLC Visible Light CommunicationV-PPM Variable Pulse Position ModulationV2I Vehicle–to–InfrastructureV2V Vehicle–to–VehicleWSMSE Weighted Sum Mean Squared ErrorxviiList of AbbreviationsZF Zero–ForcingxviiiNotationA Matrixa Vector1 All–one column vectorI Identity matrix| · | Absolute value of a real number or the cardinality of a set(·)T Transpose(·)H Hermitian transposevec(·) VectorizationZ+ The set of positive integerC The set of complex numberCm×n The space of all m× n matrices with complex-valued elementsE(·) Statistical expectation operator⊗ Kronecker productvar(·) Variance operator‖ · ‖p p-normdiag(x) A diagonal matrix with the elements of vector x on the main diagonaltr(·) Trace of a matrixxixDedicationTo my wife, parents and familiesxxChapter 1IntroductionThe mobile data traffic is surging at an incredible speed. A study conducted byCisco Systems Inc. shows that global mobile data traffic grew 63% in 2016, and themonthly global mobile data traffic will reach 49 exabytes by 2021, compared to 7.2exabytes per month at the end of 2016 and 4.4 exabytes per month at the end of2015 [1]. One of the main reasons for this huge amount of traffic increment is theincreased data consumption per mobile device. This is due to the booming of data-intensive mobile multimedia applications, especially cloud-based mobile applicationswhere mobile devices function as gateways for the access to services provided by thecloud [2]. The other major reason is the explosively growing number of connecteddevices. More cyber-physical systems are penetrating our life in this age of theInternet of Things (IoT). Huawei Technologies Co. Ltd predicts that by 2025, thetotal number of connected devices will reach 100 billion [3]. A significant portionof those connected devices will be accessing the Internet wirelessly, which leads to ahigher mobile data traffic. Moreover, the introduction of new cyber-physical systemswill, in turn, drive the creation of new multimedia applications which will furtherboost the aggregate data usage. In contrast, the radio-frequency (RF) spectrumis a very limited resource, and the resulting spectrum scarcity is holding back thecapacity enhancement of wireless networks and hindering mobile network operatorsfrom starting new wireless services [4]. Till now, the creation of small-cell networksand operation of heterogeneous networks have been the two important means to1Chapter 1. Introductionsqueeze more data traffic into the limited RF spectrum. However, eventually theusable RF spectrum is a finite resource, and the inter- and intra-cell interference willlimit the wireless network capacity.On the other hand, the lighting industry is undergoing a major technology transi-tion as light-emitting diode (LED) illumination devices are replacing legacy incandes-cent and fluorescent light lamps due to the longer life expectancy and higher energyefficiency. A McKinsey study predicts that the global LED market size in 2020 willdouble that in 2016 [5]. As LED-based lamps are relatively more reliable and have alonger lifespan, the manufacture and retail of LEDs become a less profitable businessin the long run, which is encouraging lighting companies to adjust their businessmodel from lighting equipment manufacturers to light-as-a-service (LaaS) providers[6, 7].Being at the intersection of communication and illumination, visible light com-munication (VLC) fulfills the needs of both the wireless and lighting industries asit turns illumination devices into wireless data transmitters. VLC uses LEDs as thetransmitting devices and operates over the nearly unlimited and license-free lightspectrum (380 nm – 780 nm), wherein the data signal is transmitted by means ofmodulating the output intensity of the incoherent LED light sources, i.e., via intensitymodulation (IM). At the receiver side, direct detection (DD) is applied using simplephotodiodes (PDs) or imaging receivers. Given the ongoing widespread deploymentof LED luminaires, VLC can turn such prevalent illumination devices into wirelessaccess points (APs) that provide ubiquitous indoor broadband coverage, includingareas in which RF radiation is undesirable or prohibited, such as hospitals. Besides,VLC is inherently secure as light is confined within the room that it illuminates byopaque boundaries. Visible light is also much more eye-safe than infrared links due2Chapter 1. Introductionto the inherent blink reflex of human eyes. As a result, safety regulations permitfar larger emitted optical power at visible wavelength range over infrared. Last butnot least, unlike RF front-ends and receive chains, all signals in the VLC transmit-ter and receiver are at baseband and up/down conversion is done via inexpensiveoptoelectronic components, yielding a simpler, lower power transceiver.This chapter provides an overview of the VLC technology, and it is organized asfollows. In Sections 1.1, we briefly review the literature of VLC development and itsapplications. Sections 1.2 presents an overview of the VLC channel including VLCtransceivers. System design constraints and compatible modulation schemes are alsoreviewed at the end of Section 1.2. The motivations and contributions of the thesisare provided in Section 1.3. Section 1.4 offers remarks on the alternating optimizationtechnique used throughout the thesis. Finally, the thesis organization is presented inSection 1.5.1.1 Visible Light Communication Development andApplications1.1.1 Visible Light Communication DevelopmentAt the time of writing of this thesis, there is substantial research interest in the areaof VLC, especially for the high data-rate indoor VLC network. The use of whiteLED illumination devices for indoor communications was first proposed by Komineet al. [8]. However, enthusiasm for this research topic has spread worldwide withactive research groups in the USA (e.g., Penn State U., Boston U., Rensellar Poly,Georgia Tech.), Europe (e.g., Edinburgh, Oxford, Northumbria, Fraunhofer HeinrichHertz Inst.) and Asia (e.g., Keio U., Tsinghua U.). In addition, large research3Chapter 1. Introductionprojects in VLC have been launched including the Visible Light CommunicationsConsortium (2003, Japan), OMEGA Project (2008, EU), Smart Lighting EngineeringResearch Center (2008, USA), Center on Optical Wireless Applications (2011, USA)and Canadian Research in VLC (2012). In 2014, the Visible Light CommunicationsAssociation (VLCA) was established as a successor to Visible Light CommunicationsConsortium in Japan.In 2011, the IEEE ratified 802.15.7, a wireless personal area network standardfor VLC [9]. The standardization activities were led by Samsung (Korea) and In-tel (USA). Data rates in the standard range from 11 kbps to 96 Mbps using on-offkeying (OOK), variable pulse-position modulation (V-PPM) and colour-shift keying(CSK). On the other hand, more modulation techniques for VLC, including orthogo-nal frequency-division multiplexing (OFDM), have been investigated in the researchcommunity [10, 11] and adopted by industrial companies [12]. OFDM VLC proto-type systems developed in laboratory conditions have demonstrated the potential ofVLC in providing Gb/s transmission for indoor wireless network access. In [10], aOFDM VLC link of 500 Mb/s is achieved over a 0.3 m distance where the employedhigh-power LED possesses a 3-dB modulation bandwidth of 35 MHz. In [11], a 3Gb/s OFDM VLC link over a 5 cm distance has been implemented utilizing a singlegallium nitride µLED whose 3-dB modulation bandwidth is 60 MHz.1.1.2 Visible Light Communication ApplicationsWireless Local Area NetworksGiven the trend in the widespread deployment of LED luminaires, VLC can turn theubiquitous illumination devices into numerous wireless hotspots for indoor coverage.By harnessing the vast optical spectrum resource, research [11, 13] has shown that4Chapter 1. Introductionthe data rate for a point-to-point VLC link can reach up to Gb/s. A typical VLC APcovers a service area on the order of 1−10 m2. This relatively small coverage area al-lows ultra-dense deployment of the so-called VLC attocells [14], which are analogous,but smaller in terms of the coverage area, to RF femtocells [15]. As a consequence,the area spectral efficiency (ASE) of VLC networks can be significantly increased,and more users can be accommodated within the indoor environment [16, 17]. Al-though VLC is less preferable to RF transmission (e.g., Wi-Fi, femtocell) in terms ofproviding seamless connections, indoor VLC can supplement indoor RF transmissionby providing high-speed downlink transmission for data-intensive applications likevideo downloading and live streaming. These applications have heavy demands onthe downlink bandwidth yet require minimal uplink capacity. Through offloading thedata traffic from RF transmission to VLC, the capacity of RF transmission availablecan be enhanced and better utilized.Indoor PositioningThe overall market of location-based services (LBS) is expected to increase five timesduring the period of 2016 - 2021 [18]. The Global Positioning System (GPS) has beenwidely used to provide localization service in outdoor areas, but it is not suitable forindoor positioning due to the signal attenuation and scattering in the indoor environ-ment. For indoor positioning, a possible solution is Wi-Fi-based indoor localization,but it offers relatively low accuracy [19]. On the other hand, indoor positioningbased on VLC has become a popular research topic recently [20, 21]. Comparedwith RF-based indoor positioning, VLC-based indoor positioning can be adopted inelectromagnetic interference sensitive areas like hospitals. As the number of LED lu-minaires is usually greater than that of Wi-Fi APs in the indoor environment, and thepropagation of visible light is less subject to the multipath effect and thus more pre-5Chapter 1. Introductiondictable, VLC-based indoor positioning techniques can generally provide localizationservices of higher accuracy and are strong candidates for future indoor positioningapplications.Vehicle CommunicationThe intelligent transportation system (ITS) improves the safety of transport networksand enables better traffic management. Vehicular communication is an importantpart of ITS, which falls into two categories: Vehicle to Infrastructure (V2I) and Vehi-cle to Vehicle (V2V) communications [22]. As LED luminaires are already availablein street lights, traffic lights and signs, and automotive lighting, VLC is directly ap-plicable for V2I and V2V communication. Due to the omnipresence of LED lightsin the transportation system, VLC-based vehicular communication reduces the hugecost of equipment installation. Furthermore, since VLC provides a more focusedtransmission and can be blocked by opaque objects, VLC-based vehicular commu-nication experiences less interference compared with RF-based one, which is moresuitable for high traffic density areas [23].1.2 Visible Light Communication Background1.2.1 VLC TransceiversTransmitter: Light-Emitting DiodesLEDs are used as the transmitting device in a visible light communication system.LEDs are semiconductor p-n junction diodes and emit light when activated, theeffect of which is known as electroluminescence [24]. The color of the emitted lightis determined by the band gap of the semiconductor. Among LEDs of all colors,6Chapter 1. Introductionwhite light LEDs are most widely used for illumination purpose in both indoor andoutdoor environment. However, white light cannot be directly generated by a singlematerial. According to the way in which white light is generated, commercial LEDscan primarily fall under the following two categories:• Phosphor-based LEDs: A phosphor-based LED is a blue LED chip coatedwith yellow phosphor. Phosphors are designed to absorb one specific frequencyof light and re-emit light at different frequencies. When light emitted by a blueLED passes through the phosphor coating, part of the blue light is convertedto green, yellow and red. Together with the leaked blue light, the mixture of allthe components produces white light [24]. Phosphor-based LEDs are relativelycheaper but suffer from low modulation bandwidth due to the slow response ofphosphor coating. Optical filters at the receiver side can be applied to retrievethe blue component, and thus resulting in an enhanced system bandwidth [25].• Red-Green-Blue (RGB) LEDs: The RGB LED contains three LED diceswhich are jointly packaged. The three separate monochromatic LED chips emitred, green and blue light, and the combination of the three primary colors inappropriate portions produces white light. It omits the need for the phosphor,so the modulation bandwidth is greater than that of phosphor-based LEDs.However, the light output of different colored LEDs may depreciate at differentrates throughout their lifetime, leading to color drift for the RGB LED.LEDs are current-driven devices that are able to emit incoherent light. The forwardvoltage of LEDs remains approximately constant regardless of the driving current,while the instantaneous optical power of the LED is controlled by the driving current.VLC uses IM by modulating instantaneous output optical power of the LEDs throughthe driving current signal. There exists a linear operating region for an LED wherein7Chapter 1. Introductionthe optical power is linearly proportional to the driving current, and the VLC-enabledLED needs to work within the linear operating region in order to perform IM.Though the visible light spectrum spans hundreds of terahertz (THz), the slowmodulation response of off-the-shelf LED light fixtures is the bottleneck that im-pedes the capacity enhancement of VLC links 1. Typical white-light LEDs are mostlyphosphor-based LEDs with modulation bandwidth of several megahertz (MHz), andemploying the blue optical filter at the receiver side can improve the system band-width to approximately 20 MHz [27]. Research of new LEDs has resulted in LEDswith much higher modulation bandwidth [28]. Reducing the cost and accelerating thecommercialization of high-bandwidth LEDs are critical towards the wide deploymentof high-speed VLC systems.Receiver: PhotodiodeThe photodiode is a semiconductor device that is able to convert incident light intocurrent. VLC uses photodiodes as receivers to down-convert the optical into anelectrical signal, the process of which is called DD. Another option for the VLCreceiver is the imaging sensor. It can be considered as a matrix of photodetectorson an integrated circuitry, and VLC can utilize its rolling shutter effect for datareceiving at a fast rate [29]. In this thesis, we focus on the use of photodiode as theVLC receiver.1The bandwidth of PDs is in general much wider than that of VLC LED transmitters [26].8Chapter 1. Introduction1.2.2 Channel ModelingChannel ResponseThe VLC channel response is inherently frequency-selective. While the frequencyresponse of VLC transmitters can be flattened through equalization to counteract thelow-pass characteristics of LEDs, the multipath propagation of visible light, whichresults from reflection, will lead to delay spreads. The rays of light hit surfaces in theenvironment and get reflected towards the receiver. Therefore, the channel responsehVLC comprises both a line-of-sight (LoS) component hLoS and a non-LoS (NLoS)component hNLoS:hVLC = hLoS + hNLoS . (1.1)In VLC, the LoS propagation of visible light dominates the diffuse propagation inmost situations [8]. Considering the LoS propagation only, the single-tap VLC chan-nel gain between the light source (the LED source or a reflection point on the walls)and the receiver (the user or a reflection point on the walls) can be approximated bya deterministic function of the emission pattern of the LED transmitters, as well asthe location and orientation of the VLC receiver. It can be expressed as below if weassume Lambertian radiation pattern for light sources [30]:h(D,φ, ψ) =(m+ 1)sγκ2APD2piD2 sin2(ψc)cosm(φ) cos(ψ)IA(ψ) , (1.2)where m is the Lambertian order and specifies the transmit beam divergence, γ isthe receiver (photodetector) responsivity [A/W], s is the conversion factor of thelight source (LED) [W/A], κ is the concentrator refractive index, D is the distancebetween the receiver and the light source, ψc is the width of the field of view (FoV)9Chapter 1. Introductionat the receiver, APD is the area of photodetector, ψ is the angle of incidence at whichthe light is received relative to the normal vector of the receiver plane, and φ isthe angle of irradiance at which the light is emitted relative to the normal vectorof the transmitter plane. Furthermore, IA(ψ) denotes the indicator function withA = {ψ| 0 ≤ ψ ≤ ψc}.Research in the VLC literature generally uses two methods of modeling the VLCchannel response, namely frequency-flat channel modeling and frequency-selectivechannel modeling. Frequency-flat channel modeling considers the LoS componentonly and (1.2) can be applied to calculate the channel gain between the VLC trans-mitter and the user. The neglect of NLoS components is reasonable given the factthat the modulation bandwidth of typical off-the-shelf LED luminaires will not ex-ceed 20 MHz, which is generally smaller than the inverse of the maximum excessdelay of the NLoS path in general indoor environment [27]. Therefore, the multipathdelay will not result in notable inter-symbol interference (ISI), and thus the VLCchannel can be treated as a single-tap channel.On the other hand, the multipath effect has to be taken into account in case ofrelatively broadband transmission, where the multipath phenomena will lead to ISI,and NLoS components should not be neglected any more [27]. Frequency-selectivechannel modeling takes both LoS and NLoS contributions into account, and thecorresponding channel response can be approximated using different algorithms. Asimple frequency-domain analytical model proposed by [31] for the indoor wirelessinfrared channel has been used widely in the VLC literature due to its computational-efficiency. However, the mismatch between the analytical model and the channel mea-surements increases as frequency increases [31]. In comparison, approximating thechannel response by simulations, like recursive calculation methods [32] and Monte10Chapter 1. IntroductionCarlo ray-tracing methods [33], is of higher accuracy at the cost of higher compu-tational complexity. In this thesis, we adopt the modified Monte Carlo ray-tracingmethod [34], which is a relatively faster algorithm to obtain the VLC channel responsewhen the NLoS contribution needs to be considered.Receiver NoiseThe dominant noise in VLC systems comprises thermal noise generated by the re-ceiver electronic circuits, and shot noise due to ambient light from light sources likethe sun and indoor lighting devices including VLC-enabled luminaires. The receivernoise component can be modeled as a zero-mean Gaussian variable with variance [8]σ2n = σ2th + 2eB(Irp + IbgI2) , (1.3)where σ2th is the thermal-noise variance, e is the elementary charge, B is systembandwidth, Ibg is background current, and I2 is the noise bandwidth factor (secondPersonick integral [35]). Irp is the average current due to the received signal at thereceiver, which is dependent on the illumination level of the VLC transmitter andthe user location.1.2.3 Standards and ConstraintsAppropriate lighting enables people to perform visual tasks efficiently and accurately.A VLC-enabled LED serves the dual-purpose of illumination and communication.Therefore, the VLC system design must follow the illumination standards, and it isconstrained by the property of LED transmitters at the same time.11Chapter 1. IntroductionTable 1.1: Required illuminance level for different activities specified by the EuropeanNorm (EN) 12464-1 StandardActivity Illuminance (Lx)Stairs, escalators, travelators 100Rest rooms inside buildings 100Theaters dressing room 300Eye or Ear examination rooms 500Classroom for evening classes 500Normal office work 500Illuminance and UniformityThe indoor illuminance level is determined by the DC current of LEDs. Various stan-dardization bodies across different countries defined the required illuminance level forthe indoor environment [36, 37, 38]. In this thesis, we follow the requirement of theEuropean Norm (EN) 12464-1 standard [38] for the planning and design of lightinginstallations. The area planning for indoor workplaces defines both task area andimmediate surrounding area. The task area is defined as the area in which the visualwork is carried out, while the immediate surrounding area is defined as a band sur-rounding the task area within the field of vision with a minimum width of 0.5 m. Thetask area can be used to perform different types of activities which require differentillumination levels. As specified in the European Norm (EN) 12464-1 standard, Table1.1 provides the required illuminance level for a few different activities.Aside from the illumination level, illuminance fluctuation across the indoor en-vironment should also be restricted in order to guarantee a comfortable luminousenvironment. Therefore, the term uniformity, defined as the ratio of the lowest tothe average illuminance value in a certain area, is introduced. According to theEuropean Norm (EN) 12464-1 standard, the minimum uniformity of task area andimmediate surrounding area is 0.60 and 0.40, respectively.12Chapter 1. IntroductionAmplitude ConstraintLEDs have a limited operating region which consists of both linear region and non-linear region. The output optical power is linear with the forward current if LEDsoperate within the linear region. Otherwise, the current/optical conversion will dis-play nonlinear characteristics similar to the nonlinearity of RF transmitters [39].While pre-distortion can be used to (approximately) linearize the current/opticalconversion, the driving current of LEDs still needs to stay within a limited dynamicrange, beyond which the output intensity saturates. Therefore, the channel input ofVLC systems must satisfy a certain amplitude constraint in order to avoid clippingdistortion of the transmitted signal, which is different from the power constraint thatis usually considered in RF systems.For single-carrier modulated signals, it is easier to put a constraint on its ampli-tude to avoid overdriving LEDs, and thus signal clipping can be prevented. While formulti-carrier modulation, like OFDM, signal clipping is unavoidable since the time-domain signal follows a Gaussian distribution for large Inverse Fast Fourier Transform(IFFT) sizes according to the Central Limit Theorem [40]. In this case, the currentsignal should be pre-clipped before it is injected into the LEDs so that the drivingcurrent lies within the dynamic range of the LEDs .1.2.4 Modulation TechniquesVLC systems utilize the LED, which is an incoherent light source, as the transmitter.VLC-enabled LEDs send information by varying the instantaneous intensity (i.e.power) of the optical source in time. Data are not sent in the underlying phase oramplitude of the optical carrier but rather only in its power. This modulation schemeis called IM. As a result, only non-negative signals can be sent from the transmitter.13Chapter 1. IntroductionAt the receiver, a photodiode performs the DD of the signal. It integrates the envelopeof the received field and outputs an electrical current in near proportion to the opticalpower impinging on it. In the following, we will have a brief review of several VLC-compatible modulation schemes.Single-Carrier ModulationIEEE 802.15.7 standardized three modulation schemes, namely on-off keying (OOK),variable pulse-position modulation (V-PPM) and color shift keying (CSK) [9]. Thefirst two modulation schemes are compatible with single-chip LEDs (phosphor-basedLEDs) while CSK is targeted for multi-chip light sources (RGB LEDs) and detectors.• On-Off Keying (OOK): Due to its simplicity, on-off keying is the most pop-ular IM/DD modulation scheme. Each OOK symbol represents either an “ON”state or an “OFF” state. Note that "ON" and "OFF" are just two logic levelsand do not necessarily require that the light source be turned off completely.Different line code techniques can be applied to OOK. In the simplest form ofOOK, non-return-to-zero (NRZ) OOK, digital data is represented by the pres-ence or absence of light. The IEEE 802.15.7 standard proposes the Manchestercoding instead of NRZ for VLC OOK. The Manchester line code encodes eachdata bit in either low-to-high or high-to-low transition thus it is a DC balancedcode, which can avoid possible flicker [9].• V-PPM:V-PPM combines both 2-PPM (pulse position modulation) and PWM(pulse width modulation). In 2-PPM, the symbol duration is divided into twoslots of equal duration and the pulse corresponding to a certain bit is trans-mitted in one of its two time slots within the symbol period, through whichthe binary bit 1 and 0 are represented. V-PPM incorporates the characteristics14Chapter 1. Introductionof PWM and extends 2-PPM by making the duty cycle percentage tunable in-stead of fixing it at 50%. Pulse width of V-PPM can be adjusted based on thedimming requirements. V-PPM has both the advantages of flicker avoidance(2-PPM) and dimming control capability (PWM).• Color Shift Keying (CSK): CSK applies to VLC systems that employ RGBLEDs as the transmitter. In CSK, signals are transmitted imperceptibly viavarying the light output of each chip in the RGB triplet. The luminous flux andthe average perceived chromaticity of the light source remain constant, makingCSK free from flicker. Also, CSK generally enables higher data throughputsince it divides the visible light spectrum into three different communicationchannels, in contrast to the two modulation schemes above which modulate thesame data over the entire visible light spectrum [41].Multi-Carrier ModulationBesides these standardized single-carrier modulation schemes, IM/DD compatiblemulti-carrier modulation schemes are gaining popularity in both the research com-munity [10, 11] and the industry [12]. OFDM has been widely used in RF com-munications due to its robustness towards ISI caused by the dispersive channel andthe low complexity of frequency-domain receiving equalization. The VLC channel isinherently dispersive due to the low-pass characteristics of LEDs and the reflectionsof light waves. Therefore, optical OFDM can be applied to high-speed VLC systemsto combat ISI. However, due to the nature of IM/DD, the conventional OFDM usedin RF communications needs to be modified since the time-domain optical OFDMsignals for the IM/DD channel is required to be both real and non-negative in orderto modulate light intensity. In this subsection, we will have a brief overview of two15Chapter 1. Introductionpopular variations of optical OFDM [42]. The former has the same requirement as forany baseband OFDM transmission, such as for digital subscriber lines (DSLs), whereit is also referred to as discrete multitone (DMT), or for power line communication(PLC). In comparison, the latter is truly VLC specific.• DC-Biased Optical OFDM: In DC-biased optical OFDM (DCO-OFDM),the signal input to the inverse Fast Fourier Transform (FFT) module shouldsatisfy the Hermitian symmetry so that the output is real. A DC bias is addedto ensure the unipolarity of optical OFDM signal in DCO-OFDM. However, thetime-domain OFDM signal has a high peak-to-average power ratio (PAPR). Inorder to bias all negative peaks, a large DC bias is required thus the powerefficiency decreases. Therefore, typically a moderate DC bias is used to biasmost of the negative components, while the rest of the negative components willbe clipped, and every information-carrying subcarrier will be contaminated bythe resulting clipping noise.• Asymmetrically Clipped Optical OFDM: Similar to DCO-OFDM, asym-metrically clipped optical OFDM (ACO-OFDM) also utilizes the Hermitiansymmetry to ensure a real output. The time-domain ACO-OFDM signal ismade positive by clipping all negative signal components. As the resultingclipping noise will only affect the even subcarriers, ACO-OFDM only employsodd subcarriers to carry data symbols and leave even subcarriers vacant [43].Compared with DCO-OFDM, ACO-OFDM is less spectral efficient since halfof the subcarriers are unused. However, ACO-OFDM is more power efficient interms of average optical power for small constellation sizes [44].16Chapter 1. Introduction1.3 Motivation and Contributions of the ThesisAt the time of starting the thesis work in 2012, most research on physical layertransmission techniques in the VLC literature focused on point-to-point communica-tion. However, despite the often dominating LoS propagation and the confinement oflight waves by opaque surfaces, the performance of a VLC attocell downlink can stillbe severely degraded by interference from neighboring attocells, i.e., inter-attocellinterference (IAI). Typical lighting systems in indoor environments utilize multiplewide-beam luminaires to provide user-friendly uniform illumination. From a com-munications perspective, however, the use of wide-beam luminaries gives rise to in-creased interference levels at areas in which the illumination footprints of luminairesfrom different attocells overlap.In order to alleviate the performance degradation for attocell-edge users, severalworks in the literature have considered hybrid RF-VLC systems [45, 46, 47, 48]. Insuch systems, the VLC attocells are deployed with non-overlapping footprints, andthe gaps are covered with RF femtocells. In other words, users who are beyond thecoverage of the VLC attocells are served by RF base stations. Despite its benefits,a hybrid RF-VLC system would suffer from added complexity along with increasedhandover overhead for users moving across different femtocells/attocells.A different approach towards interference management for VLC attocells is touse the so-called coordinated multipoint (CoMP) paradigm, wherein transmitters ofdifferent attocells are connected through backbone networks like wired Ethernet orpowerline, and design their signals in a collaborative way. In Chapter 2, we proposethe joint transmission (JT) of multiple VLC attocells (i.e., VLC-enabled LED lu-minaries) to turn the problem of overlap and thus interference into an advantage,with PLC used as the network backbone. In JT, all the transmitters jointly serve17Chapter 1. Introductionmultiple users. It removes the barriers between attocells and turns the previouslyunwanted IAI into constructive signal components. We suggest that since multipleLED luminaries in the same room are connected to the same power wires, PLC canbe used to serve as a backbone network to support the cooperation among multipleVLC attocells. A VLC modem in an LED transmitter can receive data from thevery power line that provides its power through a PLC modem, while in comparisonan Ethernet backbone requires modifications in the existing indoor wiring. This co-ordinated architecture2 can be considered as the VLC counterpart to RF CoMP incellular networks [49, 50]. Our numerical results for a typical VLC scenario clearlydemonstrate the improvements of receiver-side signal-to-interference-plus-noise ratio(SINR) due to the proposed coordination.Since 2013, considerable research efforts have been directed towards collaborativedesigns for VLC systems, most of which focused on JT schemes [51, 52, 53, 54, 55,56, 57, 58, 59]. JT is typically considered in the context of beamforming design orfrequency allocation among attocells. In [51], pseudo-inverse-based zero forcing (ZF)and ZF dirty-paper coding were proposed for multi-user multi-input single-output(MU-MISO) VLC systems, while a generalized-inverse-based ZF scheme was proposedin [52] to maximize the system sum-rate. In addition, ZF block diagonalizationprecoding3 schemes was considered for a multi-user multiple-input, multiple-output(MU-MIMO) VLC system in [53]. Besides ZF, linear beamforming schemes thatare based on the minimum mean squared error (MMSE) criterion have also beenconsidered in [54, 55, 56, 57]. Other JT schemes that exploit frequency allocationhave been considered in [58, 59].Despite their superior performance, the implementation of JT schemes brings two2We note that the backbone network of the coordinated architecture does not have to be PLC.3The concepts of precoding and beamforming are used interchangeably throughout the thesis.18Chapter 1. Introductionmajor difficulties. First, JT requires tight synchronization among LED transmittersof different attocells in order to ensure that the signals emitted from different lu-minaires arrive at the intended user simultaneously. Second, information exchangeamong different transmitters should involve not only downlink channel state informa-tion (CSI), but also the data symbols intended for each user. JT may not be feasibleif the backbone network that interconnects the transmitters together is band-limited.This is a particular concern considering the fact that PLC has been favored to be anattractive solution as the backbone network for the VLC front-end [60, 61, 62, 63],while the power line is a broadcast medium and thus the links to different VLC-enabled luminaires need to share the PLC capacity.In order to circumvent such difficulties, researchers have considered other CoMPschemes that require lower coordination level among attocells to seek a compromisebetween system performance and implementation complexity [64, 65, 66, 67, 68, 69,70]. Unlike JT, those coordination schemes only require the sharing of CSI amongattocells. In addition, symbol-level synchronization among attocells is not requiredas each user is served only by its assigned attocell. When the attocells are served bysingle-luminaire transmitters, the coordination can be implemented via adaptivelyallocating the time [64], frequency [64, 65, 66, 67, 68, 69, 70], or power resources[68, 69, 70] among different attocells. Such allocation schemes restrain the resourcesavailable to each attocell, and consequently, the overall data rate of the system isreduced.In Chapter 3, we propose a coordinated beamforming (CB) scheme for interferencemitigation in downlink multi-cell MU-MISO VLC systems, where different attocellshave multi-luminaire transmitters while each receiver has a single PD. The luminairesin each transmitter are modulated independently of each other using separate drivers.19Chapter 1. IntroductionThe excess degrees of freedom offered by such multiple luminaires allow forming moredirective beams towards the intended receivers while minimizing IAI. Compared withthe coordination schemes considered in [64, 65, 66, 67, 68, 69, 70], which are basedon time, frequency, or power allocation, our CB scheme exploits the spatial domainfor both multiplexing and interference mitigation purposes. In fact, our CB schemecan be integrated with the time and frequency multiplexing techniques considered in[64, 65, 66, 67, 68, 69, 70] to further enhance the overall system performance.We also note that the concepts of JT and CB are not new and have been widelystudied for RF channels (see, e.g., [71, 72, 73, 74, 75, 76, 77]). However, since VLCsystems are typically modeled with the amplitude constraint on the channel input (seeSection 1.2.3), the beamforming schemes developed for RF channels are not directlyapplicable to VLC transmitters.Most research works in VLC focus on the downlink transmission, often assumingthe existence of a perfect uplink channel. To realize an uplink, both optical and RFtransmissions are potential candidates. An optical uplink suffers from problems likeenergy inefficiency and device glare, and the link between the device and the fixeduplink receiver can be poor due to user mobility and change in device orientation[78]. Thus an RF uplink is preferred considering that most places are RF-insensitive.One choice is a WiFi uplink, because most mobile devices have WiFi radio pre-installed already. The integration of WiFi uplink with VLC has been discussed in anumber of research works in the literature, e.g., [45, 60, 78, 79, 80]. For VLC systemsusing RF uplinks, channel reciprocity is absent and VLC transmitters need to obtainthe channel information from receivers through feedback channels. In a realisticscenario, the channel information at the transmitter side will not be perfect due toerroneous or outdated estimation and/or quantization. Imperfect CSI deteriorates20Chapter 1. Introductionthe performance of VLC systems, which requires robust designs to counteract theperformance loss. This motivates us to extend our proposed design methods to takeinto account possible mismatches in channel information available to the transmitters,which constitutes the second part of Chapter 2 and Chapter 3.As has been mentioned in Section 1.2.1, the modulation response of the LEDtransmitter is the bottleneck that impedes the capacity enhancement of VLC links.The typical 3 dB modulation bandwidth of phosphor-based LEDs can be improvedto approximately 20 MHz with blue optical filters at the receiver side for better re-ception, and the bandwidth is still smaller than the inverse of the maximum excessdelay of the NLoS path in most indoor environments [27]. When the transmit sig-nal bandwidth is below the cutoff frequency of the LED, the VLC channel can beapproximated as frequency-flat, which is the assumption of both Chapters 2 and 3.However, as the modulation bandwidth of LEDs gradually increases [28], the VLCchannel cannot be modeled as frequency-flat anymore and the multipath effect inthe VLC channel should be considered. Recently, there has been a growing interestin applying OFDM to VLC due to its robustness to multipath dispersion, togetherwith its simple equalization and digital implementation. However, the high PAPR oftime-domain OFDM signals is a key challenge for VLC systems due to the limiteddynamic range of the LED, which will result in the clipping of time-domain OFDMsignal, leading to performance degradation of VLC systems.In Chapter 4, we apply OFDM to combat the multipath dispersion of VLC signals,instead of the single-carrier modulation which is considered in Chapters 2 and 3. Inparticular, we propose in this chapter a hybrid VLC-PLC (HVP) system architecturefor the indoor downlink transmission and present the analytical framework for thedata rate analysis of the HVP system. To overcome the high PAPR problem, spa-21Chapter 1. Introductiontial optical OFDM (SO-OFDM) [81] is applied across multiple luminaires, for whichwe propose several subcarrier allocation schemes to exploit the frequency selectivityof the VLC and PLC channels. Different possible and meaningful variations of theHVP system, including the choice of optical OFDM transmission, relay and multi-ple access schemes, are investigated and compared. The numerical results establishachievable rates for relevant communication scenarios and highlight the advantages ofthe proposed subcarrier allocation schemes in terms of rate and reduced peak powerof optical OFDM signals.1.4 Remark on Alternating OptimizationThe design tasks derived in this thesis are in the form of non-convex optimizationproblems. Our main tool to solve these problems is alternating optimization [82, 83].Throughout the thesis we apply an instance of alternating optimization that di-vides optimization variables into two groups, and thus the alternation is between twosubproblems. For the problems considered in this thesis, the global optimum canbe found for each subproblem in the respective optimization step. This is becausethe subproblems are either convex (Chapters 2 and 3) or classic integer program-ming problems that can be solved with polynomial-time algorithms (Chapter 4) [84].Hence, the value of the objective of the original problem improves with every it-eration of the alternating optimization. Since furthermore the objective functionsconsidered in this thesis are bounded, we are assured that the objective function willconverge monotonically through alternating optimization [83, Theorem 4.5]. Despitethis structural convergence property, we also set a maximum number of iterationswhen applying alternating optimization to the problems in Chapters 2–4, so as tolimit its computational complexity. Beyond this, however, our main focus in this the-22Chapter 1. Introductionsis is the derivation of methods to enable performance-improved VLC transmissionand not the complexity analysis or optimization of computational methods appliedfor this purpose.1.5 Organization of the ThesisThe following chapters are organized as follows. In Chapter 2, we propose a JTscheme for multiple connected VLC attocells and focus on the linear beamformingdesign based on the MMSE criterion. The materials presented in this chapter havebeen previously published in [54]. In Chapter 3, we propose a CB scheme for down-link interference mitigation among coexisting VLC attocells utilizing multi-luminairetransmitters. Compared to JT schemes, the proposed CB scheme places lower re-quirements on the network in terms of backbone traffic, and is easier to implementin a practical deployment, though at the cost of compromised performance. Theseresults have been submitted for publication. In Chapter 4, we propose a multi-carrierHVP system as a potential indoor high-speed downlink solution employing the sym-biotic relationship between PLC and VLC. To exploit the frequency selectivity ofHVP channels, as well as the multi-user and multi-transmitter diversity, we proposeseveral subcarrier allocation schemes with varying degrees of tradeoff among hard-ware, computational complexity and performance for meaningful variations of theHVP system. The materials presented in this chapter have been published in [85].Finally, Chapter 5 summarizes the contributions of this thesis and outlines areas offuture research.23Chapter 2Joint Transmission in VLC Systems2.1 IntroductionIndoor environments generally utilize multiple wide-beam luminaires to ensure user-friendly uniform illumination. From a communications perspective, however, theuse of wide-beam luminaries leads to increased interference levels. To mitigate theinterference across neighboring VLC attocells, this chapter proposes the joint trans-mission of different transmitters, i.e., LED luminaries, through a backbone network.The purpose of this coordination is to turn unwanted interference into constructivesignal components. The backbone could be realized by a wired Ethernet or power-over-Ethernet link. Another convenient manner to realize the backbone is usingexisting electrical power wiring for data communications, i.e., PLC [86]. The conceptof integrating PLC and VLC to form a hybrid system for fast data delivery to usersin indoor office buildings and homes is not new [87, 88, 89]. However, since multi-ple LED luminaries in the same room are connected to the same power wires, PLCcan also be used to serve as a backbone network to support the cooperation amongmultiple VLC attocell.This chapter focuses on the signal processing required at the VLC transmittersto benefit from coordination [62]. Multiple coordinated VLC emitters form a virtualmultiple-transmitter (or multiple-“antenna”) system. This is quite different from theindoor multiple-input multiple-output (MIMO) VLC systems for point-to-point com-24Chapter 2. Joint Transmission in VLC Systemsmunication studied in [90, 91], since we are dealing with the broadcasting of datato multiple VLC receivers (e.g. cellular phones or tablets) employing single photo-diode receivers here. Such MU-MISO systems have been widely studied for radiocommunication systems, cf. e.g. [71, 72, 77]. However, different from RF wirelesscommunication, VLC uses IM and the transmitted signal must be non-negative andconstrained in mean amplitude, i.e., average optical power. These differences rendersolutions developed for the RF case not directly applicable to VLC systems. We in-vestigate the effect of different levels of coordination of luminaries in a room, leadingto different numbers of attocells and IAI scenarios. Within a coordinated VLC sys-tem, linear MMSE precoder design is applied. This allows us to consider interferencefrom adjacent VLC transmitters that are not coordinated, as well as ambient lightfrom the sun and other non-VLC lighting devices. Furthermore, this chapter extendsthe system design to the case of imperfect knowledge of the VLC transmission chan-nel. The numerical results highlight the benefits of coordination for VLC attocellsystems by demonstrating significant gains in achievable SINR.The remainder of the chapter is organized as follows. In Section 2.2, we proposethe JT VLC architecture with PLC as its backbone network. In Section 2.3, precoderdesign strategies for VLC MU-MISO transmission with perfect CSI at the transmitterare developed. In Section 2.4, the designs are extended to the case of imperfect CSI.Simulation results are presented and discussed in Section 2.5, and finally we concludethis chapter in Section 2.6.2.2 System Model and Transmission SchemeWe consider an indoor environment with multiple LED luminaires deployed in a room,office, laboratory or similar indoor space. The main elements of the coordinated25Chapter 2. Joint Transmission in VLC SystemsFigure 2.1: Illustration of indoor coordinated VLC broadcast system.VLC broadcast system are illustrated in Figure 2.1. The luminaires function as VLCtransmitters as a secondary use, and they receive electricity and data through a PLCbackbone network. This enables some of the VLC transmitters, e.g., those connectedto the same distribution box, to operate in a coordinated fashion alike CoMP. Similarto the definition of a CoMP-cell in the context of RF wireless systems [50], we definea CoMP-attocell as the area covered by one VLC broadcasting system where all thetransmitters are coordinated by the PLC backbone network. In the case of multipleCoMP-attocells in one room, there is interference from neighbouring CoMP-attocells,which is analogous to inter-CoMP-cell interference in RF cellular systems.2.2.1 VLC ChannelBefore discussing the broadcast transmission and VLC-specific constraints, we firstbriefly elaborate on channel gain and noise models applicable to the IM/DD channel26Chapter 2. Joint Transmission in VLC Systemsin VLC.Each LED luminaire has NE LED elements with a Lambertian radiation pattern.We assume that LoS propagation of visible light dominates the diffuse propagationcomponent and thus only the former is considered [90]. Utilizing Eq. (1.2), thechannel gain hkn between the kth user and the nth LED luminaire can be expressedas [8]hkn =NE∑i=1h(Dkni , φkni , ψkni) , (2.1)where Dkni , ψkni and φkni are the distance, the angle of incidence and the angleof irradiance between the kth user and the ith LED in the nth LED luminaire,respectively.The receiver-side noise term zk (see Eq. (2.7) below) can be written aszk = ik + nk , (2.2)where ik is the interference from neighbouring CoMP-attocells with average receivedelectrical power E(i2k) = σ2ik , and the VLC noise component nk comprises shot andthermal noise. We assume that nk can be modelled as a zero-mean Gaussian variablewith variance calculated by Eq. (1.3). We observe that Ikrp is dependent on theDC current and thus illumination level and on user location, via hkn. This rendersthe optimization of broadcast transmission intractable. Therefore, we will use afixed upper bound for Ikrp in the following optimization. The accurate noise power ishowever applied for all numerical results.Finally, we denote the total interference and noise power at the kth user asσ2k = E(z2k) = σ2ik + σ2nk. (2.3)27Chapter 2. Joint Transmission in VLC Systems2.2.2 Broadcast TransmissionIn a VLC CoMP-attocell, NL LED luminaires cooperate to broadcast informationto NU single-photodiode users. OOK is applied in this work due to its popularityin optical communications and ease of implementation4 [9]. This is accomplished bymodulating a zero-mean data signal onto the DC bias currents IDC = [I1DC, . . . , INLDC]T ,which determine the brightness levels of the NL LED luminaires. In the following,we describe the pre-processing of this data signal.Let us denote dk ∈ {±1} the binary data symbol intended for the kth user, andd = [d1, · · · , dNU ]T is the data vector for all users with covariance matrixCd = I . (2.4)The broadcast signal for VLC MU-MISO is generated through linear precoding ofthe data vector with the matrix F , i.e.,s = [s1, . . . , sNL ]T = Fd . (2.5)Finally, the transmitted current signal is given asx = Fd+ IDC . (2.6)We note that the conversion to a current signal and the scaling of the binary datavector d is accomplished through matrix F . Hence, choosing dk ∈ {±1} is withoutloss of generality. Furthermore, in VLC transmission, the elements of x need to be4Higher-order pulse-amplitude modulation (PAM) schemes could also be employed in the caseof high SINRs at the receivers. The precoder design would follow a similar approach as shown herefor OOK.28Chapter 2. Joint Transmission in VLC Systemsnon-negative, which imposes constraints on F as we will discuss further below.Collecting the channel gains hkn from Eq. (2.1) for all NU × NL links into thechannel matrix H = [h1, . . . ,hNU ]T = {hkn}NU×NL , the received signal at the kthuser can be written asyˆk = hTkx+ zk = hTk fkdk + hTk∑i 6=kfidi + zk + hTk IDC , (2.7)where fk represents the kth column of F . The first term hTk fkdk is the desired signal,while the second term hTk∑i 6=k fidi represents the intra-CoMP-attocell interference.The third term zk is the sum of inter-CoMP-attocell interference and noise as intro-duced in Eq. (2.2). The fourth term hTk IDC is the DC photocurrent for illuminationthat carries no data. It is removed via AC coupling at the receiver side, providingthe information-carrying signal at the kth receiver asyk = yˆk − hTk IDC = hTk fkdk + hTk∑i 6=kfidi + zk . (2.8)2.2.3 Constraints on Precoding from VLCConsider the precoding operation in Eq. (2.5), the data signal sn at the nth luminairesatisfies− ‖fn‖1 ≤ sn ≤ ‖fn‖1, (2.9)where fn is the nth row vector of the precoding matrix F . After adding the DC bias,InDC, to adjust the brightness of each LED luminaire, the electrical transmit signal(drive current) at the nth LED luminaire is (see Eq. (2.6))xn = sn + InDC . (2.10)29Chapter 2. Joint Transmission in VLC SystemsFor simplicity, in the following we assume the same brightness level for every LEDluminaire, i.e.,InDC = IDC , ∀n . (2.11)Due to optical intensity modulation, xn ≥ 0 and thus sn ≥ −IDC from Eq. (2.10).However, similar to the nonlinearity of RF transmitters, LEDs also have a limitedlinear range [39]. While pre-distortion can be used to (approximately) linearize trans-mission, signal clipping needs to be avoided. Furthermore, if the LED is over-driven,not only will LED life-expectancy be reduced, but the self-heating effect will lead toa drop in the electrical-to-optical conversion efficiency. Considering these character-istics of LEDs, the transmit signal of each LED luminaire should satisfyIL ≤ xn = sn + IDC ≤ IU , (2.12)where IU > IL > 0 represent the upper and the lower bound of the LED drive currentin the linear region. Substituting this into Eq. (2.9), we getIDC − ‖fn‖1 ≥ ILIDC + ‖fn‖1 ≤ IU(2.13)and the constraint‖fn‖1 ≤ min (IDC − IL, IU − IDC) (2.14)for the nth row vector of the precoder matrix F . Note that, via IDC, this constraintties possible choices of VLC precoding matrices F to the user-selected illuminationlevel of the LEDs.30Chapter 2. Joint Transmission in VLC Systems2.2.4 Design ObjectivesGiven the broadcast transmission model Eq. (2.8) and constraint Eq. (2.14), weoptimize the precoding represented by F in two ways. First, we consider the perhapsmore obvious design task of maximizing the performance of MU-MISO VLC underillumination constraints, i.e., a given value of IDC. As an appropriate performancemeasure for MU-MISO VLC we adopt the sum-MSE. Secondly, we consider a VLCperformance target represented by a given set of MSE thresholds for all users, andfind the minimal illumination level required to maintain performance. This designprovides a guaranteed VLC performance under different dimming levels. The twodesign objectives are pursued in Section 2.3, assuming perfect CSI, i.e., channel gainshkn (Eq. (2.1)), are available at the VLC transmitters. In Section 2.4, we extendour derivations to the practically relevant case of imperfect channel knowledge at thetransmitter.2.3 Transmitter Design with Perfect ChannelInformationAs mentioned above, the performance metric for precoder design adopted in this sec-tion is the sum MSE, which has widely been considered for precoding optimization inRF wireless MIMO/MISO systems, e.g., [92]. In particular, we consider the modifiedMSE [93] between the received signal yk at the kth user and original data dk givenbyMSEk = Edk,zk{‖cyk − dk‖22} = Ed,zk{‖c(hTkFd+ zk)− eTk d‖22} , (2.15)31Chapter 2. Joint Transmission in VLC Systemswhere c is a scaling term, which does not need to be applied at the receiver but offersa required degree of freedom in the receiver filter optimization, and ek denotes thekth standard basis vector for the NU-dimensional space,ek = [01×(k−1) 1 01×(NU−k)]T . (2.16)2.3.1 Sum-MSE Minimization ProblemWe first consider the sum-MSE minimization under illumination constraints. In thiscase, the precoder optimization problem can be formulated asP1 : (F ∗, c∗) = argminF ,cNU∑k=1MSEkC1 : ‖fn‖1 ≤ min (IDC − IL, IU − IDC) ,∀n (2.17)Using Eq. (2.15), the objective function in P1 can be written asf(F , c) =NU∑k=1MSEk = Ed,z{‖cy − d‖22} . (2.18)The optimization problem P1 is not jointly convex in precoder F and scaling factorc. We therefore use an alternating optimization approach to, possibly suboptimally,solve this problem. Specifically, we iteratively optimize F and c while fixing the othervariable (see Algorithm 2.1).32Chapter 2. Joint Transmission in VLC SystemsFixing Receiver Gain cWe assume a fixed receiver gain c and then optimize the precoder F . In this case, itis convenient to defineσ2sum =NU∑k=1σ2k (2.19)and to write the sum-MSE asEd,z{‖cy − d‖22} = Ed,n {‖c(HFd+ z)− d‖22}= ‖c(H ⊗ I)vec(F T )− vec(I)‖22 + c2σ2sum .(2.20)Then, defining b = vec(I), A = H ⊗ I, f = vec(F T ), and V as the NLNU ×NLNUblock-diagonal matrix of the NL×NU all-one matrix, problem P1, for a fixed gain c,can be transformed intoP2 : (f ∗, t∗) = argminf,t‖cAf − b‖22 + c2σ2sumC1 : −t  f  t ,C2 : V t ≤ min (IDC − IL, IU − IDC) 1NU×1 , (2.21)where vector t is a slack variable. The constraints in this optimization problem areequivalent to the L1-norm constraint (Eq. (2.14)) resulting from the limited dynamicrange of the LED. This problem is a convex quadratic programming problem and canbe efficiently solved using, e.g., the YALMIP or CVX toolbox [94, 95, 96].33Chapter 2. Joint Transmission in VLC SystemsFixing Precoder FNow we assume the precoder matrix F as fixed and optimize for c. The optimizationproblem P1 with fixed precoder F can be simplified intoP3 : c∗ = argminc‖cAf − b‖22 + c2σ2sum .The optimal c∗ can now be computed asc∗ =sym(bTAf)‖Af‖22 + σ2sum, (2.22)wheresym(X) =X +XT2(2.23)represents the symmetric part of a matrix X.Algorithm 2.1 Alternating optimization algorithm for P11. Initialization:p⇐ 0.Update H with CSI.Initialize {F }.2. repeat3. Update c according to Eq. (2.22).4. Solve P2 and get F .5. p⇐ p+ 1.6. until ‖MSEp+1 −MSEp‖ ≤ δ (δ is a predefined threshold) or p = pmax (pmaxis a predefined maximum iteration number), where MSE =∑NUk=1 MSEk.34Chapter 2. Joint Transmission in VLC Systems2.3.2 Minimal Illumination Level ProblemWe now turn to the question of what is the minimal illumination level needed tomaintain a certain VLC performance. This is important for illumination systemswith dimming, for which VLC should be supported. Illumination is proportional toIDC, which via Eq. (2.14) affects VLC precoding. Measuring VLC performance interms of MSE and denoting by qk the constraint for the MSE of the kth user, thecorresponding optimization problem can be formulated asP4 : (F ∗, c∗, I∗DC) = argminF ,c,IDCIDCC1 : MSEk ≤ qk,∀k (2.24)C2 : ‖fn‖1 ≤ min (IDC − IL, IU − IDC) ,∀nWritingMSEk = (chTkF − eTk )(chTkF − eTk )T + c2σ2k (2.25)and definingζ = 1/c,vTk = (hTkF − ζeTk ),φk = [vTk σk],(2.26)the constraint MSEk ≤ qk can be expressed as‖φk‖2 ≤√qkζ . (2.27)35Chapter 2. Joint Transmission in VLC SystemsAccording to the Schur complement lemma [97, 98], inequality Eq. (2.27) is equivalenttoΘk = √qkζ φkφTk√qkζI  0 .Thus, P4 can be reformulated asP5 : (F ∗, ζ∗, I∗DC) = argminF ,{tk},ζ,IDCIDCC1 : −tk  F Tek  tk, ∀k,C2 : 1T tk ≤ min (IDC − IL, IU − IDC) , ∀k,C3 : Θk  0,∀k, (2.28)where vector tk is a slack variable. The problem is a convex semidefinite programmingproblem (SDP) and can be solved efficiently numerically, e.g., [94, 95].2.4 Robust Transmitter Design with ChannelUncertaintyThe quality of CSI at the transmitter is critical to the precoder design. While theVLC channel is much more benign than its RF counterpart, the assumption of perfectCSI is not necessarily practical for MU-MISO VLC. VLC systems use visible lightas the downlink medium, while the uplink medium can be RF, infrared light (IR) orvisible light [14]. In the case of VLC uplink, the uplink-downlink reciprocity will allowCSI to be estimated at the transmitter. The more practically relevant scenario forVLC using indoor illumination devices considered here is that an RF uplink is used.In this case, CSI can only be estimated at the receiver and fed back to the transmitter36Chapter 2. Joint Transmission in VLC Systemsafterwards. Imperfect CSI can then arise from noisy and quantized channel estimationand, perhaps more critically, the feedback of outdated estimates. The latter is thecase when the VLC channel varies due to terminal motion and/or changes in theenvironment since the last channel update. As an example, Figure 2.2 illustrates ascenario where the receiver terminal has moved from position p1, at which CSI isreported, to position p2, at which precoded data using this CSI is received.2.4.1 Uncertainty ModelsGiven the channel estimate hˆk, we can express the true channel gains for the kthuser ashk = hˆk + δk , (2.29)where the error vector δk represents the CSI uncertainty. According to the source ofestimation error, we consider two models for δk.Noisy CSIFor noisy CSI, we use the stochastic error model [97]δk ∼ N (0,Σk) , (2.30)i.e., δk is zero-mean Gaussian distributed with covariance matrix Σk.37Chapter 2. Joint Transmission in VLC SystemsFigure 2.2: Illustration of outdated CSI resulting from terminal mobility in a VLCsystem.Outdated CSIOutdated CSI, due to e.g. a user walking with a terminal device (see Figure 2.2), isoften modelled by a bounded uncertainty model, i.e.,‖δk‖2 ≤ k (2.31)for some error bound k, which depends on the maximal changes that happened be-tween CSI estimation and transmission using this estimation. As we show in thefollowing, k should be chosen as a function of the terminal location during chan-nel estimation, i.e., p1 in Figure 2.2. Location information could be obtained fromchannel estimation itself using various positioning techniques [99, 100].Referring to Figure 2.2, we denote L as the bound for the user movement betweentwo CSI updates, i.e., ‖p1−p2‖2 ≤ L. Furthermore, considering a single transmitter,let dv and dh be the vertical and horizontal distance between transmitter and receiver,38Chapter 2. Joint Transmission in VLC Systemsrespectively, as indicated in Figure 2.2. Then, for terminal movement in the horizontaldirection, horizontal planes at the LED transmitter and photodiode receiver, the errorboundk = max{+, −} (2.32)can be obtained, where+ = β((d2v + d21)−m+32 − (d2v + (d1 + L)2)−m+32), (2.33)− = β((d2v + (d2 − L)2)−m+32 − (d2v + d22)−m+32), (2.34)β =(m+ 1)NEsγκ2APDdm+1v2pi sin2(ψc), (2.35)and d1 and d2 satisfylog(d1d1 + L)=m+ 52log(d2v + d21d2v + (d1 + L)2), (2.36)log(d2d2 − L)=m+ 52log(d2v + d22d2v + (d2 − L)2). (2.37)The details of the derivation of (2.32)–(2.37) are delegated to Appendix A. For themore general case including multiple transmitters, the relationship between errorbound and physical system parameters is even more complicated than (2.32). Wethus resort to numerical analysis to obtain error bounds. As an example, Figure 2.3shows k as a function of the user location and the maximal location distance L. Thedetails of the room, illumination and VLC setup for this experiment are described inSection 2.5.In the following, we consider both uncertainty models to formulate robust precoderdesigns. Similar to the RF wireless case, cf. e.g. [97, 98], we aim at optimizing averageperformance for noisy CSI according to the stochastic model (2.30) and worst-case39Chapter 2. Joint Transmission in VLC Systems−2−1012−2−10120.511.5x 10−5x (m)y (m)(a)−2−1012−2−101211.522.53x 10−5x (m)y (m)(b)Figure 2.3: Error bounds obtained from simulation for (a)L = 0.25 m, (b)L = 0.5 m.Illumination and VLC setup for these results are described in Section 2.5.performance for outdated CSI with the bounded error model (2.31).2.4.2 Sum-MSE Minimization ProblemWe start with the sum-MSE minimization problem.Robust Design with Outdated CSIThe robust broadcast precoder design for CSI uncertainty according to Eq. (2.31) isan extension of P1 in Eq. (2.17):P6 : (F ∗, c∗) = argminF ,cmax‖δk‖2≤kNU∑k=1MSEkC1 : ‖fn‖1 ≤ min (IDC − IL, IU − IDC) ,∀n (2.38)40Chapter 2. Joint Transmission in VLC SystemswhereMSEk = ‖c(hˆTk + δTk )F − eTk ‖22 + c2σ2k . (2.39)Using results from [97], P6 can be transformed intoP7 : (F ∗, c∗) = argminF ,{tk},λ,µ,g,cg2C1 : −tk  F Tek  tk, ∀k,C2 : 1T tk ≤ min (IDC − IL, IU − IDC) , ∀k,C3 : Ψk  0,∀k,C4 : Φ  0 , (2.40)whereΦ =g λT cσsumλ gI 0cσsum 0 g,Ψk =λk − µk 0T chˆTkF − eTk0 µkI kcF(chˆTkF − eTk )T k(cF )T λkI.Similar to the optimization problem P1, we can obtain a local optimum of this prob-lem by alternatively optimizing over F and c. Each problem is an SDP problem andcan be efficiently solved numerically, e.g., [94, 95].41Chapter 2. Joint Transmission in VLC SystemsRobust Design with Noisy CSIAs noted above, the average sum-MSE is considered. Defining∆ = [δ1, . . . , δNU ]T , (2.41)the optimization problem can be formulated asP8 : (F ∗, c∗) = arg minF ,cE∆(NU∑k=1MSEk)C1 : ‖fn‖1 ≤ min (IDC − IL, IU − IDC) ,∀n (2.42)Following the steps in Eq. (2.18) and Eq. (2.20) and assuming Σk = σ2eI, we canwrite the objective of P8 asE∆ (f(F , c)) = (‖cAˆf − b‖22 +NUσ2ec2‖f‖22) + c2σ2sum , (2.43)where Aˆ = Hˆ⊗I, and Hˆ is the estimated channel matrix. While P8 is not a convexoptimization problem, again the application of alternating optimization for F and cturns out to be a suitable approach. When fixing the receiver gain c, we can optimizefor F viaP9 : (f ∗, t∗) = argminf,t(‖cAˆf − b‖22 +NUσ2ec2‖f‖22) + c2σ2sum (2.44)C1 : −t  f  t ,C2 : V t  min (IDC − IL, IU − IDC) 1NU×1 .42Chapter 2. Joint Transmission in VLC SystemsThis problem is a convex quadratic programming problem, which is solved numeri-cally. Fixing the precoder F leads to the closed-form solutionc∗= argminc{‖cAˆf − b‖22 +NUσ2ec2‖f‖22}+ c2σ2sum=sym(bT Aˆf)‖Aˆf‖22 +NUσ2e‖f‖22 + σ2sum.(2.45)2.4.3 Minimal Illumination Level ProblemWe finally turn to the robust design for minimizing the required illumination levelwhile achieving a required VLC performance.Robust Design with Outdated CSITo add robustness to the precoder design for minimal required brightness when CSIis outdated, the worst-case MSE needs to satisfy the required performance qk:max‖δk‖2≤kMSEk ≤ qk,∀k. (2.46)Making use of the Schur complement lemma [97, 98] and [101, Lemma 2], Eq. (2.46)is equivalent to ∃ λk ≥ 0,Ψk =√qkζ − λk vˆTk σk 0vˆk√qkζI 0 −kF Tσk 0√qkζ 00 −kF 0 λkI 0,wherevˆTk = (hˆTkF − ζeTk ) . (2.47)43Chapter 2. Joint Transmission in VLC SystemsHence, we obtain the optimization problemP10 : (F ∗, ζ∗, I∗DC) = argminF ,λ,ζ,IDCIDCC1 : −tk  F Tek  tk,∀k,C2 : 1T tk ≤ min (IDC − IL, IU − IDC) , ∀k,C3 : Ψk  0, ∀k,C4 : λk ≥ 0,∀k. (2.48)This problem is an SDP and the global optimum can be obtained on the conditionthat it is feasible.Robust Design with Noisy CSIIn the case of noisy CSI, we need to replace C1 in P4 (2.24) byEδk(MSEk) = c2vˆTk vˆk + c2σ2e‖F ‖2F + c2σ2k . (2.49)Introducing auxiliary variable r and τ k = [vˆTk r σk], Eδk(MSEk) ≤ qk becomesequivalent to‖τ k‖2 ≤ √qkζ‖F ‖F ≤ rσe(2.50)44Chapter 2. Joint Transmission in VLC SystemsTherefore, we can formulate the precoder design problem asP11 : (F ∗, ζ∗, I∗DC) = argminF ,{tk},{τk},ζ,r,IDCIDCC1 : −tk  F Tek  tk,∀kC2 : 1T tk ≤ min (IDC − IL, IU − IDC) ,∀kC3 : ‖F ‖F ≤ rσe,C4 : Υk  0,∀k (2.51)whereΥk = √qkζ τ kτ Tk√qkζI .This problem is again an SDP.2.5 Numerical Results and DiscussionsIn this section, we present and discuss the simulation results for the proposed MU-MISO VLC system assuming different coordination levels, user positions, interferencelevels and channel uncertainty scenarios in an indoor environment. We consider anexample setup of a room with NL = 4 coordinated and VLC-enabled LED luminairesat the ceiling. Room dimensions and luminaire locations are listed in Table 2.1. Thetable also summarizes the luminaire and LED parameters, where the latter applyto LXW8-PW40 Luxeon Rebel high power LEDs [102]. The illuminance level whenIDC = 500 mA, i.e., IDC = (IL + IU)/2, with this system setup is shown in Figure 2.4.According to [38], the illuminance level and uniformity (0.645 in this case) is sufficientfor office work and study. The background current of Ibg = 5100 µA accounts for45Chapter 2. Joint Transmission in VLC SystemsTable 2.1: Simulation parameters.Room SetupFixture coordinate 1 [1.25, 1.25, 3]Fixture coordinate 2 [1.25, -1.25, 3]Fixture coordinate 3 [-1.25, -1.25, 3]Fixture coordinate 4 [-1.25, 1.25, 3]Room Dimensions L × W × H 5 [m] × 5 [m] × 3 [m]Transmitter ParametersIL 400 [mA]IU 600 [mA]Semi-angle at half power φ 1260 [deg.]Dimensions of LED L × W × H 3 [cm]×3 [cm]×2 [cm]LED interval 1 [cm]Number of LEDs per luminaire NE 36 (6×6)Receiver ParametersPD area 1 cm2Refractive index of optical concentrator κ 1.5Receiver FOV 60 [deg.]System bandwidth B 10 [MHz]Noise bandwidth factor I2 0.562Background current Ibg 5100 [µA]LED conversion factor s 0.44 [W/A]PD responsivity γ 0.30 [A/W]ambient light from other sources such as sunlight or non-VLC enabled luminaries,and the thermal noise is considered negligible [8].5In the following, we assume that the VLC system transmits to NU = 4 users. Forconcreteness, we further assume that the four users are centro-symmetrically locatedon the plane at height z = 0.8 m, i.e., the user coordinates are (±x,±y, 0.8) m forsome x and y. We would like to emphasize that the specific system parameters, inparticular the values of NL and NU, are chosen for the sake of illustration of precodedtransmission only, and that our system design approach is applicable to any parameter5We also ran simulations assuming Ibg value of 620 µA [27]. We found that the main trends ofour results as discussed in the following are not affected by the value of the background current.46Chapter 2. Joint Transmission in VLC Systems−2−1012−2−1012200300400500600700x (m)y (m)Illuminance (lx)Figure 2.4: The distribution of indoor illuminance when IDC = 500 mA.pair (NL, NU).In the subsequent sections, we report performance results for different transmis-sion scenarios and precoder designs. Due to symmetry, the performance for theNU = 4 users are identical, and thus we can drop the user index for the results. Ifnot stated otherwise, perfect CSI for the precoder design is assumed. For solvingthe sum-MSE minimization problems via alternating optimization, the alternatingminimization will converge to a solution since the non-negative objective functionis minimized at each convex subproblem. The zero-forcing solution is used for ini-47Chapter 2. Joint Transmission in VLC Systemstialization and the maximum number of iterations6 is set to 20. For solving theconvex optimization problems in this chapter, we use the YALMIP toolbox [94] inconjunction with the MOSEK solver [103] to obtain the result numerically.2.5.1 User Position with Joint Transmission SetupWe first investigate the achievable performance for a VLC broadcast system whereLED luminaries are fully connected by a PLC backbone network and coordinated bya PLC controller. The users are arranged in three different setups as shown in thefirst three arrangements in Fig. 2.5, where x = y = 0.5 in Setup I, x = y = 1.25 inSetup II and x = y = 2 in Setup III, respectively. The channel matrices for thesethree setups are obtained asH I = 10−56.164 3.067 1.829 3.0673.067 6.164 3.067 1.8291.829 3.067 6.164 3.0673.067 1.829 3.067 6.164,H II = 10−59.340 1.788 0.731 1.7881.788 9.340 1.788 0.7310.731 1.788 9.340 1.7881.788 0.731 1.788 9.340,6The maximum number of iterations for Chapters 3 and 4 is also set to 20.48Chapter 2. Joint Transmission in VLC SystemsFigure 2.5: User-configurations for MU-MISO VLC are considered for numericalresults.H III = 10−56.164 0.863 0.000 0.8630.863 6.164 0.863 0.0000.000 0.863 6.164 0.8630.863 0.000 0.863 6.164.Figure 2.6 shows the results of the sum-MSE minimization problem as a functionof the DC bias IDC, i.e., the illumination level, for the three user-configurations fromFigure 2.5. Here we use the resulting optimal precoder to calculate the correspondingSINR defined asSINR =‖hTkwk‖22‖hTk∑i 6=k wi‖22 + σ2k. (2.52)First, we observe that the system performance is symmetric with respect to IDC =(IL + IU)/2. The SINR first increases as the DC bias IDC increases and then startsto decrease after IDC surpasses (IL + IU)/2. This is because the electrical SINRs atthe receivers reach their maximal values when the precoded signal sn has the largestdynamic range. Due to this symmetry property, we will only plot the results for IDCranging from IL to (IL + IU)/2 in the following figures. For varying positions of the49Chapter 2. Joint Transmission in VLC Systems400 420 440 460 480 500 520 540 560 580 600−50510152025303540IDC (mA)SINR (dB)  Setup ISetup IISetup IIIFigure 2.6: Comparison of system performance with different user positions (as shownin Figure 2.5) as a function of illumination level. Sum-MSE minimization with perfectCSI.50Chapter 2. Joint Transmission in VLC Systemsfour users, the setups in increasing order of SINR value are Setup I, Setup III andSetup II. An intuitive explanation is that since the users in Setup I are closer toeach other than in Setup III, the channels are more similar and thus more difficult toseparate through precoding. Meanwhile, the distances between the LED luminariesand users in Setup III are larger than those in Setup II, which leads to smaller channelgains in Setup III than in Setup II.The SINR defined in (2.52) can be used to approximate the symbol error rate(SER) of the VLC transmission. For this, we assume that the interference is Gaussiandistributed, so that the SER can be expressed as [104]SER = Q(√2 SINR), (2.53)where Q(·) is the Gaussian tail probability function. In Figure 2.7, we plot the SERaccording to (2.53) as the function of DC bias IDC under Setup I. We also include theSER results obtained from Monte Carlo simulations of the tranmission. We observethat the two curves do not closely overlap, which speaks to the inaccuracy of theGaussian approximation for the VLC interference. We expect that this approxima-tion becomes more accurate if more interferers are present as well as if high-ordermodulation is used. Furthermore, as expected, we note that SER monotonically im-proves with SINR also in the simulated SER case. Hence, we can well consider SINRas a proxy for the SER performance.We now highlight the benefit of coordination. To this end, we consider threedifferent coordination levels:1. Joint Transmission (JT): Transmissions for all four LED luminaires are coordi-nated.51Chapter 2. Joint Transmission in VLC Systems400 405 410 41510−610−510−410−310−210−1100IDC (mA)Symbol Error Rate (SER)  SER calculated with Equation (2.53)SER with Monte Carlo simulationFigure 2.7: Comparison of the SER calculation using Equation (2.53) with MonteCarlo simulation result.52Chapter 2. Joint Transmission in VLC Systems      (1) JT (2) PC (3) UTLED LuminaireCoMP-AttocellPower Line PLC ControllerFigure 2.8: Different transmitter coordination levels in an MU-MISO VLC system.2. Partial Coordination (PC): Transmissions for LED luminaires in the first andthe fourth quadrant and for LED luminaires in the second and the third quad-rant are coordinated. Thus there exist two VLC CoMP-attocells in one room.3. Uncoordinated Transmission (UT): Transmissions at the four LED luminairesare not coordinated, which corresponds to four VLC CoMP-attocells in oneroom.The three coordination levels are illustrated in Fig. 2.8.We consider two scenarios for user locations: Setup IV with x = 2, y = 1.25 andSetup V with x = 0.5, y = 1.25. Figure 2.9 shows the SINR for precoder designminimizing the sum-MSE as a function of IDC for different coordination levels anduser position scenarios. We observe that, since users are located closer to each otherand/or the neighbouring CoMP-attocell boundary in Setup V than for Setup IV, theachievable SINR is generally higher for the latter. We can also see the significant SINRincrease due to coordination. In particular, the JT setup is clearly outperforming the53Chapter 2. Joint Transmission in VLC Systems400 410 420 430 440 450 460 470 480 490 50005101520253035IDC (mA)SINR (dB)  JTPCUTSetup VSetup IVFigure 2.9: Comparison of system performance with different transmitter coordina-tion. Sum-MSE minimization problem with perfect CSI.PC and UT systems, whose SINR saturates quickly due to inter-cell interference.For Setup V, there is no performance difference for UT and PC systems, whichis due to the remaining large inter-CoMP-attocell interference in spite of the partialcoordination. In the PC system, each VLC transmitter tends to mostly communicateto its closest receiver, which makes the PC system equivalent to a UT system.The benefit of coordination is further demonstrated by the plots in Figure 2.10,which show the SINR for one quadrant of the room as a function of the user’s location(because of the symmetry of the four user’s location, the SINR plots for the other54Chapter 2. Joint Transmission in VLC Systems0 0.5 1 1.5 2 2.500.511.522.5  x (m) y (m)−50510152025303540SINR (dB)(a) JT system0 0.5 1 1.5 2 2.500.511.522.5  x (m) y (m)−50510152025303540SINR (dB)(b) UT systemFigure 2.10: SINR as a function of user location in one quadrant of the room andIDC = (IL + IU)/2. Sum-MSE minimization problem with perfect CSI.quadrants are mirrored versions of those in Figure 2.10) and for IDC = (IL + IU)/2.It can be seen that the SINR is severely IAI-limited in the UT case, and that thisproblem can be overcome by coordination. In particular, the SINR for the JT systemis uniformly high in almost the entire service area. Note that the lower SINR at thecell boundaries is an artifact of assuming centro-symmetrical user locations in ourexperiments, which means that at cell boundaries users are close to each other andthus interference is relatively high.2.5.2 Sum-MSE Minimization with Channel UncertaintyWe now abandon the assumption of perfect CSI and consider channel uncertaintyaccording to the models from Section 2.4.1. For the case of outdated CSI, we consideran assumed user location based on which we obtain a channel estimate hˆk. Then,given a distance bound L, we obtain a CSI bound k from numerical evaluation as55Chapter 2. Joint Transmission in VLC Systemsshown in Section 2.4.1 (see Figure 2.3). Given hˆk and k, the precoder F is obtainedvia P7 (2.40). Then, a set of actual channel gains h and associated SINRs (2.52) aregenerated by placing users uniformly at random into the uncertainty region. For thenoisy CSI case, we use Σk = σ2eI and specify the error variance σ2e .Figures 2.11 and 2.12 show the SINR performance for the JT system with robustprecoder design according to the sum-MSE criterion. The results are shown as afunction of the channel uncertainty and parametrized with DC bias IDC. Setup IIfrom Figure 2.5 with x = 1.25 and y = 1.25 is used to calculate the channel estimatehˆk and 5000 possible channel realizations hk either according to the uncertaintybound k or the normalized error standard deviation σ¯e = σe/(‖vec(Hˆ)‖1/(NLNU)).The minimum achieved SINR among channel realizations is plotted for the case ofoutdated CSI, while the average SINR over channel realizations is plotted for the caseof noisy CSI. From the figures, we can see that system performance improves as theDC bias IDC increases, until the CSI uncertainty at the transmitter limits the SINR.Furthermore, the decline of SINR with uncertainty is less pronounced for the averageperformance measure considered in Figure 2.12. The worst-case optimization for thecase of outdated CSI provides performance guarantees, which however diminish withincreasing uncertainty, as shown in Figure 2.11.2.5.3 Minimal Illumination Level ProblemWe again consider the Setup II from Figure 2.5 with x = 1.25 and y = 1.25, andJT. Figure 2.13 shows the minimum illumination level, i.e., DC bias IDC, that isrequired to meet the VLC MSE levels qk of each user terminal. The different curvesare for perfect CSI (L = 0) and outdated CSI (L > 0), and they quantify to whatextent VLC is possible when lights are dimmed. The perfect CSI case shows the best56Chapter 2. Joint Transmission in VLC Systems0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5152025303540L (m)SINR (dB)  IDC = 425mAIDC = 450mAIDC = 475mAIDC = 500mAIDCFigure 2.11: Robust sum-MSE minimization with outdated CSI. Setup II with x =1.25 and y = 1.25.possible trade-off between illumination level and achievable performance. When CSIuncertainty comes into play, it increases the required illumination level and even-tually limits the achievable performance. That is, the larger the uncertainty region(quantified by L), the earlier the problem becomes infeasible, i.e., MSE constraintscannot be met regardless of illumination level.2.5.4 Comparison between Robust and Non-Robust DesignFinally, we illustrate the benefits of the robust design in the case of CSI uncer-tainty. To this end, Figure 2.14 compares the SINR performances of the robust and57Chapter 2. Joint Transmission in VLC Systems10−3 10−2 10−1 100510152025303540σ¯eSINR (dB)  IDC = 425mAIDC = 450mAIDC = 475mAIDC = 500mAIDCFigure 2.12: Robust sum-MSE minimization with noisy CSI. Setup II with x = 1.25and y = 1.25.non-robust precoder designs when CSI is outdated. Similar to Figure 2.10, SINRperformance for one quadrant of the room is plotted as a function of the assumeduser location, according to which hˆk is obtained. The actual user location is sampledin a circle with radius L, from which the channel gain hk follows. Figure 2.14 shows,for each assumed location, the minimum SINR over the uncertainty region. The DCcurrent IDC is fixed as IDC = (IL + IU)/2.We observe that especially for locations close to the boundaries of two cells therobust design significantly outperforms the non-robust approach. This is due tothe possibly large mismatch between assumed and actual channel gains, which also58Chapter 2. Joint Transmission in VLC Systems10−4 10−3 10−2 10−1 100400410420430440450460470480490500qkI DC (mA)  L = 0.00 mL = 0.25 mL = 0.50 mFigure 2.13: Robust illuminance minimization with perfect (L = 0) and outdated(L > 0) CSI. Setup II with x = 1.25 and y = 1.25.affects the expected amount of interference, and which is not taken into accountin the non-robust design approach. For example, for the case of L = 0.25 m, theaverage SINR value on the boundaries of two cells is improved from −25.99 dB to−0.69 dB via the robust design. On the other hand, closer inspection of the resultsshows that for locations further from the boundaries between cells, the precoder fromthe non-robust design achieves a somewhat better SINR than the robust precoder.For example, at the location (x, y) = (0.375, 1.000), the worst-case SINR for therobust design is 4.4 dB, while it is 6.2 dB for the non-robust design. The reason forthis is the conservativism of the robust design, which considers the worst case for59Chapter 2. Joint Transmission in VLC Systemsall hypothetical gains from the bounded region Rk ={hk∣∣∣hk=hˆk+δk‖δk‖2≤k }, even thoughonly a subset of these channel gains do actually occur inside the location uncertaintyregion. Nevertheless, the results in Figure 2.14 demonstrate the advantage of therobust optimization for VLC broadcasting in the case of imperfect CSI, in that theSINR is more consistently high over the entire attocell area and when different usersare close to each other.2.6 ConclusionIn this chapter, we have studied transmission to multiple user terminals using VLCattocells. Considering the inter-attocell interference as a result of the broadcast na-ture of VLC, we have proposed the coordination of transmission in different attocells.These coordinated VLC attocells form CoMP-attocells, similar to CoMP-cells in RFcellular networks. We have derived new linear precoding schemes that reduce intra-CoMP-attocell interference with the objective of optimizing system performance givenan illumination level and retaining a required performance at minimal illuminationlevel, respectively. Our numerical results for a typical VLC scenario have clearlydemonstrated the improvements of receiver-side SINR due to the proposed coordina-tion. As a second important contribution, we have extended the precoding methodsto include channel uncertainty, which would occur, for example, in the case of mov-ing terminals. Simulation results have shown that these robust precoding schemesmitigate performance drops that stale channel information causes when assumed tobe accurate.60Chapter 2. Joint Transmission in VLC Systems0 0.5 1 1.5 2 2.500.511.522.5  x (m) y (m)−15−10−505101520253035SINR (dB)(a) Robust Design (L=0.25m)0 0.5 1 1.5 2 2.500.511.522.5  x (m) y (m)−15−10−505101520253035SINR (dB)(b) Non-Robust Design (L=0.25m)0 0.5 1 1.5 2 2.500.511.522.5  x (m) y (m)−15−10−505101520253035SINR (dB)(c) Robust Design (L=0.5m)0 0.5 1 1.5 2 2.500.511.522.5  x (m) y (m)−15−10−505101520253035SINR (dB)(d) Non-Robust Design (L=0.5m)Figure 2.14: Comparison between robust and non-robust design for sum-MSE mini-mization problem with outdated CSI.61Chapter 3Coordinated Beamforming in VLCSystems3.1 IntroductionAs we can see from the previous chapter, uncoordinated VLC attocells will stronglyinterfere with each other. In fact, it has been shown that the degradation in SINR forusers at the edge of the attocell can be as severe as 30 dB. The proposed JT schemecan greatly enhance the user performance through transmitter cooperation. However,both the global user data and channel state information need to be exchanged amongtransmitters of different attocells in the JT scheme, which puts a high requirementon the backbone network. What is more, in order to ensure that signals emitted fromdifferent transmitters arrive at the receiver at the same time, tight synchronizationis required among the scattered VLC transmitters. In this chapter, we propose theCB scheme for downlink interference mitigation among coexisting VLC attocells uti-lizing multi-luminaire transmitters. Compared to the JT scheme, the proposed CBscheme places lower requirements on the network in terms of backbone traffic, andis easier to implement in a practical deployment, though at the cost of compromisedperformance. In this chapter, we investigate the downlink transmission of coordi-nated VLC attocells and focus on its transmitter design. We adopt the weighted summean square error (WSMSE) as the performance metric to take into consideration62Chapter 3. Coordinated Beamforming in VLC Systemsinterference, noise, and fairness among users in system optimization. We considerthe WSMSE minimization problem with linear beamforming restricted by amplitudeconstraints. Such constraints arise from dynamic range limitations in typical LEDs.Moreover, similar to Chapter 2, we extend our design method to take into accountpossible mismatches in channel information available to the transmitters. We providenumerical examples to illustrate the performance of the proposed CB scheme in typi-cal VLC scenarios. We also quantify the performance gap among several coordinationschemes including JT and CB.The remainder of the chapter is organized as follows. We introduce the systemmodel and transmission scheme in Section 3.2. In Section 3.3, the design algorithmsfor CB are proposed assuming perfect downlink CSI at VLC transmitters. In Section3.4, the design for CB is extended to the case of imperfect CSI. Numerical resultsand discussions are provided in Section 3.5, and finally, we conclude the chapter inSection 3.6.3.2 System Model and Transmission SchemeIn this section, we first describe the system model and transmission scheme for theconsidered multi-cell VLC system. We then specify the constraints imposed on thelinear beamformer to satisfy the amplitude constraints on the transmitted signal.3.2.1 System ModelWe consider a downlink VLC system composed of NA coordinated attocells that canexchange information with each other through a band-limited backbone network (seeFigure 3.1). Each attocell is composed of one VLC transmitter that employs NLLED luminaires, and each luminaire has NE LED bulbs. Such luminaires can be63Chapter 3. Coordinated Beamforming in VLC SystemsCentralized Controller NA VLC attocellsBackbone NetworkMulti-luminaire VLC transmitter LED luminaire Single-photodiode VLC userNL Luminaires per TransmitterFigure 3.1: Illustration of the CB structure.modulated independently of each other using separate drivers. Each attocell servesNU single-PD users, and each user is served by a single attocell. Therefore, we havea multi-cell MU-MISO scenario.3.2.2 Transmission SchemeWe considerM -ary pulse amplitude modulation (M -PAM) as the modulation scheme,with M = 2, 4, 8, 16, . . . . Let dik ∈ {−1, 3−MM−1 , 5−MM−1 , . . . , 1}, i = 1, . . . , NA, k =1, . . . , NU, denote the data symbol intended for the kth user in the ith attocell, andlet di = [di1 , . . . , diNU ]T denote the vector of data symbols intended for all the users inthe ith attocell. Note that the entries of di are independent, and thus the covariance64Chapter 3. Coordinated Beamforming in VLC Systemsmatrix of di is η2I, where I represents the identity matrix andη =√M + 13(M − 1) . (3.1)Using linear beamforming, the transmitted signal vector at the ith attocell is con-structed asxi = F idi + IiDC , (3.2)where F i ∈ RNL×NU is the beamforming matrix, and I iDC = [I i1DC, I i2DC, · · · , IiNLDC ]T isa DC term that sets the illumination level. Note that the zero-mean nature of thedata vector di ensures that the illumination level is unaffected by data transmission.For the kth user in the ith attocell uik , the received signal can be decomposed intothree parts:1) Intra-attocell Signal: We use yintraik to represent the signal component generatedwithin the ith attocell and it is given byyintraik = hTikixi = hTikifki dik + hTikiNU∑m=1,m 6=kfmi dim + hTikiI iDC , (3.3)where hikj ∈ RNL×1 denotes the channel gain vector between uik and the VLC trans-mitter of the jth attocell, and fki is the kth column vector of F i.2) Inter-attocell Interference: Besides the intra-attocell signal, user uik also re-ceives interfering signals from neighboring attocells. The total interfering signal fromall the other attocells yinterik can be expressed asyinterik =NA∑j=1,j 6=ihTikjxj =NA∑j=1,j 6=iNU∑m=1hTikjfmj djm +NA∑j=1,j 6=ihTikjIjDC . (3.4)65Chapter 3. Coordinated Beamforming in VLC Systems3) Receiver noise: The dominant noise at user uik , denoted as nik , can be modelledas a zero-mean Gaussian variable with variance calculated by Eq. (1.3), where theaverage current due to the useful received signal at the user uik , Iik (Irp in Eq. (1.3)),can be calculated byIik =NA∑j=1hTikjIjDC . (3.5)The total received signal yˆik at user uik is the sum of the three components mentionedabove, and can be expressed asyˆik = yintraik+ yinterik + nik (3.6)= hTikifki dik︸ ︷︷ ︸desired signal+ hTikiNU∑m=1,m 6=kfmi dim︸ ︷︷ ︸intra-attocell interference+NA∑j=1,j 6=iNU∑m=1hTikjfmj djm︸ ︷︷ ︸inter-attocell interference+NA∑j=1hTikjIjDC︸ ︷︷ ︸DC photocurrent+ nik︸︷︷︸noise.At the receiver, the DC component∑NAj=1 hTikjIjDC is removed via AC coupling, leavingthe information-carrying signal at uik asyik = yˆik −NA∑j=1hTikjIjDC . (3.7)3.2.3 Design ConstraintsFor the illumination uniformity of the indoor environment, we shall assume that allthe LEDs are driven by an equal DC bias, i.e.,I ikDC = IDC, ∀i, k. (3.8)66Chapter 3. Coordinated Beamforming in VLC SystemsFor typical current-driven LEDs, though the nonlinear characteristic for current-light conversion can be compensated by pre-distorters installed before the LED, thedynamic range of LEDs is still inherently limited. Thus, the current signal shouldsatisfy a certain amplitude constraint to avoid signal clipping. To ensure that theLED operates within its physical limits, the beamforming matrix F i should satisfythe constraint (2.14):‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k, (3.9)where fki represents the kth row in F i, and IU > IL > 0 represent the upper and thelower bound of the LED drive current in the linear region.3.3 Transmitter Design with Perfect ChannelInformationSimilar to Chapter 2, we consider MMSE beamforming design in this chapter. Linearbeamformers can achieve reasonable throughput performance with considerably lowercomplexity relative to their nonlinear counterparts. Two major linear beamformingtechniques are ZF beamforming and MMSE beamforming. ZF beamforming cancelsout multi-user interference through channel inversion. However, ZF is infeasible whenthe number of luminaries in each attocell is less than the total number of users of allthe coordinated attocells [74]. Furthermore, ZF has relatively poor performance inlow SNR regions [105]. In comparison, MMSE beamforming has less strict require-ments on the number of luminaires per attocell, and outperforms ZF beamformingin noise-limited scenarios as it also takes into account the receiver noise in designoptimization [106].67Chapter 3. Coordinated Beamforming in VLC SystemsWe consider a linear receiver at the VLC user, so the estimated received signaldˆik at uik can be expressed asdˆik = cikyik , (3.10)where the scaling factor cik is the receive filter for user uik . Then the mean squareerror (MSE) for user uik can be calculated asMSEik = Ed,n‖dˆik − dik‖22 (3.11)= η2‖cikhTikiF i − eTk ‖22 + η2NA∑j=1,j 6=i‖cikhTikjF j‖22 + c2ikσ2ik ,where ek is the kth standard basis vector for the NU-dimensional space and is ex-pressed in (2.16). Note that the second term results from the inter-attocell interfer-ence and is absent in the MSE expression of JT (See Eq. (2.25)). In this section,we aim at optimizing the system performance subject to the LED dynamic rangeconstraint (3.9) assuming the availability of perfect CSI at the transmitters. We usethe WSMSE as the performance measure so that the possibly different priorities ofdifferent users can be considered in system design. More specifically,WSMSE =NA∑i=1WSMSEi =NA∑i=1NU∑k=1wikMSEik , (3.12)where WSMSEi represents the WSMSE of the ith attocell, and wik > 0 denotesthe priority (weight) of user uik at the current scheduling slot according to somecriteria. Considering the constraint (3.9) on the beamforming matrix, the WSMSE68Chapter 3. Coordinated Beamforming in VLC Systemsminimization problem can be formulated asP1 : min{F i},{cik}WSMSE (3.13)C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k .When wik = 1 ∀i, k, P1 degenerates to the sum-MSE optimization problem whichmay impose unfairness across users. More generally, the weights wik can be updatedover time to maintain fairness among terminals. Designing the optimal weights forthe system is outside the scope of the chapter. Instead, we focus on obtaining thesolution to the optimization problem for a given set of weights. The objective functionin optimization problem P1 is biconvex in terms of beamforming matrices {F i} andscaling factors {cik} [83]. Fixing either of these two groups of variables will result ina (convex) quadratic optimization problem. Here we use the alternating optimizationmethod to, possibly suboptimally, solve the problem. Fixing beamforming matrices{F i}, we can obtain the closed-form expression for the optimal MMSE receiving filterc∗ik =η2hTikifkiη2∑NAj=1∑NUm=1 ‖hTikjfmj ‖22 + σ2ik,∀i, k. (3.14)We also need to acquire the optimal beamforming matrices {F i} given fixed scalingfactors {cik}. For notational simplicity, we defineH ij = [hi1j,hi2j, . . . ,hiNUj]T ,Ci = diag([ci1 , ci2 , · · · , ciNU ]T ),W i = diag([√wi1 ,√wi2 , · · · ,√wiNU ]T ),ni = [ni1 , ni2 , . . . , niNU ]T .69Chapter 3. Coordinated Beamforming in VLC SystemsThen WSMSEi can be expressed asWSMSEi =NU∑k=1wikMSEik = Ed,ni{∥∥W i(Ci( NA∑j=1H ijF jdj + ni)− di)∥∥22} (3.15)= η2∥∥((W iCiH ii)⊗ I) vec (F Ti )− vec (W i)∥∥22+ η2NA∑j=1,j 6=i∥∥((W iCiH ij)⊗ I) vec (F Tj )∥∥22 + NU∑k=1w2ikc2ikσ2ik .Define wi = vec (W i), Aij = (W iCiH ij)⊗I, f j = vec(F Tj), and V as the NLNU×NUNL block-diagonal matrix of the NL × NU all-one matrix. With fixed {cik}, P1can be transformed intoP2 : min{f i}NA∑i=1(η2 ‖Aiif i −wi‖22 + η2NA∑j=1,j 6=i∥∥Aijf j∥∥22 + NU∑k=1w2ikc2ikσ2ik)C1:− ti ≤ f i ≤ ti, ∀i ,C2: V ti ≤ min (IDC − IL, IU − IDC) 1NLNU×1, ∀i .P2 is a convex quadratic programming problem and can be efficiently solved by theMOSEK solver [103]. Once P2 is solved, the optimal beamforming matrices F j canbe retrieved from vector f j.For the suboptimal alternating optimization, the ZF beamformer can be used asthe initialization point to secure a satisfactory solution. Define the concatenation ofall channel matrices asH = [HT11, . . . ,HTNA1, . . . ,HT1NA , . . . ,HTNANA].When NL ≥ NANU, the general form for the transmit ZF beamformer of the ith70Chapter 3. Coordinated Beamforming in VLC Systemsattocell can be expressed as [74]:F ZFi =( NA∑j=1NA∑m=1NU∑k=1hjkmhTjkm)−HTii diag(Λi) =(HHT)−HTii diag(Λi) , (3.16)where Λi = [Λi1 ,Λi2 , . . . ,ΛiNU ]T and(HHT)−=(HHT)†+(I−(HHT )†(HHT )U i).Λik > 0 represents the symbol gain for dik , and U i is an arbitrary matrix. Then wehaveHjiFZFi = 0 i 6= j ,diag(Λi) i = j .In this chapter, we setU i =(HHT)†(HHT),Λi =min (IDC − IL, IU − IDC)maxm(∑NUk=1∣∣∣∣((HHT )†HTii)m,k∣∣∣∣)1NU×1 ,and we getF ZFi =(HHT)†HTii diag(Λi) . (3.17)Such a ZF beamforming matrix satisfies the constraint of P1 and can be used asthe initialization point for the alternating optimization algorithm. We note thatwhen NL < NANU, the inter-attocell and intra-attocell interference cannot be fullycanceled with the beamforming matrix (3.17). However, (3.17) still remains a wisechoice for the initialization purpose [74]. The algorithm for solving P1 is summarizedin Algorithm 3.1.71Chapter 3. Coordinated Beamforming in VLC SystemsAlgorithm 3.1 Alternating optimization algorithm for P11. Initialization:p⇐ 0.Update H ij with CSI.Initialize {F i}.2. repeat3. Update {cik} according to Eq. (3.14).4. Update {Aij} with {cik}.5. Solve P2 and get {F i}.6. p⇐ p+ 1.7. until ‖WSMSEp+1 −WSMSEp‖ ≤ δ (δ is a predefined threshold) or p = pmax(pmax is a predefined maximum iteration number).3.4 Robust Transmitter Design with ChannelUncertaintyThe linear beamforming design in the previous section is based on the premise ofperfect CSI. In practice, however, CSI at the transmitter side is usually contaminateddue to various factors like quantization, erroneous channel estimation or outdatedfeedback. Assuming an additive channel uncertainty model, the actual channel gaincan be expressed ashikj = hˆikj + δikj , (3.18)where hˆikj represents the channel estimate, and δikj represents the error vector re-sulting from channel uncertainty. As a result, the MSE for user uik can be expressed72Chapter 3. Coordinated Beamforming in VLC SystemsasMSEik = η2‖cik(hˆTiki+ δTiki)F i − eTk ‖22 + η2NA∑j=1,j 6=i‖cik(hˆTikj+ δTikj)F j‖22 + c2ikσ2ik .Typically, there are two classes of models to characterize δikj: the deterministicmodel and the stochastic model. For the deterministic model, we assume the actualchannel gain vector, although not exactly known, lies within a certain region withthe estimated nominal value at the center of the region. In this chapter, we assume‖δikj‖ ≤ , where  is some known constant and represents the level of uncertainty7.The goal of robust design with the deterministic model is to guarantee a certainperformance level for every possible channel realization, which is achieved throughoptimizing the worst-case performance by solving a min-max optimization problem[97, 107]. For the stochastic model, we model the elements of error vector δikj asGaussian distributed random variables. Particularly in this chapter, we assume δikj iszero-mean Gaussian distributed with covariance matrix σ2eI, where σe is some knownconstant. With the stochastic model, we aim at optimizing the average performance[97, 107].3.4.1 Robust Design with the Deterministic ModelIn this subsection, we apply the deterministic model to characterize the CSI imper-fection and aim at ensuring worst-case robustness through beamforming design. P17 We assume the same level of CSI uncertainty for each user in this chapter.73Chapter 3. Coordinated Beamforming in VLC Systemsis modified to the min-max optimization problemP3 : min{F i},{cik}max‖δikj‖2≤WSMSE =NA∑i=1NU∑k=1wikMSEik (3.19)C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k ,Using the Schur complement lemma [108] and [101, Lemma 2], P3 can be transformedintoP4 : min{F i},{ci},{λikj},{tikj},{gik}z2 (3.20)C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k ,C2 : Ψikj  0, ∀i, j, k ,C3 : Φik  0, ∀i, k ,C4 : λikj ≥ 0, ∀i, j, k ,C5 : κ  0,74Chapter 3. Coordinated Beamforming in VLC SystemswhereΨikj =tiki − λiki η(cikhˆTikiF i − eTk ) 0η(cik(hˆTikiF i)T − ek) tikiI ηcikF Ti0 ηcikF i λikiI i = j ,tikj − λikj ηcikhˆTikjF j 0ηcik(hˆTikjF j)T tikjI ηcikFTj0 ηcikF j λikjI i 6= j .(3.21)κ= z ωTω zI,Φik =gik tik1 . . . tikNA cikσiktik1... gikItikNAcikσik,ω = [w11g11 , . . . , w1NUg1NU , . . . , wNANUgNANU ]T .Similar to Algorithm 3.1 for P1, a local optimum of P4 can be obtained throughalternatively optimizing over {F i} and {ci}. Each problem is an SDP and can besolved numerically.75Chapter 3. Coordinated Beamforming in VLC Systems3.4.2 Robust Design with the Stochastic ModelFor the stochastic error model, we would like to secure the average system perfor-mance in the robust design. The optimization problem can be formulated asP5 : min{F i},{cik}E (WSMSE) =NA∑i=1NU∑k=1wikE (MSEik) (3.22)C1 : ‖fki ‖1 ≤ min (IDC − IL, IU − IDC) , ∀i, k .Alternating optimization can also be used to solve P5 which is a non-convex opti-mization problem. Fixing {cik}, P5 can be transformed intoP6 : min{F i}NA∑i=1(η2∥∥∥Aˆiif i −wi∥∥∥22+NA∑j=1,j 6=iη2∥∥∥Aˆijf j∥∥∥22+ Tr(W 2iC2i )η2σ2eNA∑j=1∥∥f j∥∥22+NU∑k=1w2ikc2ikσ2nik)C1:− ti  f i  ti, ∀i ,C2: V ti ≤ min (IDC − IL, IU − IDC) 1NLNU×1, ∀i ,where Aˆij =(W iCiHˆ ij)⊗ I and Hˆ ij =[hˆi1j, hˆi2j, . . . , hˆiNUj]T. P6 is a convexquadratic programming problem and can be solved numerically. Fixing {F i}, wehavec∗ik =η2hˆTikifkiη2∑NAm=1∑NUj=1(‖hˆTikmf jm‖22 + σ2e‖f jm‖22) + σ2ik,∀i, k.76Chapter 3. Coordinated Beamforming in VLC Systems3.5 Numerical Results and DiscussionsIn this section, we present our simulation results to demonstrate the performance ofthe proposed CB scheme. First, we compare the performance of VLC systems underdifferent coordination schemes. Then we show that a careful choice of the weightingvector can significantly improve fairness among users. Finally, we demonstrate theperformance gain of the adopted robust beamforming design given imperfect CSI.3.5.1 Simulation SetupWe consider OOK as the modulation scheme for the simulation, i.e., M = 2, andthus η = 1. This is perhaps the most practical transmission scheme for IM systemsbecause of simplicity and immunity to nonlinear distortion. We consider an indoorenvironment illustrated in Figure 3.2a for our simulation purposes. The coordinatesystem and the area planning8 are both shown in Figure 3.2b. The room dimensionsare 10×5×3 m3. Two multi-luminaire VLC transmitters (NA = 2) are installed in theceiling and are interconnected through a backbone network. Simulation parametersfor VLC transmitters and receivers are listed in Table 3.1. We consider two lightingsetups, where NL = 2, NE = 64 for Lighting Setup I (LS-I) and NL = 4, NE = 36 forLighting Setup II (LS-II). The coordinates of LED luminaires in each setup are listedin Table 3.2.As the primary function of VLC transmitters is illumination, we first investigatethe illumination performance of the two lighting setups. The illuminance distributionwith LS-I and LS-II are shown in Figure 3.3a and Figure 3.3b when IDC = 500 mA,8According to the DIN EN 12464-1 standard [38] for the planning and design of lighting instal-lations, the area planning for indoor workplaces defines both task area and immediate surroundingarea. The task area is defined as the area in which the visual task is carried out. The immediatesurrounding area is defined as a band surrounding the task area within the field of vision with aminimum width of 0.5 m.77Chapter 3. Coordinated Beamforming in VLC SystemsTable 3.1: Simulation parametersTransmitter ParametersIL 300 [mA]IU 700 [mA]Lambertian order m 1LED conversion factor s 0.44 [W/A]System Bandwidth B 10 [MHz]Receiver ParametersPD area APD 1 [cm2]Concentrator refractive index κ 1.5Receiver FoV ψc 60 [deg.]Noise bandwidth factor I2 0.562Background current Ibg 100 [µA]PD responsivity γ 0.30 [A/W]respectively. The corresponding average illuminance and uniformity of the task areaand the immediate surrounding area under both lighting setups are shown in Ta-ble 3.3. According to the DIN EN 12464-1 standard [38], the illuminance and uni-formity of both setups satisfy the requirements for office work and study. In thissection, we use the SINR as expressed in Eq. (3.23) as the metric for performancecomparison.SINRik =η2‖hTikifki ‖2η2∑NUj=1,j 6=k ‖hTikif ji ‖2 + η2∑NAj=1,j 6=i∑NUm=1 ‖hTikjfmj ‖2 + σ2ik(3.23)If not stated otherwise, we assume NU = 2 in the following. Note that the specificvalues of the system parameters M , NU, NA and NL chosen in this section are solelyfor the purpose of simulation illustration, and the system design can be applied toany values of M , NU, NA and NL.78Chapter 3. Coordinated Beamforming in VLC Systems(a) Room Illustration.10 m5 myxzabbabbaa(b) Illustration of office areas. The yellow zone is the immediate surrounding area, andthe red area is the task area. b = 0.5 m. Illuminance calculations can ignore a marginalstrip extending a = 0.5 m from the walls according to [38].Figure 3.2: Room Setup.79Chapter 3. Coordinated Beamforming in VLC SystemsTable 3.2: Luminaire coordinates of LS-I and LS-II(a) Lighting Setup I (LS-I), NL = 2, NE = 64.Attocell ILuminaire 1 [2.5, 1.25, 3]Luminaire 2 [2.5, -1.25, 3]Attocell IILuminaire 3 [-2.5, 1.25, 3]Luminaire 4 [-2.5, -1.25, 3](b) Lighting Setup II (LS-II), NL = 4, NE = 36.Attocell ILuminaire 1 [3, 1.25, 3]Luminaire 2 [3, -1.25, 3]Luminaire 3 [2, 1.25, 3]Luminaire 4 [2, -1.25, 3]Attocell IILuminaire 5 [-2, 1.25, 3]Luminaire 6 [-2, -1.25, 3]Luminaire 7 [-3, 1.25, 3]Luminaire 8 [-3, -1.25, 3]Table 3.3: Illumination performance of LS-I and LS-IILS-IIlluminance (lx) Uniformitytask area 624.7 0.604immediate surrounding area 506.6 0.496LS-IIIlluminance (lx) Uniformitytask area 695.6 0.662immediate surrounding area 571.3 0.5273.5.2 Comparison of Different Coordination LevelsWe first investigate the benefit of coordinated transmission for VLC systems. Weconsider three different coordination levels:1. Joint Transmission (JT): Both user data and CSI are shared among attocells,and the two attocells essentially merge into one single attocell, and operatetogether as a single MU-MISO system [57, 55, 54, 51, 56].2. Coordinated Beamforming (CB): Different from JT, only CSI is shared amongthe attocells. Based on the shared channel information, beamforming matricesfor different attocells are designed collaboratively to alleviate IAI.80Chapter 3. Coordinated Beamforming in VLC SystemsTable 3.4: User coordinates(a) User Distribution I (UD-I)Attocell IUser 1 [x1, 1.25, 0.8]User 2 [2.5, -1.25, 0.8]Attocell IIUser 3 [-2.5, 1.25, 0.8]User 4 [-2.5, -1.25, 0.8](b) User Distribution II (UD-II)Attocell IUser 1 [0.25, 0.25, 0.8]User 2 [0.25, -0.25, 0.8]Attocell IIUser 3 [-0.25, 0.25, 0.8]User 4 [-0.25, -0.25, 0.8](c) User Distribution III (UD-III)Attocell IUser 1 [0.25, 1.25, 0.8]User 2 [0.25, -1.25, 0.8]Attocell IIUser 3 [-0.25, 1.25, 0.8]User 4 [-0.25, -1.25, 0.8](d) User Distribution IV (UD-IV)Attocell IUser 1 [0.25, 2.5, 0.8]User 2 [0.25, -2.5, 0.8]Attocell IIUser 3 [-0.25, 2.5, 0.8]User 4 [-0.25, -2.5, 0.8]3. Uncoordinated Transmission (UT): Attocells are uncoordinated, and each atto-cell operates as an independent MU-MISO system when NL ≥ 2 and NU ≥ 2.In this subsection, we consider User Distribution I (UD-I) listed in Table 3.4. We setwik = 1,∀i, k, and thus P1 reduces to a sum-MSE minimization problem. We focuson the area wherein users will suffer from IAI, namely the region of −2 m ≤ x ≤ 2 munder our system setup (see Figure 3.2b).The benefit of the CB scheme is demonstrated in Figure 3.4. Figure 3.4a andFigure 3.4b plot the SINR of User 1 as a function of its x-axis coordinate x1 withLS-I and LS-II, respectively. In Figure 3.4a with LS-I, we can observe that JTproduces the best performance among the three schemes. As User 1 moves closer tothe edge of the neighboring attocell, i.e., x1 approaches zero, the achievable SINR81Chapter 3. Coordinated Beamforming in VLC Systemsy (m) x (m)02.55500Illuminance (lx)010000-2.5 -5(a) LS-Ix (m)y (m)02.55500Illuminance (lx)010000-2.5 -5(b) LS-IIFigure 3.3: The distribution of indoor illuminance for two lighting setups when IDC =500 mA.decreases dramatically due to the increasing interference from neighboring attocell,and the UT scheme suffers the most significant performance degradation due to thelack of coordination. For LS-I with NL = 2, CB provides an intermediate achievableSINR between that of JT and UT. For LS-II with NL = 4, as can be seen fromFigure 3.4b, the achievable SINR of User 1 with CB is almost the same as that withJT. In comparison to LS-I, LS-II has more transmission power and more degrees offreedom in the beamforming design, thus the resulting beamformer can direct moretransmission power onto the targeted user and leak relatively less interference toneighboring users at the same time.From Figure 3.4, it may seem that CB can replace JT as long as NL is largeenough. However, CB does have its limitations. In Figure 3.5, we consider three userdistributions for each lighting setup: UD-II, UD-III and UD-IV as listed in Table 3.4.The similarity of the three setups is that all users are located at the attocell edgeand are close to users in the neighboring attocell. For LS-I, we can observe that JTsignificantly outperforms CB and UT schemes, and the CB scheme can barely improve82Chapter 3. Coordinated Beamforming in VLC Systemsthe performance to a decent level. For LS-II, while CB can significantly increase theSINR in UD-III, the performance of UD-II still barely improves with CB. An intuitiveexplanation is that all users in UD-II are closer to each other, making the beamformerdifficult to target one user without interfering with another one. While for UD-IV,CB provides no improvement compared with UT for both lighting setups. The reasonis that each user in UD-IV can only be reached by one single luminaire of its belongingattocell, making interference mitigation through beamforming impossible.From the above results, we can see that although CB often displays comparableperformance with JT, the performance gap between JT and CB may become largewith specific user distributions. A possible solution is to apply Coordinated Schedul-ing (CS) jointly with the CB scheme across attocells to make sure that users withsuch distribution do not get served in the same time slot, so that we can enjoy thearchitectural benefit of CB while maintaining a comparable performance to JT.3.5.3 Importance of WeightFairness considerations are of particular importance for multiuser VLC systems. Un-like RF wireless communication, indoor VLC channels are free from multipath fadingdue to the large photodiode size compared with the optical wavelength. Consequently,the deterministic nature of the VLC channel will fix attocell-edge users in an infe-rior position if sum-MSE maximization is the only objective in system optimization.Therefore, the WSMSE design criterion is a desirable feature to ensure some level offairness among the users. In the WSMSE optimization problem P1, the weight vari-able wik represents the priority of user uik . The weight provides a tradeoff betweenmaximizing the total system throughput and balancing the fairness among users. Inthis subsection, we consider UD-I with x1 = 1 m and define w = [w11 , w12 , w21 , w22 ]T .83Chapter 3. Coordinated Beamforming in VLC Systems0 0.5 1 1.5 2x1 (m)020406080SINR  of  User 1 (dB)UTCBJT(a) LS-I (NL = 2)0 0.5 1 1.5 2x1(m)020406080SINR of User 1 (dB)UTCBJT(b) LS-II (NL = 4)Figure 3.4: SINR of User I as a function of its x-axis coordinate x1.84Chapter 3. Coordinated Beamforming in VLC SystemsWhen w = [1, 1, 1, 1]T , the user scheduling reduces to sum-MSE minimizing schedul-ing. The SINR values of 4 users when w = [1, 1, 1, 1]T are shown in Figure 3.6a. Wecan observe that SINR of User 1 is much lower than the rest of users. This is becausethe location of User 1 leads to strong inter-attocell interference from Attocell II. User1 will continuously suffer from low SINR as long as all users remain still. To maintaina level of fairness across users, we can adjust the weights of the users. For example,the SINR plot when w = [50, 10−7, 1.4, 2.2]T is shown in Figure 3.6b. We can observethat by tuning the weight, fairness across the users can be greatly improved, thoughthe sum-MSE is slightly compromised.3.5.4 Comparison between Robust and Non-Robust DesignIn this section, we assume NU = 1 for the ease of illustration, and present the benefitof robust design under CSI uncertainty. We plot the minimum SINR value as afunction of the assumed user location, according to which we obtain {hˆikj}. For afixed assumed user location, 105 realizations of actual channel vectors are generatedaccording to the error model Eq. (3.18) given a fixed  or σe. The minimum SINRvalue among those realizations can then be obtained. For concreteness, we furtherassume that the two users are symmetrically located on the plane of z = 0.8 m, i.e.,the user coordinates are (±x, y, 0.8) m for some x and y. Due to the symmetry,we only plot the SINR performance for one quadrant of the room in Figure 3.7 andFigure 3.8. From Figure 3.7 and Figure 3.8, we can observe that the expansion ofuncertainty region will deteriorate the system performance, and the robust design canimprove the performance of CB compared with the non-robust approach, especiallyin the region where attocell boundaries lie. The robust approach improves the VLCtransmitter design to avoid the large beamformer mismatch with the actual channels85Chapter 3. Coordinated Beamforming in VLC Systemsin spite of the CSI uncertainty, and keeps the SINR consistently high over the indoorenvironment, including attocell boundaries.3.6 ConclusionAttocell-edge users suffer from serious inter-attocell interference if universal frequencyreuse is applied in VLC systems. Although joint transmission can be applied as a so-lution to this problem, it puts high requirement on the VLC infrastructure in termsof backbone capacity and inter-attocell synchronization. In this chapter, an alter-native solution, i.e., coordinated beamforming, has been proposed for interferencemitigation in VLC downlinks, which requires less collaboration among attocells ascompared to joint transmission. We focused on the beamforming design subject tothe limited dynamic range of LED transmitters. Robust beamforming designs havealso been investigated to combat the uncertainty in CSI. Numerical results show thatthe coordinated beamforming scheme provides a good tradeoff between system per-formance and complexity, and validate the capability of the robust design againstchannel uncertainty.86Chapter 3. Coordinated Beamforming in VLC SystemsUD-II UD-III UD-IV-1001020304050SINR (dB)JTCBUT(a) LS-I (NL = 2)UD-II UD-III UD-IV-1001020304050SINR (dB)JTCBUT(b) LS-II (NL = 4)Figure 3.5: Comparison of system performance with different coordination levels forUD-II, UD-III and UD-IV.87Chapter 3. Coordinated Beamforming in VLC SystemsUser 1 User 2 User 3 User 4010203040506070SINR (dB)User 1 User 2 User 3 User 4010203040506070SINR (dB)Figure 3.6: (a) Left : w = [1, 1, 1, 1]T . (b) Right: w = [50, 10−7, 1.4, 2.2]T .88Chapter 3. Coordinated Beamforming in VLC Systems0 1 2 3 4 5x (m)00.511.522.5y (m)-20-100102030SINR (dB)(a) Non-Robust Design ( = 10−5)0 1 2 3 4 5x (m)00.511.522.5y (m)-20-100102030SINR (dB)(b) Robust Design ( = 10−5)0 1 2 3 4 5x (m)00.511.522.5y (m)-20-100102030SINR (dB)(c) Non-Robust Design ( = 2× 10−5)0 1 2 3 4 5x (m)00.511.522.5y (m)-20-100102030SINR (dB)(d) Robust Design ( = 2× 10−5)Figure 3.7: Comparison between robust and non-robust design with the deterministicmodel.89Chapter 3. Coordinated Beamforming in VLC Systems0 1 2 3 4 5x (m)00.511.522.5y (m)-20-10010203040SINR (dB)(a) Non-Robust Design (σe = 10−6)0 1 2 3 4 5x(m)00.511.522.5y(m)-20-10010203040x (m)SINR (dB)(b) Robust Design (σe = 10−6)0 1 2 3 4 5x (m)00.511.522.5y (m)-20-10010203040SINR (dB)(c) Non-Robust Design (σe = 5× 10−6)0 1 2 3 4 5x (m)00.511.522.5y (m)-20-10010203040SINR (dB)(d) Robust Design (σe = 5× 10−6)Figure 3.8: Comparison between robust and non-robust design with the stochasticmodel.90Chapter 4The Hybrid VLC-PLC System4.1 IntroductionMoving forward from the previous chapters, we specifically consider the PLC back-bone network for VLC front-ends in this chapter. PLC seems a more pragmatic choicethan Ethernet given that PLC is possible to leverage existing infrastructure alreadyin place at each luminaire [109, 110]. We note that the integration of VLC and PLCis not new, e.g., [87, 88]. However, the coordinating role of PLC for VLC in sucha hybrid HVP system, in which the PLC modem is connected to the outside accessnetwork and acts not only as a data source for VLC luminaires but also as a cen-tral controller for multiple luminaires, has only been presented recently [51, 55, 62].Backbone PLC systems are typically broadband in nature and employ OFDM [111].OFDM has also been adopted for VLC transmission, e.g., [11, 12, 112], to deal withthe frequency selectivity of the VLC channel. One of the challenges for an opticalOFDM implementation is the high PAPR of the time-domain signal. It leads to signaldistortion due to the non-negativity constraint for the optical time-domain signal anda reduced energy-efficiency for practical LED drivers with limited dynamic range. Toalleviate the PAPR problem, recently [81] designed and analyzed SO-OFDM schemes,in which (possibly overlapping) subsets of OFDM subcarriers are transmitted oversubsets of LEDs of a luminaire, and the entire OFDM signal results from spatialsumming. In the extreme case of a single subcarrier per LED, this leads to a PAPR91Chapter 4. The Hybrid VLC-PLC Systemof only 3 dB.In this chapter, we propose an HVP system for indoor downlink optical wirelessaccess utilizing the SO-OFDM technique. Compared to traditional VLC-PLC in-tegration, our system enables end-to-end use of OFDM modulation, alleviates thehigh PAPR problem of OFDM for LED transmitters, and enables the cooperationof multiple spatially distributed luminaires to overcome inter-luminaire interferenceand increase robustness against possible signal obstruction from a single luminaire.To this end, we make the following contributions.1. We develop the HVP system together with an analytical framework for itsachievable rate. Inspired by cooperative transmission techniques widely stud-ied in the RF domain, we consider the HVP system as a relay-assisted two-hopcommunication system without a direct link between the source and the des-tination. The LED luminaires act as full-duplex relays (transmit and receivesignals at the same time) and retransmit the received PLC signal to the uservia VLC. Considering the channel characteristics of PLC and VLC and the factthat VLC uses intensity modulation, i.e., the transmitted signal must be non-negative and operates under a peak amplitude constraint, we derive expressionsfor the rate that can be supported by the HVP system.2. We generalize SO-OFDM proposed in [81] by considering the joint subcarrierallocation (SA) among multiple spatially distributed LED luminaires, and wepropose several SA schemes for this SO-OFDM HVP system to exploit the fre-quency diversity of PLC and VLC channels, and multi-user diversity in the caseof multiple users. This includes a subcarrier pairing method that adaptivelymatches between incoming and outgoing subcarriers at the LED luminaire toaccount for the frequency selectivity of the two channels.92Chapter 4. The Hybrid VLC-PLC System3. For multi-user HVP systems, the SA schemes are developed for two possiblemultiple access schemes: OFDM time-division multiple access (OFDM-TDMA)and orthogonal frequency-division multiple access (OFDMA). SA of multi-userHVP systems is a non-trivial task due to the coupling of subcarrier pairing,relay selection and user selection, and the limited number of subcarriers perLED luminaire set by SO-OFDM. To reduce the computational complexity ofSA, we investigate the performance of chunk-based SA [113] and propose severalsuboptimal polynomial-time SA algorithms. We note that the contribution ofour work is not dependent on any specific OFDM signal format employed bythe VLC link. We adopt two variations of OFDM signal formats as the VLCmulticarrier solutions in this chapter due to their popularity. However, theproposed optimization framework can be easily extended to any other OFDMsignal formats in SO-OFDM-based HVP systems.The remainder of the chapter is organized as follows. In Section 4.2, we introducethe SO-OFDM-based HVP system, and present the channel and noise models forthe PLC and VLC links. In Section 4.3, different optical OFDM formats and relayprotocols are investigated for the HVP system, and the corresponding achievable rateexpressions are presented. In Section 4.4, computationally efficient SA algorithms,with and without SP, are proposed for the two multi-access schemes. Simulationresults for different variations of HVP systems are presented and discussed in Sec-tion 4.5. Finally, the conclusions are drawn in Section 4.6.93Chapter 4. The Hybrid VLC-PLC System4.2 System Model4.2.1 Problem ScenarioWe propose an SO-OFDM-based HVP system for downlink transmission to NU userslocated in the same room and served via the cooperation of NL LED luminaires,and each luminaire consists of NE LEDs. Figure 4.1 illustrates the system structureshowing a single user. The power line acts as the backbone network that feeds datato and coordinates cooperation among the multiple VLC-equipped LED luminaires,which in turn operate as full-duplex relays which process the received PLC signal andforward it via VLC to indoor users. Applying SO-OFDM across multiple luminaires,each luminaire only emits a subset of the data symbols from the received PLC OFDMsignal. The VLC signals from multiple LED luminaires superpose at the photo-diodedetectors of the users, where a conventional OFDM receiver can be used to decode theinformation. To achieve this, accurate time and frequency synchronization is requiredfor the VLC hop. Since both VLC and PLC OFDM are baseband modulated, carrierfrequency offset is absent and only timing needs to be taken care of. To resolve thetime synchronization problem resulting from the time difference of arrivals of users’signal at the luminaires, we can ensure that the cyclic prefix length of the OFDMsymbol is longer than the time difference of arrivals. Further considering the factthat the LoS link plays the major role in VLC systems [8], and the inter-luminairedistances between VLC transmitters in the indoor environment are relatively small,the situation here is relatively simpler compared to CoMP systems with RF imple-mentation [114]. In the rest of the chapter, we assume VLC transmitters are perfectlysynchronized. For the HVP uplink, one preferred choice is WiFi uplink (see Section1.3). The WiFi uplink, for the HVP system specifically, can be implemented through94Chapter 4. The Hybrid VLC-PLC SystemLED Luminary 1WiFi UplinkPLC modemOFDMDemodulationSubcarrierSelectionSubcarrierPermutationOFDMModulationLED Luminary 2OFDMDemodulationSubcarrierSelectionSubcarrierPermutationOFDMModulationOFDMDemodulationSubcarrierSelectionSubcarrierPermutationOFDMModulationLED Luminary NLPLC-WiFi integrated modemPLC Network...Figure 4.1: Block diagram of the HVP system.a PLC-WiFi integrated modem (which could act as the coordinator point), as illus-trated in Figure 4.1. Such an uplink would provide the CSI about the VLC links tothe coordinator point for system optimization.4.2.2 Transmitter and Receiver ModelFigure 4.2 shows a detailed block diagram of the SO-OFDM HVP system with respectto a specific luminaire relay. We note that the baseband OFDM signals transmit-ted over the PLC and VLC links satisfy the Hermitian symmetry property in thefrequency domain, and in the following, we will only describe the processing for theindependent information-carrying subcarrier sets (Pinfo and Vinfo in Section 4.3).In the PLC hop, the PLC modem broadcasts the same wideband OFDM signalto every LED luminaire containing Np independent information-carrying subcarriers.In the VLC hop, SO-OFDM is applied, and the kth luminaire re-modulates Nk of thereceived PLC data symbols onto Nk of Nv available VLC subcarriers. The Nv −Nkunused subcarriers are set to zero. The subcarrier subsets across different luminaires95Chapter 4. The Hybrid VLC-PLC Systemare disjoint and we have∑NLk=1Nk = Np. At each LED luminaire, we consider asubcarrier pairing approach which adaptively matches incoming with outgoing sub-carriers to fully exploit the frequency diversity of both PLC and VLC channels. Thenumber of subcarriers Nk and thus subcarrier pairs assigned to the kth luminairecannot exceed an upper limit in order to limit the PAPR of the OFDM signal at eachLED luminaire.We consider two operating modes for the LED luminaire relay, namely amplify-and-forward (AF) and decode-and-forward (DF). An AF-mode VLC relay demodu-lates the PLC signal, scales the selected subcarrier signals, and re-modulates themapplying subcarrier pairing. In addition to this, a DF-mode relay also decodes the re-ceived signal. Only if decoding is deemed successful, based on an outer error-detectioncode, the DF-mode relay will re-encode and re-modulate the data, and then forwardit to the destination.At the user side, the VLC analog front-end (AFE) consists of a photo-diodedetector to convert the optical to an electrical received signal and an AC coupler toremove the DC signal component, which is responsible for the primary illuminationfunction of the LED luminaires. This is followed by a conventional OFDM receiver.4.2.3 Channel and Noise ModelPower Line CommunicationTo faithfully model the signal transfer over the low-voltage power line network, weapply the bottom-up approach based on transmission-line theory as presented in[115, 116] and implemented in a simulator in [117], which leads to a distinctive PLCchannel for each LED luminaire based on the cable characteristics of its correspondingpower line branch. The noise in PLC systems consists of colored background noise,96Chapter 4. The Hybrid VLC-PLC SystemCyclic prefixremovalFFTQAM ModulationData input Hermitian symmetryInsertionIFFTPLC AFECyclic prefixinsertionPLCAFEPLCChannelPLC noiseS/P P/SS/PP/SDemodulationDecodeEncodeS/PModulationSubcarrierPairingIFFT P/SCyclic prefixinsertionPowerscalingClipping D/ADC biasVLC AFEVLCChannelVLC noiseCyclic prefixremovalFFTVLCAFES/PP/SDemodulationDecodeData outputPLC TransmitterLED LuminaryVLC ReceiverSubcarrierSelectionFigure 4.2: Detailed block diagram of the SO-OFDM HVP downlink system for oneluminaire and one user. Blocks with dashed lines are not present in LED luminairesoperating in amplify-and-forward mode.narrowband disturbance, and impulsive noise [111]. We model the first two termsthrough the combined power spectral density (PSD) of the shape as in [118, Eq.(4)], as also adopted in the IEEE 1901 standard [119, Annex F.3.5.2]. Impulse noiseis modeled as a non-stationary random process. For the purpose of mathematicaltractability, we disregard the impulse noise in the rate optimization. This is justifiedas the impulse noise events occur with relatively low probability (see. e.g. [120]) andif significant lead to outage events. Furthermore, one of the major components ofimpulse noise in the low-voltage power line is random aperiodic impulse noise. In thiscase, rate optimization considering the aperiodic noise for the purpose of adaptivetransmission is ineffective. Note that in all the numerical results presented in Section4.5, we will consider the impulse noise for the purpose of simulation accuracy, and weapply the two-state approximation as in [121, Eq. (19)] to calculate the achievable97Chapter 4. The Hybrid VLC-PLC Systemrate. To enable the reproducibility of the numerical results, we have made the PLCnoise simulator available online [122].Visible Light CommunicationThe VLC channel is frequency selective due to the low-pass characteristics of theLED emission and the multipath dispersion of the VLC signal. The latter startsto play a role when the transmitted signal is broadband [27], which is the case forthe considered HVP system. In this chapter, we take both the LoS link and NLoSlink (reflections) into consideration for the VLC channel modeling. We assume thatpropagation from either the LED source or a reflection point on the walls follows theLambertian radiation pattern. The channel gain h between the receiver (the user or areflection point on the walls) and the light source (the LED source or a reflection pointon the walls) can then be expressed using Eq. (1.2). Based on Eq. (1.2), we applythe modified Monte Carlo method presented in [34] to obtain the frequency-domainchannel gain HCL(f) in our simulations, and our source code written in MATLABis available at [123]. The first three reflections are taken into account as they carrymost of the VLC signal power. Together with the frequency response for the LEDemissions which can be approximated by [124]HLED(f) =11 + j ffLED, (4.1)with fLED representing the 3 dB cutoff frequency of the LED low-pass characteristics,the overall VLC channel gain can be expressed asHv(f) = HLED(f)HCL(f). (4.2)98Chapter 4. The Hybrid VLC-PLC SystemThe noise in VLC systems comprises shot noise, which is induced by ambient light,and thermal noise. The variance of the total VLC noise can be modeled as a zero-mean Gaussian random variable with variance σ2vn calculated by Eq. (1.3).4.3 Rate Analysis of the HVP SystemIn this section, we derive the expressions for the achievable rates for downlink trans-mission with the HVP system using different relaying strategies. More specifically,we consider the rate associated with a single OFDM subcarrier pair of the PLC-VLClink to a single user. Since different subcarriers are orthogonal and users are multi-plexed over orthogonal subcarriers or time slots, rate expressions of the total HVPsystem follow then immediately.4.3.1 Signal at the PLC HopThe baseband PLC OFDM signal uses the set Pinfo of information-carrying subcarri-ers, where |Pinfo| = Np. Denoting the PLC frequency-domain transmitted symbol atsubcarrier l as Xp(l), and with the usual assumptions about sufficient cyclic-prefixlength, synchronization, and channel time-invariance, the PLC frequency-domain sig-nal Y kp (l) at subcarrier l received by the kth LED luminaire can be expressed asY kp (l) = Hkp(l)Xp(l) +Nkp (l) , (4.3)where Hkp(l) and Nkp (l) are the PLC channel gain and noise for subcarrier l at thekth LED luminaire, respectively. The corresponding SNR isSNRkp(l) =∣∣Hkp(l)∣∣2σ2pσ2pn,k(l), (4.4)99Chapter 4. The Hybrid VLC-PLC Systemwhere σ2p = E[|Xp(l)|2] and σ2pn,k(l) = E [∣∣Nkp (l)∣∣2].4.3.2 Signal at the VLC HopThe kth VLC transmitter modulates Nk subcarriers from the set Vinfo of activeinformation-carrying subcarriers, and |Vinfo| = Nv. Denoting the frequency-domaintransmitted symbol over subcarrier l as Xkv (l) and the size of the discrete Fouriertransform applied for VLC as Nvfft, the time-domain samples at each element of thekth luminaire can be expressed asxkv,info(n) =1√NvfftNvfft−1∑l=0Xkv (l)exp(j2pinlNvfft), (4.5)where Hermitian symmetry Xkv (l) =(Xkv (Nvfft − l))∗ holds, and only 2Nk out of NvfftXkv (l) are non-zero due to SO-OFDM (see Section 4.2.2). The signal xkv,info(n) isused to modulate the intensity of the LED luminaire. To make the signal compatiblewith the IM/DD channel, in the following we consider both DCO-OFDM and ACO-OFDM, which are the two popular forms of intensity-modulated optical OFDM [43,44].Since an LED as a transmitter has a limited dynamic range, the time-domainOFDM signal may be clipped due to a high PAPR [39]. Let IL and IU represent thelower and upper bound of the LED forward current, respectively, and IDC be the DCbias current. Then, the clipped signal can be expressed asxkv,clip(n) = FCLIP(xkv,info(n)) , (4.6)100Chapter 4. The Hybrid VLC-PLC Systemwhere [40]FCLIP(x) =b, x ≤ b ,t, x ≥ t ,x, otherwise ,(4.7)and t = IU−IDC, b = IL−IDC for DCO-OFDM, and t = IU−IDC, b = max(IL−IDC, 0)for ACO-OFDM. Neglecting possible differences among LEDs located at the sameluminaire, we obtain the equivalent transmitted signal of the kth LED luminaire asxkv,sum(n) = NE(xkv,clip(n) + IDC). (4.8)We note that the level of the bias current, which together with clipping ensures thenon-negativity of the transmit signal, is determined by the illumination requirementon the luminaire.To proceed with formulating the received signal after the VLC link, we needto distinguish between the OFDM modalities used at the VLC transmitter (DCO-OFDM or ACO-OFDM) and the relaying methods (DF or AF) to obtain Xkv (l).This is done in the next subsection, where we derive the associated expressions forachievable rates for a single subcarrier pair of the HVP system.4.3.3 Achievable Rate Expression for Each Subcarrier PairDCO-OFDMFor DCO-OFDM, Vinfo = {1, 2, . . . , Nv}. According to Bussgang’s theorem [125], theclipped signal at the kth luminaire can be modeled as an attenuation of the original101Chapter 4. The Hybrid VLC-PLC Systemsignal plus a non-Gaussian uncorrelated noise component [126]:xkv,clip(n) = Akxkv,info(n) + nkc(n) , (4.9)where nkc(n) is the non-Gaussian clipping noise term with variance σ2clip,k and Akis the attenuation factor. Given the electrical power of the VLC signal P kv =∑Nvfft−1l=0 E[|Xkv (l)|2] /Nvfft and the constants from the clipping function (4.7), anddefining the normalized clipping levels bk = b/√P kv and tk = t/√P kv , we have[40, 127]Ak = Q(bk)−Q (tk) , (4.10)andσ2clip,k =Pkv(Ak − (φ(bk)− φ(tk) + (1−Q(bk)) bk +Q(tk)tk)2 − (Ak)2+(1−Q(bk)) (bk)2 +Q(tk)(tk)2 + φ(bk)bk − φ(tk)tk) , (4.11)where Q(·) and φ(·) are the tail probability function and the probability densityfunction of the standard normal distribution.Substituting (4.9) into (4.8) gives the output signal at the kth LED luminaire asxkv,sum(n) = NEAkxkv,info(n) +NEnkc(n) +NEIDC . (4.12)Correspondingly, we can write for the frequency-domain signal at the lth subcarrierXkv,sum(l) = NEAkXkv (l) +NENkclip(l) , (4.13)where the DC component NEIDC is not present for l ∈ Vinfo and Nkclip is the discrete102Chapter 4. The Hybrid VLC-PLC SystemFourier transform of nkc . According to the central limit theorem (CLT), Nkclip canbe modeled as an additive complex-valued Gaussian variable with zero mean andvariance of σ2clip,k [40]. We now consider the two relaying schemes.DF Scheme In DF, the relay will only forward the message if it was detectedcorrectly as verified by an outer error-detection code. Then, we will have Xkv (l) =αXp(m), where subcarrier m ∈ Pinfo from the PLC link is paired with subcarrier l ∈Vinfo for the VLC link, and the factor α adjusts the VLC signal strength. The pairingwill be discussed in more detail in Section 4.4. The received signal on subcarrier l atuser u when served from luminaire k follows asY k,uv (l) = Hk,uv (l)Xkv,sum(l) +Nuv (l) (4.14)= NEαAkHk,uv (l)Xp(m) +NEHk,uv (l)Nkclip(l) +Nuv (l) ,where Hk,uv (l) is the VLC channel gain for subcarrier l between the kth luminaireand user u, and Nuv (l) is the VLC noise on subcarrier l at user u. The correspondingsubcarrier SNR isSNRk,uv (l) =|NEαAkHk,uv (l)|2σ2p|NEHk,uv (l)|2σ2clip,k + σ2vn,u, (4.15)where σ2vn,u = E[|Nuv (l)|2]. As both clipping and VLC receiver noise can be approxi-mated as i.i.d. Gaussian noise when Nk ≥ 64 [126], the corresponding per-subcarrierrate can be calculated as (in bit per use)9 [128]Rk,u(l,m) = min(log2(1 + SNRkp(m)), log2(1 + SNRk,uv (l))).9Both Eq. (4.16) and Eq. (4.18) can be derived from [128, Eq. (15)] and [128, Eq. (12)], respec-tively, via setting the direct link channel gain to 0. The absence of the coefficient 12 is due to thefull-duplex property of the luminaire relay.103Chapter 4. The Hybrid VLC-PLC SystemAF Scheme For AF, we have Xkv (l) = βYp(m), where β is the amplification factorfor the AF scheme. Similar to (4.14), Y k,uv (l) can be expressed asY k,uv (l) = NEAkβHk,uv (l)Hkp(m)Xp(m) +NEAkβHk,uv (l)Nkp (m) (4.16)+NEHk,uv (l)Nkclip(l) +Nuv (l) ,and the corresponding SNR at user u is given bySNRk,uv (l,m) =∣∣NEAkβHk,uv (l)Hkp(m)∣∣2 σ2p∣∣∣NEAkβHk,uv (l)∣∣∣2 σ2pn,k(m) + ∣∣∣NEHk,uv (l)∣∣∣2 σ2clip,k + σ2vn,u . (4.17)Using again the fact that the total noise is Gaussian, the achievable rate follows asRk,u(l,m) = log2(1 + SNRk,uv (l,m)). (4.18)ACO-OFDMDifferent than DCO-OFDM, only odd subcarriers in ACO-OFDM carry information,i.e., Vinfo = {1, 3, . . . , 2Nv − 1}, which allows for zero-level clipping and reduces theminimum level of DC bias at the cost of reduced bandwidth efficiency [43]. Theclipped ACO-OFDM signal can be expressed asxkv,clip(n) = 2AkU(xkv,info(n))xkv,info(n) + nkc(n) , (4.19)104Chapter 4. The Hybrid VLC-PLC Systemwhere U(·) is the Heaviside step function [129] and the variance of the clipping noisenkc(n) is [40]σ2clip,k = Pkv(Ak((bk)2 + 1)− 2(Ak)2 − bk (φ(bk)− φ(tk))− φ(tk)(tk − bk) +Q(tk)(tk − bk)2) . (4.20)With this, the expression for the frequency-domain signal at the lth subcarrier forl ∈ Vinfo is the same as in Eq. (4.13). Accordingly, the SNR expressions for DFrelaying in (4.15) and AF relaying in (4.17) also apply to ACO-OFDM and can beused in the rate expression (4.16) and (4.18), respectively, to obtain the associatedachievable rate.4.4 Subcarrier Allocation in HVP SystemsWe now use the rate expressions from the previous section to optimize the rate of theoverall HVP system. Since multiple users compete for resources, we integrate a notionof fairness into the rate optimization. In particular, we introduce a weight variable wuthat represents the priority of user u. For example, in the case of a proportional fair(PF) scheduling policy that prioritizes the user with the lowest average data-rate, wehave wu = 1/Ruavg(n) for long-term fairness consideration, where Ruavg(n) is computedasRuavg(n) =(1− 1Nres)Ruavg(n− 1) +1NresRu(n− 1) , (4.21)and Ru(n) is the data rate at instance n and Nres is the response time of the low-passfilter [130]. We note that the optimization framework presented in this section is105Chapter 4. The Hybrid VLC-PLC Systemindependent of the specific scheduling policy that is applied.The optimization of the achievable rate of the HVP system is accomplishedthrough SA schemes, for which we propose two variants. The first variant, whichwe refer to as SA without subcarrier permutation (SP), retains the subcarrier as-signment when transitioning from PLC to VLC link. Assuming for simplicity andwithout loss of generality that Nv = Np, we have Pinfo = Vinfo and thus l = m in(4.16) and (4.18) for DCO-OFDM. Since Vinfo = {1, 3, . . . , 2Nv−1} for ACO-OFDM,we have l = 2m − 1, m ∈ Pinfo, in this case. The second scheme applies subcarrierpermutation at the relays, and we refer to it as SA with SP. It makes use of the factthat the per-subcarrier link qualities of the PLC and VLC hop are independent ofeach other.Since the number of subcarriers in broadband HVP systems can be very large, anSA scheme considering each individual subcarrier will not only have large computa-tional complexity, but also requires significant signaling overhead. To mitigate thecomputational and coordination complexity, a chunk-based SA scheme can be applied[113]. This means that a set of Ns adjacent subcarriers is grouped into a chunk, andthe chunk is used as the minimum unit in SA. Hence, in the following we considerthat Nc chunks are available in total, where Np = Nv = NsNc, of which Ck chunksare assigned to kth luminaire, i.e., Nk = NsCk. Obviously, Ns = 1 is the special caseof single-subcarrier-based allocation. Given that a codebook of size Sc (Sc = 2q) isemployed for the channel gain vector space Huv(l) = [H1,uv (l), H2,uv (l), . . . , HNL,uv (l)],qNc bits of CSI feedback are required for one OFDM block per VLC user. We definethe binary variable xk,ui,j ∈ {0, 1}, i, j ∈ {1, 2, . . . , Nc}, with xk,ui,j = 1 indicating thatith chunk in the PLC hop together with the jth chunk in the VLC hop are assignedto user u with the assistance of the kth VLC-enabled luminaire. Furthermore, we will106Chapter 4. The Hybrid VLC-PLC Systemneed in the following xu = [xk,ui,j ]i,j=1,...,Nc, k=1,...,NL as the Nc ×Nc ×NL SA tensor foruser u and x = [x1, . . . ,xNU ] as the Nc×Nc×NLNU tensor for SA across all users, andwe will use the sets Nc = {1, 2, . . . , Nc}, NL = {1, 2, . . . , NL} and NU = {1, . . . , NU}in the following, where Nc, NL and NU are the sets of chunk indices, luminaire indicesand user indices, respectively.Next, we present the SA methods first for HVP with OFDM-TDMA and then forHVP with OFDMA.4.4.1 OFDM-TDMAWith OFDM-TDMA, the whole frequency spectrum is owned exclusively by the userwith the highest priority weight wu in a certain time slot. Hence, SA is performedfor one user only at a time.SA without SPFor SA without SP, we have xk,ui,j = 0 for i 6= j, and the rate maximization problemcan be formulated asP1 : x∗u = argmax{xu}∑i∈Nc∑k∈NLxk,ui,i Rk,ui,i (4.22)C1 :∑k∈NLxk,ui,i = 1,∀i ∈ Nc,C2 :∑i∈Ncxk,ui,i = Ck,∀k ∈ NL,C3 : xk,ui,i ∈ {0, 1}, ∀i ∈ Nc, ∀k ∈ NL ,where Rk,ui,j represents the rate of the chunk pair (i, j) for user u and PLC-VLC relayk. Constraint C1 guarantees that each subcarrier pair is assigned to one and only one107Chapter 4. The Hybrid VLC-PLC Systemrelay, and C2 ensures the number of subcarriers pairs allocated to each relay. P1 canbe categorized as a linear semi-assignment problem and can be solved with a timecomplexity of O(N2cNL) [131]. For the simulation results in the next section, we usethe YALMIP [94] toolbox in conjunction with the MOSEK solver [103] to obtain asolution numerically.SA with SPHere we generalize P1 and allow subcarrier permutation at the relays. In this case,the optimization problem for user u can be formulated asP2 : x∗u = argmax{xu}∑i∈Nc∑j∈Nc∑k∈NLxk,ui,j Rk,ui,j (4.23)C1 :∑j∈Nc∑k∈NLxk,ui,j = 1,∀i ∈ Nc ,C2 :∑i∈Nc∑k∈NLxk,ui,j = 1,∀j ∈ Nc ,C3 :∑i∈Nc∑j∈Ncxk,ui,j = Ck,∀k ∈ NL ,C4 : xk,ui,j ∈ {0, 1},∀i, j ∈ Nc, ∀k ∈ NL ,where C1 and C2 guarantee that each subcarrier is assigned to exactly one relay forthe PLC and VLC hop, respectively, and C3 controls the number of assigned subcar-rier pairs per relay. P2 can be categorized as a constrained linear 0-1 programmingproblem, which is NP-hard. We therefore apply a heuristic alternating optimizationmethod to solve P2 suboptimally within polynomial time [132]. To this end, we108Chapter 4. The Hybrid VLC-PLC Systemintroduce vectors {yui,j} and {zk,ui } with xk,ui,j = yui,jzk,ui , and P2 is transformed intoP2.1 : (y∗u, z∗u) = argmax{yu,zu}∑i∈Nc∑j∈Nc∑k∈NLyui,jzk,ui Rk,ui,jC1 :∑j∈Ncyui,j = 1,∀i ∈ Nc,C2 :∑i∈Ncyui,j = 1,∀j ∈ Nc,C3 :∑k∈NLzk,ui = 1,∀i ∈ Nc,C4 :∑i∈Nczk,ui = Ck,∀k ∈ NL,C5 : yui,j, zk,ui ∈ {0, 1},∀i, j ∈ Nc, ∀k ∈ NL ,where yu = [yui,j]i,j∈Nc and zu = [zk,ui ]i∈Nc,k∈NL . P2.1 is a bilinear 0-1 programmingproblem, and we obtain a suboptimal solution by alternately optimizing on yu andzu. When yu is fixed, we can ignore constraints C1 and C2, and P2.1 will degenerateto P1 with Rk,ui,i replaced by Tk,ui =∑j∈Nc yui,jRk,ui,j , which will be referred to as P2.2.When zu is fixed, we define Sui,j =∑k∈NL zk,ui Rk,ui,j and P2.1 becomesP2.3 : y∗u = argmax{yu}∑i∈Nc∑j∈Ncyui,jSui,jC1 :∑j∈Ncyui,j = 1,∀i ∈ Nc,C2 :∑i∈Ncyui,j = 1, ∀j ∈ Nc,C3 : yui,j ∈ {0, 1},∀i, j ∈ Nc ,which is a classic assignment problem and can be solved by the Hungarian algorithmwith a computational complexity of O(N3c ) [133, 134]. The algorithm of the alter-109Chapter 4. The Hybrid VLC-PLC Systemnating optimization for P2 is summarized in Algorithm 4.1 and the time complexityis O(N3c +N2cNL).Algorithm 4.1 Alternating Optimization for P21. Initialization:u∗ = argmaxu∈NU{wu}.Calculate {Rk,u∗i,j }.y0u∗ ⇐ INc×Nc , p⇐ 0.2. repeat3. Update {T k,u∗i } with ypu∗ .4. Solve P2.2 according to [131] and get zpu∗ .5. Update {Su∗i,j} with zpu∗ .6. Solve P2.3 and get yp+1u∗ .7. p⇐ p+ 1.8. until ‖yp+1u∗ − ypu∗‖ ≤ δ (δ is a predefined threshold)9. Compute xu∗ according to xk,u∗i,j = yu∗i,jzk,u∗i .10. Update {wu}u∈NU according to rate update (4.21).4.4.2 OFDMAOFDMA accomplishes multiple access by assigning different subcarriers to differentusers. This allows for a more flexible SA scheme that can exploit multi-user diversity.110Chapter 4. The Hybrid VLC-PLC SystemSA without SPWithout SP at the relays, again xk,ui,j = 0 for i 6= j, and the maximization problemfor the weighted sum rate isP3 : x∗ = argmax{x}∑u∈NUwu∑i∈Nc∑k∈NLxk,ui,i Rk,ui,i (4.24)C1 :∑u∈NU∑k∈NLxk,ui,i = 1,∀i ∈ Nc,C2 :∑u∈NU∑i∈Ncxk,ui,i = Ck,∀k ∈ NL ,C3 : xk,ui,i ∈ {0, 1},∀i ∈ Nc, k ∈ NL, u ∈ NU .Similar to problem P2, we introduce vectors {ai,u} and {bi,k} with xk,ui,i = ai,ubi,k, andsuboptimally solve P3 with alternating optimization based on the transformation intoP3.1 : (a∗, b∗) = argmax{a,b}∑u∈NUwu∑i∈Nc∑k∈NLai,ubi,kRk,ui,iC1 :∑u∈NUai,u = 1,∀i ∈ Nc ,C2 :∑k∈NLbi,k = 1,∀i ∈ Nc ,C3 :∑i∈Ncbi,k = Ck, ∀k ∈ NL ,C4 : ai,u, bi,k ∈ {0, 1}, ∀i ∈ Nc, k ∈ NL, u ∈ NU ,where a = [ai,u]i∈Nc,u∈NU and b = [bi,k]i∈Nc,k∈NL . Let Eui =∑k∈NL bi,kRk,ui,i , F ki =∑u∈NU ai,uwuRk,ui,i , and function u∗i = argmaxu∈NU{wuEui }. We observe that theoptimal solution of P3.1 with b fixed is a vector a∗ with ai,u∗i = 1 and zero otherwise.When a is fixed, we can ignore constraints C1 in P3.1, and P3.1 will degenerate to P1111Chapter 4. The Hybrid VLC-PLC Systemwith Rk,ui,i replaced by F ki and xk,ui,i replaced by bi,k, which will be referred to as P3.2.The algorithm of the alternating optimization for P3 is summarized in Algorithm 4.2,and the time complexity is O(N2cNL +NcNUNL).Algorithm 4.2 Alternating Optimization for P31. Initialization:Calculate {Rk,ui,i }.a0 ⇐ INc×NU , p⇐ 0.2. repeat3. Update {F ki } with ap.4. Solve P3.2 according to [131] and get bp.5. Update {Eui } with bp.6. Find u∗i and obtain ap+1.7. p⇐ p+ 1.8. until ‖ap+1 − ap‖ ≤ δ (δ is a predefined threshold)9. Compute x according to xk,ui,i = ai,ubi,k.10. Update {wu}u∈NU according to rate update in (4.21).SA with SPAllowing subcarrier permutation at the relays, the weighted sum rate maximizationproblem can be expressed asP4 : x∗ = argmax{x}∑u∈NUwu∑i∈Nc∑j∈Nc∑k∈NLxk,ui,j Rk,ui,jC1 :∑u∈NU∑j∈Nc∑k∈NLxk,ui,j = 1,∀i ∈ Nc ,C2 :∑u∈NU∑i∈Nc∑k∈NLxk,ui,j = 1,∀j ∈ Nc ,C3 :∑u∈NU∑i∈Nc∑j∈Ncxk,ui,j = Ck, ∀k ∈ NL ,C4 : xk,ui,j ∈ {0, 1}, ∀i, j ∈ Nc, k ∈ NL, u ∈ NU .112Chapter 4. The Hybrid VLC-PLC SystemP4 is a constrained linear 0-1 programming problem, which is NP-hard. Here wepropose a heuristic subcarrier offloading algorithm that can solve the problem sub-optimally within polynomial time. First we relax the constraints of P4 and considerP4 without C3, which will be referred to as P4.1. P4.1 can be solved with the al-gorithm proposed in [135] within a polynomial time of O(NLNUN2c + N3c ), and thesolution is denoted as {x˜k,ui,j }. Define NL1 and NL2 as the sets of luminaires thatdo and do not exceed the assigned value Ck, respectively, with NL1 = {k|ck > Ck},NL2 = {k|ck < Ck}, where ck =∑u∈NU∑i∈Nc∑j∈Nc x˜k,ui,j . Define Rˆk,ui,j = wuR˜k,ui,jand set R = {Rˆk,ui,j |x˜k,ui,j = 1, k ∈ NL1}. Then we can execute the subcarrier offload-ing algorithm summarized in Algorithm 4.3 and obtain the solution x∗ to P4. Thetime complexity of Algorithm 4.3 is O(NcNLNU + Nc log(Nc)). So the total timecomplexity of solving P4 will be O(NLNUN2c +N3c ).Algorithm 4.3 Subcarrier Offloading Algorithm1. Sort R in increasing order and store it in array AR2. for Rˆk,ui,j in AR3. Initialize Rˆmaxi,j ⇐ 0, (k∗, u∗)⇐ (0, 0)4. for k′ ∈ NL2, u′ ∈ NU5. if Rˆk′,u′i,j > Rˆmaxi,j6. Rˆmaxi,j ⇐ Rˆk′,u′i,j , (k∗, u∗)⇐ (k′, u′)7. end if8. end for9. x˜k,ui,j ⇐ 0, x˜k∗,u∗i,j ⇐ 1, update ck, NL1 and NL2.10. if NL1 = ∅11. break12. end if13. end for14. update {xk,ui,j } ⇐ {x˜k,ui,j }.113Chapter 4. The Hybrid VLC-PLC System4.5 Numerical Results and DiscussionsWe now evaluate the performance of the proposed SO-OFDM-based HVP system.We consider an example setup of a 5 m × 5 m room with NL = 4 coordinatedVLC-enabled LED luminaires, each of which contains NE = 36 LEDs. The setupof the HVP system and the applied coordinate system are illustrated in Figure 4.3.Denoting the length of the power line connecting the ith luminaire and the PLCmodem as li, we consider an example setup where l1 = 7 m, l2 = 8 m, l3 = 9 m,l4 = 10 m. The LEDs have an operating range of IL = 300 mA to IU = 700 mA, witha 3 dB bandwidth WLED = 10 MHz with blue filtering [102]. The DC bias is set toIDC = (IL + IU)/2 = 500 mA, which provides a sufficient illumination for office workand study with this system setup [54].The HVP system has Np = 1024 independent information-carrying subcarriers,and we set Ck = 256, k = 1, . . . , 4. For the PLC link, the minimum subcarrier fre-quency is 2.026 MHz and the subcarrier spacing is 24.4 kHz [119]. For the VLC link,we adopt the same subcarrier spacing as the PLC link, but the first data carryingsubcarrier is at frequency 24.4 kHz. The PLC transmit PSD is set to -50 dBm/Hz ac-cording to the HomePlug AV standard [136] so that conducted and radiated emissionlimits are met. The PLC noise in the simulation includes background, narrowband,and impulse noise, where the PSDs and the corresponding measurement-based param-eters of the former two are described in [137] and [118], respectively. For the impulsenoise, we adopt the model from the IEEE 1901 standard [119, Annex F.3.5.2], whichincludes periodic synchronous, periodic asynchronous and aperiodic noise compo-nents, and we apply the parameters from measurements provided in [138]. The PLCnoise simulator we developed and used here is available online [122]. For simulationaccuracy, we apply the two-state approximation as in [121, Eq. (19)] to calculate114Chapter 4. The Hybrid VLC-PLC Systemthe average achievable rate, which takes into account all of colored background noise,narrowband disturbance and impulsive noise. The average achievable rate can be cal-culated as the weighted sum of the achievable rates of the system with and withoutimpulse noise:Ravg = (1− p)Rwithout_imp + pRwith_imp , (4.25)where Ravg denotes the average achievable rate, Rwithout_imp denotes the achievablerate of the system when impulse noise is absent and only colored background noiseand narrowband disturbance are considered, and Rwith_imp denotes the achievablerate of the system when impulse noise is present. p denotes the probability of im-pulse noise occurrence, and we let p = 0.01 in the simulation based on the PLCnoise measurement [120]. According to the measurement, p < 0.01 in even heavilydisturbed power line environment, thus our simulation results can be considered as alower bound of the average achievable rate. Further system parameters are listed inTable 4.1.4.5.1 Single-User SystemWe first consider the single-user scenario and focus on analyzing the system perfor-mance with different optical OFDM, relay and SA schemes. In the following, we useDF-DCO, DF-ACO, AF-DCO and AF-ACO to identify the cases where DF or AFrelaying at the luminaires is used together with DCO-OFDM or ACO-OFDM for theoptical OFDM scheme, respectively.Figure 4.4 compares the achievable rates of the four transmission schemes as afunction of the user location in the x-y plane. The user height is assumed to bez = 0.8 m. We observe that for all four schemes, the system achieves the highest rate115Chapter 4. The Hybrid VLC-PLC SystemTable 4.1: Simulation parameters.Room SetupFixture coordinate 1 [1.25, 1.25, 3]Fixture coordinate 2 [1.25, -1.25, 3]Fixture coordinate 3 [-1.25, -1.25, 3]Fixture coordinate 4 [-1.25, 1.25, 3]Room Length L × W × H 5 [m] × 5 [m] × 3 [m]VLC ParametersLambertian order m 1PD area APD 1 [cm2]Concentrator refractive index κ 1.5Receiver FOV ψc 85 [deg.]Noise bandwidth factor I2 0.562Background current Ibg 100 [µA]LED conversion factor s 0.44 [W/A]PD responsivity γ 0.30 [A/W]when the user is near the center of the room and rate decreases as the user movescloser to the walls. SA without SP and SA with SP can improve the achievablerate notably across the room compared with a random SA at the luminaire relays,which we refer to as Random SA. In Figure 4.4, we also notice that the DCO-OFDMscheme achieves a higher system rate than ACO-OFDM. This is due to the factthat ACO-OFDM only utilizes odd subcarriers for data transmission, which makesit less bandwidth-efficient than DCO-OFDM. In particular, for the same numberof information-carrying subcarriers in DCO-OFDM and ACO-OFDM, ACO-OFDMuses a broader frequency spectrum and thus suffers from stronger channel attenuationat higher frequencies. For the results in Figure 4.4, we set α =√10 and β = 10,which is a reasonable choice as will be discussed next.For the results in Figure 4.5 and Figure 4.6, we fix the user location to x = −0.5 m,y = 1.5 m, and z = 0.8 m. In Figure 4.5, we show the achievable rate as a functionof the relay gain α and β, respectively. When the relay gain is small and thus the116Chapter 4. The Hybrid VLC-PLC Systemtransmission power for the VLC hop is relatively low, the system performance is VLC-noise limited. Increasing the relay gain will increase the SNR, but at some point LEDclipping distortion becomes the dominant noise source and curbs further performanceimprovements. Hence, there is an optimal relay gain for each of the four transmissionsschemes, which depends on the magnitude of VLC noise, VLC channel (e.g., receiverorientation, etc). Figure 4.6 compares the performance of Random SA, SA without SPand SA with SP as a function of chunk size Ns. We can observe that SA without SPand SA with SP can greatly enhance the system performance compared with RandomSA. Note that for SA without SP in the AF-DCO system, modulation/demodulation,FFT/IFFT and encode/decode blocks shown in Figure 4.2 are not required, and thesignal transition between PLC and VLC can be done in the analogue domain. Basedon the results, a chunk size of Ns = 16 seems to provide close to optimal performance,while providing computational complexity savings when solving the SA optimizationproblem.We next investigate whether the PLC or the VLC hop is limiting the performanceof the HVP system, for which we focus on the DF-mode and SA with SP. Since thePLC and VLC channels are frequency selective, we count the number NVLC_BL ofsubcarrier pairs for which the VLC hop is the bottleneck link when the maximumachievable rate is attained. Figure 4.7 plots the NVLC_BL as a function of the userlocation in the x-y plane with z = 0.8 m for both DF-DCO and DF-ACO. The 3 dBbandwidth of WLED = 10 MHz used for the results in Figure 4.7a corresponds to thecurrent system setup with a blue filter at the photodiode, and WLED = 2 MHz forthe results in Figure 4.7b corresponds to a photodiode receiver without blue filtering[139]. We observe that NVLC_BL of DF-DCO is generally smaller than that of DF-ACO due to the stronger channel attenuation of ACO-OFDM at higher frequencies.117Chapter 4. The Hybrid VLC-PLC SystemIn Figure 4.7a, NVLC_BL is typically less than 60 out of Np = 1024 subcarrier pairsfor both DF-DCO and DF-ACO, which shows that the PLC link is the main bottle-neck for the end-to-end performance of the HVP system. This changes notably andespecially for the system operating in the DF-ACO mode when the LED bandwidthis reduced to 2 MHz. Here, the VLC hop limits the system performance, as shownin Figure 4.7b.4.5.2 Multi-User SystemWe now consider the scenario of multiple VLC users. We perform simulations forboth OFDM-TDMA and OFDMA to evaluate the corresponding achievable rate anduser fairness. In this section, we use AF-ACO as the example transmission scheme.Figure 4.8 shows the average sum achievable rate against the number of VLC users.For a given value of NU, a set of sum achievable rates are calculated and averaged bydistributing NU users uniformly at random over the indoor environment. For a fixedlocation of NU users, we evaluate the average sum achievable rate over 100 time slots,and the weights {wu} in schemes with PF scheduling are updated with Nres = 20 in(4.21). For schemes without PF, OFDM-TDMA without PF represents an OFDM-TDMA scheme with wu set to 1 and the user scheduling degrades to a Round-Robin(RR) scheme. OFDMA without PF represents an OFDMA scheme with wu set to 1,and the user scheduling degrades to a sum-rate maximizing scheduling and fairnessacross users is neglected. From Figure 4.8, we can see that as NU increases, the sumachievable rates of OFDMA schemes grow monotonically while the sum achievablerates of OFDM-TDMA remain almost unchanged. OFDMA outperforms OFDM-TDMA since it exploits the multi-user diversity. Not imposing the PF constraintprovides further gains due to the increased multi-user diversity.118Chapter 4. The Hybrid VLC-PLC SystemThe benefit of schemes with PF is illustrated in Figure 4.9. We consider a fixedlocation profile forNU = 4 users and plot the average achievable rate for each user over100 time slots (we assume that users remain static during this time period). We cansee that PF can improve the data rate fairness across users for both OFDM-TDMAand OFDMA schemes, and PF is significantly important for OFDMA scheme. Forthe setup in Figure 4.9, due to the poor channel conditions, no subcarrier is allocatedto User 4 in the OFDMA scheme without PF. Unlike RF wireless communication,there is no multipath fading for indoor VLC channels due to the large photodiode sizecompared with the optical wavelength. The deterministic nature of the VLC channelwill fix users in low SNR channels to become complete neglected in user schedulingif PF scheduling is not applied. As expected, although PF results in lower overallrate, it is a desirable feature to ensure some level of fairness among the users of theproposed HVP system.4.6 ConclusionIn this chapter, we have proposed a multicarrier HVP system as a potential indoorhigh-speed downlink solution employing the symbiotic relationship between PLC andVLC. Compared with traditional multicarrier-based VLC-PLC integration, the pro-posed HVP system alleviates the PAPR problem for VLC transmitters and elim-inates the inter-luminaire interference through the cooperation of LED luminairespiggybacked on the powerline backbone. We have considered the HVP system as atwo-hop relay system and investigated different approaches of signal transition be-tween PLC and VLC systems. To exploit the frequency selectivity of HVP channels,as well as the multi-user and multi-transmitter diversity, we have proposed severalsubcarrier allocation schemes with varying degrees of tradeoff among hardware, com-119Chapter 4. The Hybrid VLC-PLC Systemputational complexity and performance for meaningful variations of the HVP sys-tem. As another important contribution, we have investigated and compared twomulti-access schemes for the HVP system, i.e., OFDMA and OFDM-TDMA. Severalpolynomial-time SA algorithms are proposed correspondingly. At the cost of highercomputational complexity, OFDMA has been shown to outperform OFDM-TDMAfor the HVP system in multi-user situations. For future work, power and bit loadingfor the SO-OFDM-based HVP system can be investigated, where the linear period-ically time varying (LPTV) properties of PLC channels can be exploited to reducethe complexity of implementation [140].120Chapter 4. The Hybrid VLC-PLC SystemLED luminaryAccess NetworkVLC User PLC modem1234PowerlinezxyFigure 4.3: The setup of HVP system.121Chapter 4. The Hybrid VLC-PLC System02.5502.55120140160180 x (m)(a) AF−DCOy (m) Achievable rate (Mbits/s)02.5502.5580100120140160 x (m)(b) AF−ACOy (m) Achievable rate (Mbits/s)02.5502.55100150200 x (m)(d) DF−ACOy (m) Achievable rate (Mbits/s)SA with SPSA without SPRandom SA02.5502.55160170180190200 x (m)(c) DF−DCOy (m) Achievable rate (Mbits/s)Figure 4.4: Achievable rate as a function of user location. Nc = 16, α =√10, β = 10.122Chapter 4. The Hybrid VLC-PLC System100 101 1026080100120140160180βAchievable rate (Mbits/s)(a) AF−DCO  100 101 10220406080100120140160βAchievable rate (Mbits/s)(b) AF−ACO  100 101 10280100120140160180200αAchievable rate (Mbits/s)(c) DF−DCO  SA with SPSA without SPRandom SA100 101 10280100120140160180200αAchievable rate (Mbits/s)(d) DF−ACO  Figure 4.5: Achievable rate versus relay gain (α or β). Nc = 16. User location isx = −0.5 m, y = 1.5 m, z = 0.8 m.123Chapter 4. The Hybrid VLC-PLC SystemFigure 4.6: Comparison of different SA schemes with different chunk size Ns. α =√10, β = 10. User location is x = −0.5 m, y = 1.5 m, z = 0.8 m.124Chapter 4. The Hybrid VLC-PLC System02.5502.5501020304050607080DF−DCONVLC_BL02.5502.55020406080100120DF−ACONVLC_BL(a) WLED = 10 MHz.02.5502.55020406080100120140DF−DCONVLC_BL02.5502.550100200300400500600700800DF−ACONVLC_BL(b) WLED = 2 MHz.Figure 4.7: NVLC_BL as a function of user location. Nc = 16. NVLC_BL is the numberof subcarrier pairs for which the VLC hop is the bottleneck link when the maximumachievable rate is attained. 125Chapter 4. The Hybrid VLC-PLC SystemNu = 1 Nu = 2 Nu = 3 Nu = 4 Nu = 5145150155160165170175180Number of usersAchievable rate (Mbits/s)  OFDM−TDMA without PFOFDM−TDMA with PFOFDMA without PFOFDMA with PFOFDM−TDMAOFDMAFigure 4.8: Achievable rate versus the number of users NU. SA with SP and AF-ACOare applied. β = 10, Nc = 16.126Chapter 4. The Hybrid VLC-PLC SystemUser 1 User 2 User 3 User 401020304050(a) OFDM−TDMA without PFAchievable rate (Mbits/s)User 1 User 2 User 3 User 40510152025303540(b) OFDM−TDMA with PFAchievable rate (Mbits/s)User 1 User 2 User 3 User 401020304050607080(c) OFDMA without PFAchievable rate (Mbits/s)User 1 User 2 User 3 User 401020304050(d) OFDMA with PFAchievable rate (Mbits/s)Figure 4.9: Comparison of multi-access schemes with and without PF for NU = 4.The example locations are (x = −1.25, y = 1.25, z = 0.8) m, (x = −1.25, y =−1.25, z = 0.8) m, (x = 1.25, y = 1.25, z = 0.8) m and (x = 2.5, y = 2.5, z = 0.8) mfor User 1, User 2, User 3 and User 4, respectively. SA with SP and AF-ACO areapplied. Nc = 16, β = 10.127Chapter 5Conclusion5.1 SummaryMost research in physical-layer VLC transmission schemes focus on point-to-pointcommunication, however, typical rooms are usually equipped with multiple LEDluminaires instead of just one to ensure the uniformity of indoor illumination level.Multiple independent point-to-point links will lead to strong interference among usersas the illumination footprints of neighboring LED luminaires usually have significantoverlap. To mitigate the co-channel interference, the simplest method is traditionalfrequency planning that assigns different sub-bands to neighbouring attocells. An-other method is to position VLC luminaires separately to avoid overlapping foot-prints, and the gap between attocells is covered by RF base stations. In comparisonwith frequency planning, this hybrid RF-VLC scheme allows full frequency reuseamong VLC attocells.Different from the previous methods, the research work in this thesis presented analternative approach which achieves interference mitigation through coordination ofdifferent VLC attocells. The thesis focused on developing transmission schemes forcoordinated VLC attocells. We considered three different coordinated architecturesfor VLC downlink transmission. Chapter 2 proposed the full cooperation amongVLC attocells and the multiple coordinated VLC emitters form a virtual multiple-transmitter system. The system design in Chapter 2 focused on the MMSE precoder128Chapter 5. Conclusiondesign subject to lighting constraint. Chapter 3 extends the work in Chapter 2 byconsidering looser coordination among neighboring attocells with multiple luminaireseach, which puts less requirement on the inter-attocell communication and synchro-nization, though at the cost of compromised system performance. Numerical resultsshow that the coordination scheme proposed in Chapter 3 provides a good tradeoffbetween system performance and complexity. While Chapter 2 and 3 assumed theexistence of backbone network for VLC transmitter, Chapter 4 delved deeper into thepower line backbone network for the proposed hybrid VLC-PLC system. In addition,SO-OFDM was applied across multiple neighboring VLC transmitters to alleviate thePAPR problem for each VLC transmitter, and several subcarrier allocation schemesare proposed to exploit the frequency selectivity of the VLC and PLC channels. Dif-ferent possible and meaningful variations of the HVP system, including the choice ofoptical OFDM transmission, relay and multiple access schemes, are investigated andcompared.5.2 Future WorkIn Chapter 2 and Chapter 3, we focus on developing the spatial multiplexing tech-niques at the transmitter side to serve multiple indoor VLC users simultaneously. Itwill be interesting to investigate the joint optimization of user scheduling and beam-forming to enhance the system performance when the number of users exceeds thatof VLC-enabled LED luminaires. What’s more, the designs proposed by Chapter 2and Chapter 3 only apply to the single-carrier modulation, more specifically, PAM.The optimal multi-carrier beamforming designs for both JT and CB, to the author’sknowledge, have yet to be studied.In fact, our ultimate goal is to build a Cloud VLC Access Network (C-VAN) which129Chapter 5. Conclusionis similar to its counterpart Cloud Radio Access Network (C-RAN) in RF systems[141]. Individual signal processing units for different VLC attocells are replaced bya centralized unit. The LED luminaires operate as access points for the users, andare connected to the centralized unit which coordinates the transmission for all theattocells. The advantages of deploying C-VAN for indoor VLC systems are multi-fold.First, smoother handover across different VLC attocells can be realized. Second, C-VAN increases system adaptability to non-uniform indoor traffic by dynamic resourceallocation at the centralized unit. Third, C-VAN reduces the deployment cost forVLC-enabled luminaires since luminaires in C-VAN require no baseband processingmodule. Last, and most importantly, C-VAN can achieve higher system capacityand lower IAI through collaboration among VLC transmitters. The research workin this thesis is the first step towards a practical C-VAN system. 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Surveys Tuts., vol. 17, no. 1, pp. 405–426, Firstquarter 2015.143Appendix AProof of Outdated CSI BoundFor the terminal movement in the horizontal direction, the terminal can either moveaway from or towards the VLC transmitter. In the former case, the resulting differ-ence in the scalar channel gain between two consecutive CSI updates can be expressedas a function of dh and calculated according to Equation (1.2):+(dh) = hp1 − hp2 (A.1)=(m+ 1)NEsγκ2APD2pi(d2v + d2h)(dv√d2v + d2h)m+1− (m+ 1)NEsγκ2APD2pi(d2v + (dh + L)2)(dv√d2v + (dh + L)2)m+1= β((d2v + d2h)−m+32 − (d2v + (dh + L)2)−m+32 ) ,whereβ =(m+ 1)NEsγκ2APDdm+1v2pi sin2(ψc). (A.2)Based on the three facts:1. +(0) > 0 ,2. d +(dh)d dh∣∣∣dh=0> 0 ,3. limdh→+∞ +(dh)→ 0 ,144Appendix A. Proof of Outdated CSI Boundit can be deduced that there exists one maximum in (0, +∞). Therefore, there existsat least one d1 ∈ (0,+∞) that satisfies d +(dh)d dh∣∣∣dh=d1= 0, and one of those d1 iscorresponding to the maximum. To obtain d1, we calculate the derivative of equation(A.1):d +(dh)d dh∣∣∣∣dh=d1= 0⇒ log(d1L+ d1)=m+ 52log(d2v + d21d2v + (L+ d1)2). (A.3)So the maximum channel gain difference between two consecutive CSI updates whenthe user terminal moves away from the VLC transmitter is+ = maxdh+(dh) = β((d2v + d21)−m+32 − (d2v + (d1 + L)2)−m+32), (A.4)where d1 satisfies (A.3). Similarly, if the user terminal moves towards the VLC trans-mitter, the maximum difference in the scalar channel gain between two consecutiveCSI updates can be expressed as− = β((d2v + (d2 − L)2)−m+32 − (d2v + d22)−m+32), (A.5)where d2 satisfieslog(d2d2 − L)=m+ 52log(d2v + d22d2v + (d2 − L)2). (A.6)So the error bound for the kth user can be expressed as k = max{+, −}, togetherwith (A.3)–(A.6).145

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