Applied Science, Faculty of
Electrical and Computer Engineering, Department of
DSpace
UBCV
Naterer, Jordan
Master of Applied Science - MASc
University of British Columbia
Internet application and mobile service demands have continuously driven the need for increased data rates throughout global communication networks. One bottleneck of global network capacity is the backhaul network, which is responsible for connecting intermediate links throughout the core network. The backhaul network is commonly established either via high capacity optical fibre lines or low cost fixed microwave wireless antennas. Due to their low cost, microwave links are currently used for over 50% of the world's backhaul networks, as opposed to optical fibre connections. However, these links must follow strict regulation on the wireless bandwidths and pulse shapes they are allowed to occupy. The goal of this thesis is to improve the spectral efficiency within a transmission channel's regulated pulse shapes. The spectrum regions we intend to utilize are the sidebands outside the primary pulse, or spectrum "skirts''. While these skirts are commonly intended for adjacent channel usage, it has been shown that they typically go unused. We investigate two modular methods to take advantage of these unused sidebands, a superposition and multi-carrier approach. While the first method overlaps a primary and secondary pulse in the time domain, the other places the pulses adjacent to one another in the frequency domain. The superposition method must deal with the interference caused by overlapping pulse shapes. Simulations show that the primary stream cancellation is essential to this system's performance. The multi-carrier method requires custom pulse shapes that fit under the spectrum mask to match performance. Simulation results demonstrate that without phase noise impairments, the superposition scheme yields the highest performance. However when transmitting with phase noise, the multi-carrier scheme is predicted to transmit the most data under practical channel conditions.
Modular Spectrum Utilization for Next-GenerationFixed Transmission NetworksbyJordan NatererB. Eng., Memorial University of Newfoundland, 2018A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Electrical and Computer Engineering)The University of British Columbia(Vancouver)August 2020c© Jordan Naterer, 2020The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Modular SpectrumUtilization for Next-Generation Fixed Trans-mission Networkssubmitted by Jordan Naterer in partial fulfillment of the requirements for thedegree of Master of Applied Science in Electrical and Computer Engineering.Examining Committee:Lutz Lampe, Electrical EngineeringSupervisorJahangir Hossain, Electrical EngineeringSupervisory Committee MemberiiAbstractInternet application and mobile service demands have continuously driven theneed for increased data rates throughout global communication networks. Onebottleneck of global network capacity is the backhaul network, which is responsi-ble for connecting intermediate links throughout the core network. The backhaulnetwork is commonly established either via high capacity optical fibre lines or lowcost fixed microwave wireless antennas. Due to their low cost, microwave linksare currently used for over 50% of the world’s backhaul networks, as opposed tooptical fibre connections. However, these links must follow strict regulation onthe wireless bandwidths and pulse shapes they are allowed to occupy.The goal of this thesis is to improve the spectral efficiency within a transmis-sion channel’s regulated pulse shapes. The spectrum regions we intend to utilizeare the sidebands outside the primary pulse, or spectrum “skirts”. While theseskirts are commonly intended for adjacent channel usage, it has been shown thatthey typically go unused. We investigate two modular methods to take advantageof these unused sidebands, a superposition and multi-carrier approach. While thefirst method overlaps a primary and secondary pulse in the time domain, the otherplaces the pulses adjacent to one another in the frequency domain.The superposition method must deal with the interference caused by over-lapping pulse shapes. Simulations show that the primary stream cancellation isessential to this system’s performance. The multi-carrier method requires custompulse shapes that fit under the spectrum mask to match performance. Simula-tion results demonstrate that without phase noise impairments, the superpositioniiischeme yields the highest performance. However when transmitting with phasenoise, the multi-carrier scheme is predicted to transmit the most data under prac-tical channel conditions.ivLay SummaryImprovements to wireless microwave transmission technology have become nec-essary to meet the modern demands for data transmission throughout global com-munication networks. While microwave spectrum usage is highly regulated, oneoverlooked feature for potential data rate improvement is the spectrum “skirts”.These skirts can be understood as side regions within the frequency domain thatare intended for adjacent communication links. However, it has been found thatthese adjacent links typically go unused. This thesis proposes several modularschemes in order to take advantage of these skirts, while ensuring that commonspectrum regulations are not violated. The superposition scheme is the main fo-cus of this thesis, but an additional multi-carrier approach is also evaluated. Theseschemes are finally validated and compared to show overall communication sys-tem improvements.vPrefaceThis dissertation is original, unpublished, independent work by the author, J.Naterer.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 QAM Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Achievable Information Rate . . . . . . . . . . . . . . . . . . . . 102.4 Spectrum Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 Channel Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . 14vii2.6 Dispersive Fading . . . . . . . . . . . . . . . . . . . . . . . . . . 182.7 Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.8 Phase Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Superposition Transmission for Using Spectrum Skirts . . . . . . . 283.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2 Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 313.3 Phase Noise Estimation . . . . . . . . . . . . . . . . . . . . . . . 364 Multi-Carrier Transmission for Using Spectrum Skirts . . . . . . . 394.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2 Pulse Shape Design . . . . . . . . . . . . . . . . . . . . . . . . . 414.3 Dual-Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Numerical Results and Discussion . . . . . . . . . . . . . . . . . . . 485.1 Superposition Transmission with BCJR Phase Estimation . . . . . 495.2 Superposition Transmission with Improvements . . . . . . . . . . 505.3 Comparing Superposition and Multi-Carrier Transmission . . . . . 535.4 Multi-Carrier Dual-Polarized Transmission . . . . . . . . . . . . 556 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61viiiList of FiguresFigure 1.1 Spectrum skirt pulse shapes for 25.6 MHz bandwidth RRC,superposition, and multi-carrier transmission schemes. . . . . 4Figure 2.1 RC transmitter and receiver block diagram with linear equal-ization, phase noise tracking, and FEC coding. . . . . . . . . . 8Figure 2.2 QAM constellation maps for 4-QAM, 16-QAM, and 32-QAM. 9Figure 2.3 Analytical and simulated SERs for an AWGN channel with210-QAM, 212-QAM, 214-QAM, and 215-QAM constellations. 10Figure 2.4 AIR for an AWGN channel with 210-QAM, 212-QAM, 214-QAM, and 215-QAM constellations. . . . . . . . . . . . . . . 13Figure 2.5 (7,4) Hamming code parity check matrix with Tanner graph. . 15Figure 2.6 BERs for an AWGN channel with a 4/5 LDPC code-rate and210-QAM, 212-QAM, 214-QAM, and 215-QAM constellations. 17Figure 2.7 BERs for a 212-QAM AWGN channel under various Rummlerchannel instances. . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 2.8 AIR for a 212-QAM AWGN channel under various Rummlerchannel instances. . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 2.9 BERs for a 212-QAM AWGN channel at various phase noiselevels with p= 50 pilot spacing. . . . . . . . . . . . . . . . . 27Figure 2.10 AIRs for a 212-QAM AWGN channel at various phase noiselevels with p= 50 pilot spacing. . . . . . . . . . . . . . . . . 27Figure 3.1 Pulse shape for 51.2 MHz superposition transmission scheme. 30ixFigure 3.2 Transmitter architecture for superposition scheme. . . . . . . . 31Figure 3.3 Receiver architecture for superposition scheme with linear equal-ization, phase noise tracking, and FEC coding. . . . . . . . . . 31Figure 4.1 Pulse shape for 51.2 MHz multi-carrier transmission scheme. . 41Figure 4.2 Transmitter architecture for multi-carrier scheme. . . . . . . . 41Figure 4.3 Receiver architecture for multi-carrier scheme with linear equal-ization, phase noise tracking, and FEC coding. . . . . . . . . . 42Figure 4.4 Modified pulse shape for 51.2 MHz multi-carrier transmissionscheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 4.5 Channel model for dual-polarization scheme. . . . . . . . . . 45Figure 5.1 AIR for multiple Rummler channel instances with 214-QAMRC transmission and [212,24]-QAM superposition transmission. 50Figure 5.2 AIR for various phase noise levels with 214-QAM RC trans-mission and [212,24]-QAM superposition transmission. . . . . 51Figure 5.3 Secondary stream AIR for various Rummler channel recon-structions with [212,24]-QAM superposition transmission. . . 52Figure 5.4 Secondary stream AIR for various phase noise re-estimationmethods with [212,24] and [214,24]-QAM superposition trans-mission with phase noise at −90dBc/Hz. . . . . . . . . . . . . 52Figure 5.5 AIR for 214-QAM RC, [212,24]-QAM superposition, and [214,24]-QAM multi-carrier transmission with phase noise at−90dBc/Hzand a 5dB-notch Rummler channel. . . . . . . . . . . . . . . 54Figure 5.6 BER for 214-QAM RC, [212,24]-QAM superposition, and [214,24]-QAM multi-carrier transmission with phase noise at−90dBc/Hzand a 5dB-notch Rummler channel. . . . . . . . . . . . . . . 54Figure 5.7 BER for [212,22/24]-QAM superposition, and [212,22/24]-QAMmulti-carrier transmission with phase noise at−90dBc/Hz anda 5dB-notch Rummler channel with a 0.75 rate LDPC code. . 56xFigure 5.8 AIR for 212-QAM RC dual-polarized transmission with phasenoise at −90dBc/Hz and a 3.5dB-notch Rummler channel. . . 56Figure 5.9 BER for 212-QAM RC dual-polarized transmission with phasenoise at −90dBc/Hz and a 3.5dB-notch Rummler channel. . . 57Figure 5.10 AIR for 212-QAM RC and [212,24]-QAM multi-carrier dual-polarized transmission with phase noise at −90dBc/Hz and a3.5dB-notch Rummler channel. . . . . . . . . . . . . . . . . . 58xiGlossaryAIR Achievable Information RateAWGN Additive White Gaussian NoiseBCJR Bahl, Cocke, Jelinek and RavivBICM Bit-Interleaved Coded ModulationCAGR Compound Annual Growth RateC-RAN Centralized Radio Access NetworksDAC Digital-to-Analog ConverterDFT Discrete Fourier TransformDP Dual PolarizationDVB Digital Video BroadcastingETSI European Telecommunications Standards InstituteFBMC Filter Bank Multi-CarrierFEC Forward Error CorrectionFTN Faster-than-NyquistGMI Generalized Mutual InformationxiiIC Interference CancellationIID Independent and Identically DistributedIoT Internet of ThingsIP Internet ProtocolISI Inter-Symbol InterferenceLDPC Low-Density Parity CheckLLR log likelihood ratiosMAP Maximum A Posterior ProbabilityMMSE Minimum Mean Square ErrorOFDM Orthogonal Frequency Division Multiple AccessQAM Quadrature Amplitude ModulationRAN Radio Access NetworkRC Raised CosineRRC Raised-Root CosineSIC Successive Interference CancellationSNR Signal-to-Noise RatioXPI Cross-Polarization InterferencexiiiChapter 1Introduction1.1 OverviewThe insistent rise of Internet application and mobile service demand continuouslyincreases the data requirements for global communication networks. Furthermore,the fifth generation of wireless communications places greater emphasis on datarequirements for use-cases such as ultra reliable low latency communications instock trading, and massive machine type communications in consumer Internet ofThings (IoT) devices. Referencing quantitative predictions, Cisco’s most recentVisual Networking Index Forecast predicts that global fixed broadband speedswill double and mobile cellular speeds will triple between 2018 and 2023 [1].Global machine-to-machine connections are estimated to grow from 1.2 billion to4.4 billion at a Compound Annual Growth Rate (CAGR) of 30% within the sametime period, and Global Data Center Networking is expected to grow at a CAGRof 12%. These speeds along with other network demands are predicted to resultin a CAGR of 26% for global Internet Protocol (IP) traffic.Gradually over the years, the bottleneck of Radio Access Network (RAN)capacity has shifted from the radio interface to the backhaul network. This back-haul network is responsible for connecting intermediate links throughout the corenetwork, or more specifically, connecting base stations with their associated mo-1bile switching nodes. One paradigm shift that has assisted the advancement ofbackhaul network capacity is the Centralized Radio Access Networks (C-RAN)architecture, which shifts many base station responsibilities to a centralized cloudlocation, connected via a fronthaul network. This change combats the densifica-tion of base stations in small-cell backhaul networks and improves efficiency bypooling baseband resources.Backhaul links are commonly established either by high capacity optical fi-bre lines, or low cost fixed microwave wireless antennas. While optical fibre canachieve significantly higher data rates and larger capacities, it is typically associ-ated with a much higher cost. However, a study in 2014 observes that optical fibrebackhaul is not available nationwide in Europe and current microwave networkscannot sustain the traffic growth of LTE and LTE-A [2], signifying the importanceof improving current microwave technologies.Traditionally, these microwave links have used carrier frequencies between 6-42GHz, while millimetre wave research is pushing towards the V-Band (57 - 66GHz) and the E-Band (71 - 76 & 81 - 86 GHz) to allow larger bandwidths andcapacity. These higher frequencies along with additional technologies such asantenna polarization, link aggregation, and adaptive coding & modulation drivedown operating costs for providers while increasing flexibility and efficiency.1.2 Problem StatementThe goal of this project is to improve the spectral efficiency within a single linkmicrowave transmission channel. The proposed changes require no major archi-tectural changes and have the ability to increase capacity without leasing addi-tional frequency bands. While the target application is towards microwave links,the techniques discussed are equally applicable to any communication channelwith a defined spectrum limit. Throughout this work we use the limits definedby the European Telecommunications Standards Institute (ETSI) as our primaryspectral constraints [3].Spectrum limit standards are typically enforced to ensure that adjacent chan-2nels do not interfere with one another. However, it is observed in many microwavelinks that adjacent channels at high carrier frequencies often go unused throughoutthe year. This is due to the large number of channels still available for licensingor purchase at high frequency bands. Therefore, this thesis intends to utilize thespectrum “skirt” regions while still conforming to the spectrum limits defined byETSI. We also assume that transmission is maintained at high Signal-to-NoiseRatio (SNR) values, as experienced by fixed microwave links for the majority oftime each year.We introduce two transmission architectures to take advantage of the sideskirts, a superposition and multi-carrier approach. While the first method over-laps a strong primary and weaker secondary pulse, the second method places twoweaker pulses adjacent to the strong primary pulse while remaining orthogonal inthe frequency domain. The superposition method must deal with the interferencecaused by overlapping pulse shapes while the multi-carrier method requires cus-tom pulse shapes to fit under the spectrum mask. Transmission impairments suchas a dispersive channel and phase noise are also accounted for as experienced inpractical microwave link settings. The final pulse shapes selected for comparisonare illustrated in Fig. 1.1. It can be seen that the superposition scheme overlaps aweaker and wider pulse below the spectrum skirts, while the multi-carrier schemeadds a custom-shaped pulse that does not interfere with the primary pulse shape.1.3 Thesis ContributionsOur main contributions throughout this work is the development of the superposi-tion approach and the addition of dual-polarization to the multi-carrier approach.Typically, the transmission of data over a microwave link requires an extensiveamount of experimental data to acquire reliable performance results. Therefore,we model and simulate a microwave system via analytic relations that have beenverified in practical scenarios.We implement a superposition microwave link that can reconstruct and sub-tract a primary stream in order to detect a secondary stream under ideal channel30 10 20 30 40 50Frequency Offset From Carrier (MHz)-60-50-40-30-20-10010Amplitude Frequency Response (dB)Ideal RRCSuperposition MaskMulti-Carrier MaskETSI Spectrum MaskFigure 1.1: Spectrum skirt pulse shapes for 25.6 MHz bandwidth RRC, su-perposition, and multi-carrier transmission schemes.conditions. We notice that the reconstruction accuracy is essential to this system’sperformance and must be as precise as possible in order to achieve maximum datarates. Next, we add phase noise and dispersive channel impairments under theassumption that the receiver has full knowledge of the channel conditions. Onceadding phase noise estimators and channel equalizers to relax these constraints,we introduce additional techniques to reduce equalization overhead and improvephase noise estimates.After tuning superposition transmission parameters to reach the scheme’s max-imum potential, we compare it to the multi-carrier approach and notice that it isoutperformed under practical channel conditions. We deduce that this is due to theinterference caused by overlapping signals, and how the multi-carrier approach ismore effective at utilizing the spectrum skirts with minimal interference. Once4having the ability to commit to one approach, we implement dual-polarizationwith linear equalizers. The linear equalizer’s dual convolution operation does re-quire breaking each transmission packet into smaller chunks to fit into memory,but eventually this addition nearly doubles data rates. We believe that this multi-carrier approach is the most effective tool at utilizing spectrum skirts to improvespectral efficiency.1.4 Thesis OutlineThis thesis is organized as follows. In Chapter 2 we introduce the system model ofa general point to point microwave communication link and channel impairmentssuch as dispersive fading and phase noise. In Chapter 3 we discuss the superposi-tion transmission model and several novel improvements to improve channel esti-mation and phase noise compensation. In Chapter 4 we discuss the multi-carriertransmission model and introduce dual-polarization to significantly improve themaximum achievable data rate. Chapter 5 evaluates the results of various numeri-cal simulations in order to compare the two modular spectrum utilization schemes.Finally, Chapter 6 draws conclusions from the results and suggests potential futurework regarding the outcomes of this thesis.5Chapter 2System ModelIn order to effectively discuss spectrum utilization methods, this chapter outlinesthe overall microwave link transmission model used throughout the thesis. Webegin by introducing a baseband transmission model with QAM modulation andgeneral pulse shape filters to fit within our spectral mask. We then introduce chan-nel coding in order to improve system performance. Next, we discuss a disper-sive Rummler channel impairment, and how linear Minimum Mean Square Error(MMSE) equalization is required to reduce the effect of inter-symbol-interference.Finally, phase noise is added to our overall channel model and handled via a dis-cretized sequence estimator.2.1 OverviewThe purpose of a digital communication system is to transmit information over ananalog channel between a transmitter and a receiver [4]. This information signalhas the characteristics of a random process in order to convey information mostefficiently. While these signals are always transmitted over an analog channel, wetypically analyze the effects of impairments in the digital domain.The most common transmission model is the Additive White Gaussian Noise(AWGN) channel. It contains an additive noise whose power distribution is uni-6form across the frequency band of the communication system. The noise sam-ples follow a Gaussian normal distribution with an average value of zero. Thecontinuous-time representation of this channel is expressed asr(t) = s(t)+n(t), (2.1)where s(t) is the initial signal transmitted at power Ps, and n(t) denotes the AWGNwith a constant power spectral density across all frequencies.The process of converting data between a digital and analog domain is calledmodulation and demodulation respectively. The modulation schemes are associ-ated with alphabets, where a specific number of digital bits represents a specificsymbol in the alphabet’s finite signal space. In order to simplify probabilistic re-lations, each symbol in the modulation alphabet is considered equally likely to betransmitted and received.We use filters to transmit the data over a finite frequency range, allowing usto transmit multiple signals simultaneously. Using a finite frequency range allowsus to transmit multiple signals simultaneously. This frequency range is also re-ferred to as the bandwidth and is equivalent to the symbol rate of the transmissionsystem. While transmitting each symbol over a finite bandwidth causes the signalto theoretically occupy an infinite space in time, a slight tolerance in the form ofspectrum skirts are commonly allowed which cause minimal interference to theadjacent symbols sent. In order to receive the data, the signals are filtered to con-sider the frequency band of interest, and then sampled at constant time intervals.The most common transmitter and receiver pulse shape is the Raised-Root Co-sine (RRC) pulse, which is easy to implement with electronics and fits well underthe required spectral mask constraints. Since the two pulse shapes are identical,they are referred to as matched filters, an optimal solution to receiving data overan AWGN channel. A signal that passes through both of these filters encountersan Raised Cosine (RC) pulse. This RC pulse follows the Nyquist Inter-SymbolInterference (ISI) criterion which ensures that at each sampling instance of thereceived signal, the time shifted adjacent signals do not interfere.7FEC EncoderQAMMapperAnalog Up-conv.FEC DecoderQAMDemapperLinear EQ + Phase Noise TrackingRRC Matched FilterAnalog Down-conv.T-Sampling(a) Transmitter(b) ReceiverBits InBits OutDACRRC Pulse ShapeFigure 2.1: RC transmitter and receiver block diagram with linear equaliza-tion, phase noise tracking, and FEC coding.The block diagram to illustrate the signal chain is displayed below in Fig. 2.1.At the transmitter end, the binary data is first passed to a channel encoder to im-prove error performance, then mapped to a signal constellation in preparation fordigital to analog conversion. The newly formed symbols then pass through adigital RRC pulse shaping filter at an oversampled rate, then are converted intoan analog signal by the Digital-to-Analog Converter (DAC). Finally the analogsignal is upconverted to the carrier frequency and transmitted over the intendedchannel. At the receiver end, the process unfolds mostly in reverse order. How-ever, instead of the pulse shaping filter, an RRC matched filter is employed tomaintain the ISI criterion. Additionally, linear equalization and phase noise track-ing is employed to handle the impairments that are discussed in more detail in thefollowing sections.2.2 QAMModulationQuadrature Amplitude Modulation (QAM) is the most common modulation pat-tern choice for mapping binary data to a finite symbol space. This modulationformat simultaneously transmits two carriers known as the in-phase and quadra-ture components respectively. These two parallel streams are each associated withan amplitude and can be visualized together as real and imaginary components ina constellation diagram. When mapping the binary data to symbols, a Gray code80111 1000(a)1000 10011010 10110001 00000011 00100111 01100101 01001110 11111100 1101(b)10100 011000010011010 001100101000000 1000011100 0001010110 0111001000 1100010010111011101 000110110110001 010010000101011 110111001100101 101011100100111 10111 01111 11111(c)Figure 2.2: QAM constellation maps for 4-QAM, 16-QAM, and 32-QAM.is commonly used to ensure that neighbouring constellations only differ by onebit. Various symbol mappings are illustrated in Fig. 2.2 as a square or symmetriccross shape depending on the bit order.The in-phase and quadrature baseband components can be expressed asxI(t) =∑nai[n]p(t−nT ) (2.2)xQ(t) =∑naq[n]p(t−nT ), (2.3)where T denotes a sampling time interval, and p(t) denotes our pulse shape whichsatisfies the Nyquist ISI criterion. The terms ai and aq represent the discrete-timeamplitudes of the in-phase and quadrature components.At the transmitter side, the overall QAM passband signal is expressed ass(t) = xI(t)cos(2pi fct)− xQ(t)sin(2pi fct), (2.4)where fc denotes the carrier frequency, and cos(2pi fct) and sin(2pi fct) denote theorthogonal carriers which allow simultaneous transmission of two data streams.At the receiver end, the overall QAM baseband signal is expressed asxI(t) = LPF[cos(2pi fct)s(t)] (2.5)920 25 30 35 40 45 50 55 60SNR [dB]10 -410 -310 -210 -110 0Symbol Error Rate (SER)Analytical, m = 10Analytical, m = 12Analytical, m = 14Analytical, m = 15Simulation, m = 10Simulation, m = 12Simulation, m = 14Simulation, m = 15Figure 2.3: Analytical and simulated SERs for an AWGN channel with 210-QAM, 212-QAM, 214-QAM, and 215-QAM constellations.xQ(t) = LPF[−sin(2pi fct)s(t)], (2.6)where LPF represents our low-pass matched filter associated with p(t).An example of our simulation matching analytical results is illustrated inFig. 2.3 with the probability of symbol error [4], where m denotes the set ofM = 2m possible symbol mappings. The x-axis sweep parameter is the SNR,representing the ratio between the transition power and discrete-time AWGN vari-ance.2.3 Achievable Information RateIn addition to uncoded SER curves, another metric which takes into account thechannel capacity can be used to accurately compare operation parameters. The10channel capacity is difficult to measure, but is effectively expressed by the max-imum net rate at which information can be reliably transmitted, or an Achiev-able Information Rate (AIR). The Generalized Mutual Information (GMI) es-timates this AIR for bit-wise decoders by using the statistical distributions, orlog-likelihoods, of each received sample [5, 6]. It has been shown that the GMI isa more reliable measure than the uncoded SER when applying channel coding toa communication system [7]. While the GMI is measured in bits per channel use,it can give an estimate of the overall data rate in bits/s by using the transmissionsystem’s baud rate.In order to calculate the GMI, we estimate the symbol-wise mutual informa-tion between each transmitted and received symbol. The derivation assumes amemoryless channel with a uniform discrete input distribution, such as a QAMconstellation. The average mutual information between the transmitted and re-ceived symbols is expressed asI(X;Y) = EXY[log2pY|X(Y|X)pY(Y)], (2.7)where X is the random variable denoting the input element belonging to its respec-tive QAM constellation with cardinality M = 2m, while Y is the random variabledenoting the channel output element. The probability pY|X denotes the conditionalmemoryless channel transition distribution while the probability pY denotes thechannel output density.By utilizing the weak law of large numbers, the following expression con-verges to the actual mutual information via Monte-Carlo simulations:limN→∞1NN∑i=1log2pY|X(yi|xi)pY(yi)→ I(X;Y). (2.8)While the transition probabilities can take on any distribution, we use anAWGN channel where pY|X(y|xi) ∼ N (xi,σ2N). The channel is assumed to bememoryless and the input variables are generated from a uniform distribution.11We also assume a bit-wise channel where dependencies between bits within thesame symbol are neglected, known as Bit-Interleaved Coded Modulation (BICM).The GMI is then estimated according to [8, Eq. (6)] asRGMI = m− 1Nm∑k=1N∑i=1log2(1+ exp((−1)bk,iLLRk,i)). (2.9)The log likelihood ratios (LLR) are given byLLRk,i = log2∑x∈X k1 exp(− |yi−x|2σ2N)∑x∈χk0 exp(− |yi−x|2σ2N) , (2.10)χk1 is the set of constellation points where the kth bit is 1,χk0 is the set of constellation points where the kth bit is 0,and can be calculated via the max-log approximationLLRk,i = log2maxx∈X k1 exp(− |yi−x|2σ2N)maxx∈χk0 exp(− |yi−x|2σ2N) . (2.11)Returning to the simulations in Fig. 2.3, the AIR for BICM over an AWGNchannel are illustrated in Fig. 2.4. As expected, the AIR reaches increasinglyhigher maximums at higher QAM orders and SNR values. We label our y-axis inunits of bits / RRC channel use, where the denominator corresponds to the currenttransmission system in use. This will be used as a benchmark to compare otherschemes through the remainder of this thesis.2.4 Spectrum UseWe briefly review the use of frequency bands relevant to backhaul networks [9].Below 3 GHz frequencies have low channel attenuation to travel long distances,but have limited bandwidths available. Applications typically include utilities,1220 25 30 35 40 45 50SNR [dB]02468101214161820AIR [bits / RRC channel use]m = 10m = 12m = 14m = 15Figure 2.4: AIR for an AWGN channel with 210-QAM, 212-QAM, 214-QAM, and 215-QAM constellations.public safety, and communication to remote locations. The systems which usespectrum from 3 GHz to 10 GHz can accomplish 50km hops, and are used forlong-haul connections in the backhaul network. Due to the reasonable bandwidthsavailable with long distance capabilities, they continue to play a key roll in fixedwireless systems. The main bands currently in use today fit between 10 GHz to 57GHz whose systems are capable of 20km distances. In North America, the bandsbetween 11 GHz - 23 GHz are primarily used for microwave backhaul.The 57 GHz - 66 GHz V-Band shows promising results, but experience strongatmospheric absorption between 59 - 64 GHz. While these frequencies could beused for private small cell links, the outer frequencies can be utilized for theirlarge available bandwidths. Unfortunately, these bands have seen scattered regu-lations between the US and Europe, and will likely not see significant use in the13upcoming push for 5G backhaul usage [10]. Finally, the 71 - 76 and 81 - 86 GHzE-Band is also capable for high-capacity transmission, as they do not encounterthe atmospheric effects at 59-64 GHz frequencies. While this band is deemedas incapable of supporting 5G use, it is a strong candidate for a global backhaulband.In terms of spectral usage throughout the thesis, the standard parameters weuse for our benchmark RC transmission system are as follows:• Symbol Rate: Rsym = 25.6×106 symbols/s• Symbol Duration: Tsym = 1/Rsym = 39.06 ns• Rolloff Factor: βRC = 0.15• Bandwidth: BRC = (1+βRC)Rsym = 29.44 MHz• Oversampling Factor: SPSRC = 2• Sampling Interval: Tsam = Tsym/SPSRC = 19.53 ns• Sampling Rate: Rsam = 1/Tsam = 51.2×106 samples/s• Frequency Band: 17-30 GHz [3]2.5 Channel CodingIn order to improve error-rate performance, Forward Error Correction (FEC) maybe implemented to reduce the error rate to near zero. While algebraic blockand convolutional codes offer simplicity and low latency, they cannot achieve theperformance of other modern graph based coding schemes. Low-Density ParityCheck (LDPC), Polar, and Turbo codes have been thoroughly compared accord-ing to throughput per chip area, low complexity, latency, and suitability at shortand long block lengths [11]. Based on previous comparison studies, LDPC codes14H=1 1 0 1 1 0 01 0 1 1 0 1 00 1 1 1 0 0 11234567123Figure 2.5: (7,4) Hamming code parity check matrix with Tanner graph.have traditionally been selected for many high throughput and low latency scenar-ios while Polar codes have been chosen for ultra reliable control information.LDPC codes can be implemented or viewed as block codes or convolutionalcodes. However, these codes can conveniently be visualized with a tool calledthe Tanner Graph. Fig. 2.5 illustrates an example of a Tanner Graph with sevenvariable nodes and three check nodes. The circular variable nodes correspond tothe number of codeword symbols (column count) while the square check nodescorrespond to the parity check equations (row count). While the code displayed isnot an LDPC code, they generally have a relatively small number of graph edgessince the parity check matrix is considered low-density or sparse.By representing the parity check matrix as a graph-like problem, moderngraphical model message passing algorithms can be utilized. While simple bit-flipping algorithms exist based on a tree representation of the Tanner Graph, themost notable algorithm used for decoding LDPC codes is belief propagation, orthe sum-product algorithm [12]. Instead of performing hard-decisions iterativelyuntil a convergence is met, soft probability values are used to speed up the process.The sum-product algorithm efficiently calculates the marginalsfi(xi) =∑∼xif (x1,x2, . . . ,xn), (2.12)for each bit using the full factor graph.15It makes use of how the global function f (x1,x2, . . . ,xn) is a factor of somelocal functions depending on a subset of variables. For example, if the globalfunction can be expressed as the productf (x1,x2,x3,x4,x5,x6,x7,x8) =g1(x1)g2(x2)g3(x1,x2,x3,x4)g4(x4,x5,x6) (2.13a)g5(x5)g6(x6,x7,x8)g7(x7),thenf4(x4) =(∑x1,x2,x3g1(x1)g2(x2)g3(x1,x2,x3,x4))(2.13b)(∑x5,x6g4(x4,x5,x6)g5(x5)(∑x7,x8g6(x6,x7,x8)g7(x7)))can be used to yield less computation relative to the general case.The process of decoding begins by estimating an initial node or symbol, andthen sending messages out in opposite directions across the graph edges to con-tinue estimations until convergence. Note that the algorithm is expected to con-verge in a finite number of steps if the graph is cycle-free, while graphs with cyclescannot guarantee convergence.While Polar codes are a more recent invention that show promise, we selectedLDPC codes to model high throughput transmission. LDPC codes are currentlyused in Digital Video Broadcasting, 10 Gigabit Ethernet, and WiFi MIMO stan-dards.The BER curves for transmission with various QAM constellation sizes overan AWGN channel are illustrated in Fig. 2.6. The code rate applied is a 4/5 codeprovided by MATLAB’s Digital Video Broadcasting (DVB) standard library. Thislibrary provides a limited number of available LDPC parity check matrices at ablock length of 64800 bits, in order to simulate LDPC correction. This blocklength is a constraint that must be considered when generating data streams, andpadding is often added to ensure that the block sizes are divisible by the QAM1620 25 30 35 40 45SNR [dB]10 -410 -310 -210 -110 0Bit Error Rate (BER)m = 10m = 12m = 14m = 15Figure 2.6: BERs for an AWGN channel with a 4/5 LDPC code-rate and210-QAM, 212-QAM, 214-QAM, and 215-QAM constellations.order and pilot spacing that is discussed below. Also, there are only ten avail-able code rates to choose from, which limit simulation precision in desired BERdropoff location.The dropoff locations are estimated via the AIR curves in Fig. 2.4. By tracinga horizontal line at the AIR value of the QAM order multiplied by the code rate,the intersection of the simulated curve is the SNR value predicted for dropoff. Forexample, by drawing a horizontal line at 8 bits and matching it with the m = 10curve, the SNR value of 25.48dB is predicted for a dropoff. For these particularsimulations, the actual dropoff occurs between 1.0-1.5dB after the ideal dropoff.172.6 Dispersive FadingAside from the AWGN channel, dispersive fading is another impairment that mustbe handled when operating at microwave frequencies on a line-of-sight path. Dis-persive fading can be understood as an inter-symbol interference, where one sym-bol interferes with other symbols at different time instances. It is also associatedwith multi-path fading, where a radio signal reaches the receiver at different timeinstances due to taking various propagation paths. While this impairment takesplace in the passband frequency range, the baseband continuous-time representa-tion of a dispersive fading channel is expressed asr(t) =∫ ∞−∞s(τ)c(t− τ)dτ+n(t), (2.14)where c(t) is the cascade of our lowpass transmit and receive RRC filters, andsome dispersive channel h(t).Our system uses a Rummler two-path model [13] that is typically utilizedwhen operating at carrier frequencies below 11 GHz [14,15]. While our spectrummask assumes using higher microwave carrier frequencies between 17-30 GHz[3], we follow the channel models that have been utilized by similar microwavesystem designs [16].The complex baseband frequency response is modelled asH( f ) = a[1−be j2pi( f− f0)τ0], (2.15)where the coefficients a and ab represent the first and second transmission pathsrespectively, while the time constant τ0, typically fixed at 6.3ns, represents an ex-pected delay between the two paths. The frequency f0 corresponds to the offsetwith respect to the carrier frequency where the attenuation notch is located. Thisnotch can be modelled by the depth and shape via the a and b parameters. Thesmall time delay was chosen [13] to allow the a and b values to effectively deter-mine the shape of the frequency response. The specific value of 6.3ns was chosen18to align with a factor multiple of 1.1 MHz, the frequency spacing at which thechannel attenuation was originally measured during experiments.The transmission path coefficients a and b are generated via the random vari-ablesA=−20log10(a) (2.16a)B=−20log10(1−b), (2.16b)where B denotes the notch depth and A denotes the overall attenuation.While the notch depth can be set as a constant, it is typically modelled as a ran-dom variable according to an exponential distribution with mean µB= 3.8dB. Theoverall attenuation follows a normal distribution A∼N (A0,5), but also dependson the notch depth asA0 = 24.6B4+500B4+800. (2.17)In order to generate the offset frequency, a relative phase φ = 2pi f0τ0 of thesecond multipath is generated according to the piecewise functionPΦ(φ) =1/216 |φ | ≤ pi/21/1080 pi/2 < |φ |< pi. (2.18)While a time varying Rummler channel is possible to model, it is enough toassume a particular notch depth and offset frequency and model many simulationsbased on a select number of Rummler channels. In our simulations, we typicallylook at three channels, each with a decreasing level of performance correspondingto increasing notch depth and notch frequency depending on the method used.2.7 EqualizationIn order to handle dispersive fading caused by multiple transmission paths, anequalizer must be utilized to handle the time-shift echoes of the desired signal.While many linear equalizers utilize adaptive filter taps in practice, we assume19that the training phase is complete, and a stable channel prediction is achieved.Many equalizers today are implemented digitally and must take into account thein-phase and quadrature components of the complex input. Equalizers may alsotake samples than the signal rate to better handle frequency distortion near thebandwidth edges. These fractionally-spaced equalizers are known to outperformmany synchronous ones with the same number of taps [16].We represent the continuous-time transmitted and received signals ass(t) =∑kI[k]p(t− kT ) (2.19)r(t) =∑kI[k]c(t− kT )+n(t), (2.20)wherec(t) =∫ ∞−∞p(τ)h(t− τ)dτ, (2.21)denotes the cascade of the band-limited RC pulse shape p(t) and the channel re-sponse h(t). I[k] represents discrete-time information sequence of QAM symbolsand n(t) represents the continuous-time additive white Gaussian noise.After receiving the data sequence, we a apply a finite-length equalizer filter toreceive symbol estimates expressed asIˆ[k] =∑jf [ j]r[k− j], (2.22)where f [k] denotes the equalizer filter taps.Our goal is to minimize the error of symbol detection denoted asε[k] = I[k]− Iˆ[k], (2.23)by utilizing the MMSE criterion expressed as an expectationE|I[k]− Iˆ[k]|2. (2.24)20We then assume that the covariance between the error and received signalsequence r[k] is zero. This orthogonality principle is expressed asE[ε[k]r∗[k− l]] = 0 −∞< l < ∞. (2.25)By substituting the symbol estimate (2.22) into (2.25) and incorporating theexpectation over l into the summation, we simplify the expression asE[(I[k]−∑jf [ j]r[k− j])r∗[k− l]]= 0 (2.26a)∑jf [ j]E(r[k− j]r∗[k− l]) = E(I[k]r∗[k− l]), −∞< l < ∞. (2.26b)We simplify the left term asE(r[k− j]r∗[k− l]) =L∑n=0c∗[n]c[n+ l− j]+σ2Nδ [l− j], (2.27)by observing that it is the autocorrelation of the channel response c[k] with anisolated noise term at power level σ2N .We simplify the right term asE(I[k]r∗[k− l]) = c∗[−l], (2.28)by observing that it is the channel response reversed.In order to practically implement this linear equalizer, the convolution oper-ation is modelled with a matrix multiplication by rearranging the channel vectorinto a Toeplitz Matrix. This matrix follows the property where each diagonal de-scending from left to right is constant. The newly formed convolution operationis expressed asr[k] =L∑l=0c[k− l]I[l] (2.29a)21r=c[0] 0 . . . 0c[1] c[0] . . . 0...... . . . 0c[L−1] c[L−2] . . . c[0]I[0]I[1]...I[k] . (2.29b)By utilizing this matrix rule, equations (2.26b), (2.27), and (2.28) are used tosolve for the equalizer coefficients(CHC+σ2NI)f= c∗ (2.30a)f= (CHC+σ2NI)−1c∗, (2.30b)where f denotes the vector of equalizer filter coefficients, andC denotes the Toeplitzrepresentation of the channel response. While this equalization method requiresknowledge of the noise power at the receiver, we assume that this value is knownthroughout our model.Fig. 2.7 and Fig. 2.8 illustrate the results of a 212 QAM constellation undervarious Rummler channel instances once equalization is applied. While all AIRsreach the same final value, an increase in notch depth shifts the performance re-quirements by several dB of SNR. The effects of a Rummler channel are exag-gerated at higher QAM orders, and the 3.5dB notch channel instance is typicallyused for future simulations.2.8 Phase NoiseAnother significant impairment we consider is phase jitter of the transmitter andreceiver voltage controlled oscillators. Regarding a QAM constellation map, thiseffect results in random rotations of each symbol around the mapping. This im-pairment is especially damaging at the high QAM orders we simulate.While this impairment takes place in the passband frequency range, the base-band continuous-time representation of a phase noise impaired channel is ex-2230 35 40 45 50 55 60SNR [dB]10 -410 -310 -210 -110 0Bit Error Rate (BER)No Rummler3.5dB notch6dB notch13dB notchFigure 2.7: BERs for a 212-QAM AWGN channel under various Rummlerchannel instances.30 35 40 45 50SNR [dB]0246810121416AIR [bits / RRC channel use]No Rummler3.5dB notch6dB notch13dB notchFigure 2.8: AIR for a 212-QAM AWGN channel under various Rummlerchannel instances.23pressed asr(t) = s(t)e jφ(t)+n(t), (2.31)where n(t) denotes the continuous-time representation of the AWGN, and φ(t) isthe continuous-time phase noise.For our simulation purposes, we model the phase noise channel as a discrete-time impairment expressed asr[k] = s[k]e jφ [k]+n[k], (2.32)where n[k] denotes the discrete-time AWGN with variance σ2N , and φ [k] denotes adiscrete-time representation of the phase noise.A Wiener process is used to model phase noise variation, which implies anaccumulation of phase noise steps. This process is expressed asφ [k] = φ [k−1]+∆[k], ∆[k]∼N (0,σ2φ ) (2.33)p(φ [k] | φ [k−1]) = 1√2piσ2φe−|φ [k]−φ [k−1]|22σ2φ , (2.34)i.e., each step is a zero-mean Independent and Identically Distributed (IID) Gaus-sian variable with variance σ2φ . The transition probabilities p(φ [k] | φ [k−1]) aremodelled by a normal distribution.We make use of the Bahl, Cocke, Jelinek and Raviv (BCJR) algorithm [17,18]to perform Maximum A Posterior Probability (MAP) pilot-assisted phase noisesequence estimation at high-order QAM transmission. For this purpose, we dis-cretize the phase noise to form a trellis. Following [17], we define a phase noiseresolution that is fine enough for high accuracies, and a maximum span region. Pi-lot symbols are transmitted to limit the maximum phase span region of the trellisat constant intervals so the phase noise does not expand indefinitely.The aforementioned BCJR algorithm [18] is a general algorithm not specificto phase noise, that is used to optimally estimate a posteriori probabilities of a24hidden finite Markov process. It generates forward and backward probabilitiesexpressed asαk(φ) =∑φ ′αk−1(φ ′) · γk(φ ′,φ) ∀φ ′,φ ∈Φ (2.35a)βk(φ) =∑φ ′′βk+1(φ ′′) · γk(φ ,φ ′′) ∀φ ,φ ′′ ∈Φ, (2.35b)where the phase states φ ′,φ ,φ ′′ represent the previous, present, and future phasestate values respectively. The γ term must also be calculated, which represents theprobability of the received symbol given two adjacent phase states. This probabil-ity is expressed asγk(φ ′,φ) = p(φ ′|φ) 1√piσ2N e−|r[k]e− jφ−sˆ[k]|2σ2N ∀φ ′,φ ∈Φ (2.36a)γk+1(φ ,φ ′′) = p(φ |φ ′′) 1√piσ2N e−|r[k]e− jφ ′′−sˆ[k]|2σ2N ∀φ ,φ ′′ ∈Φ, (2.36b)where sˆ[k] denotes the symbol we have tentatively decided upon. These valuesmust be calculated for every possible symbol within the QAM mapping.Also note that a max-log approximation can be used to maintain numericalstability. The forward and backward recursions can be represented aslnαk(φ) = ln(∑φ ′αk−1(φ ′) · γk(φ ′,φ))≈maxφ ′[αk−1(φ ′) · γk(φ ′,φ)] (2.37a)lnβk(φ) = ln(∑φ ′′βk+1(φ ′′) · γk(φ ,φ ′′))≈maxφ ′′[βk+1(φ ′′) · γk(φ ,φ ′′)]. (2.37b)As a final step, the estimator selects the phase noise state value that maximizesthe a posteriori probability φˆ [k] = argmaxφαk(φ) ·βk(φ).In order to simulate the phase noise, a random step model must be selectedto determine the variance of the Markov process. In order to account for the25bandwidth, phase noise measurements are typically measured in units of dBc/Hz,representing the noise power K0 relative to the carrier frequency contained in a 1Hz bandwidth centred at the offset frequency foffset [19]. The denominator canbe modified in order to apply phase noise at sample rate instead of symbol rate,expressed asσ2φ =K04pi2 foffsetfsym. (2.38)Without a Rummler channel, the uncoded BER and AIR for 212-QAM AWGNtransmission under varying phase noise levels are illustrated in Fig. 2.9 and Fig. 2.10respectively. We use a signal bandwidth of 25.6 MHz and a phase noise offset fre-quency of 100 kHz. While a noise floor appears at an uncoded BER order of 10−3,we can obtain practically zero error rates with strong enough FEC coding. Theerror floor is dependent on many factors, but QAM order seems to be the mostsignificant due to the state space of the BCJR algorithm.2630 35 40 45 50 55SNR [dB]10 -410 -310 -210 -110 0Bit Error Rate (BER)Figure 2.9: BERs for a 212-QAM AWGN channel at various phase noiselevels with p= 50 pilot spacing.30 35 40 45 50 55SNR [dB]0246810121416AIR [bits / RRC channel use]Figure 2.10: AIRs for a 212-QAM AWGN channel at various phase noiselevels with p= 50 pilot spacing.27Chapter 3Superposition Transmission forUsing Spectrum SkirtsIn this chapter, we introduce the superposition transmission scheme for efficientspectrum utilization through microwave links. We begin by describing the sys-tem’s baseband transmission model and illustrating the general additive transmis-sion and sequential receive processes. We then outline a novel channel estimationmethod which makes use of the narrowband channel knowledge in order to extrap-olate the wideband channel to reduce equalization overhead. Finally, we outlinea phase noise re-estimation method which uses FEC-aided symbol estimates inorder to improve signal reconstruction accuracy.3.1 System ModelThe primary spectrum utilization method we study is an aggressive approach,which overlaps two carrier signals at the transmitter. Our superposition trans-mission scheme makes use of Interference Cancellation (IC) [20] at the receiverin order to sequentially detect a strong primary and weak secondary signal. Whilesome interference cancellation techniques operate in parallel over multiple itera-tions to improve signal detection.28We apply Successive Interference Cancellation (SIC), which decodes signalssuccessively. Once one signal is successfully detected, it is subtracted from thefull combination of signals before the next signal is detected. While the firstsignal must deal with the interference from the second signal, the second signalenjoys the benefit of having the first signal’s interference already removed, albeitan approximate removal. SIC is suitable for our superposition transmission due tothe large power disparity of the superposed signals.The continuous-time representation of our superposition transmission modelis expressed ass(t) =∑kI1[k]p1(t− kT1)+∑kI2[k]p2(t− kT2), (3.1)where I1[k] and I2[k] are the QAM symbols of the primary and secondary streamscaled by power P1 and P2 respectively. The pulse shapes p1(t) and p2(t) rep-resent the narrowband and wideband pulses used to shape our primary and sec-ondary pulses, while T1 and T2 denote each stream’s symbol interval. While weassume T1 = 2T2 throughout our simulations to ease the sampling process, this isnot required.The continuous-time representation of the signal we receive is expressed asr(t) = e jφr(t)∫ ∞−∞s(τ)e jφt(τ)h(t− τ)dτ+n(t) (3.2)where h(t) denotes our multipath Rummler channel and n(t) denotes the zero-mean additive Gaussian noise. The signals φt(t) and φr(t) represent the trans-mitter and receiver phase noise processes. After receiving r(t), the primary andsecondary streams are separated with a narrowband and wideband receive filterrespectively.Regarding pulse shapes, the superposition scheme allows the second streamto incorporate a larger bandwidth to effectively utilize the spectrum skirts. Thecombined pulse shapes with bandwidths 25.6 MHz and 51.2 MHz are displayedin Fig. 3.1, relative to a standard benchmark RC scheme.29The difference of the filter gain at frequency 0 is chosen as 40dB to allowusage of a channel bandwidth of exactly double the primary stream. Using thisbandwidth allows for straightforward pulse synchronization. A gap of roughly2dB from the spectral mask is used to allow for fluctuations of the transmitterelectronics.The transmitter architecture in Fig. 3.2 is similar to the RC scheme in Chap-ter 2, with a signal chain added to the primary stream before analog up-conversionand antenna transmission. The QAM orders of each stream may vary based onchannel and phase noise conditions.The receiver architecture in Fig. 3.3 is more complex, as it requires removal ofthe primary stream to detect the second stream. Once the primary stream has beendecoded, it is re-encoded and sent over an estimation of how the channel appears.After re-applying channel impairments, it is subtracted from the received signalat a larger bandwidth, and the secondary stream can effectively be decoded. Themain bottleneck of this receiver architecture is the effective reconstruction of theprimary stream. While an accurate secondary stream equalization and phase noise0 10 20 30 40 50Frequency Offset From Carrier (MHz)-60-50-40-30-20-10010Amplitude Frequency Response (dB)Superposition MaskIdeal RRCETSI Spectrum MaskFigure 3.1: Pulse shape for 51.2 MHz superposition transmission scheme.30FEC EncoderQAMMapperAnalog Up-conv.Primary Stream Bits InFEC EncoderQAMMapperSecondary Stream Bits InRRC Pulse 25.6 MHz DACDACRRC Pulse 51.2 MHzFigure 3.2: Transmitter architecture for superposition scheme.QAMDemapperLinear EQ & Phase Noise TrackingRRC Filter 25.6 MHzAnalog Down-conv.T-SamplingPrimary StreamBits OutQAMDemapperLinear EQ & Phase Noise TrackingRRC Filter 51.2 MHzT/2-SamplingSecondary StreamBits OutFEC EncoderQAM MapperRRC 25.6MHzRe-apply Rummler & Phase NoiseRRC Filter 51.2 MHz+-FEC DecoderFEC DecoderFigure 3.3: Receiver architecture for superposition scheme with linearequalization, phase noise tracking, and FEC coding.compensation is important at lower signal power, the residual ISI and phase noiseof an incorrectly reconstructed primary stream is amplified when detecting thesecondary stream due to the large power difference.3.2 Channel EstimationOne challenge related to the equalization of the spectrum skirts is the necessity ofwideband channel knowledge. While the primary stream can send pilot symbolsin order to estimate the narrowband Rummler channel, the secondary stream is ata much weaker SNR and requires knowledge of the wideband Rummler channelresponse for equalization and detection. Adaptive equalization or training is pos-sible at the lower SNR, but another approach is to use the information from thenarrowband channel response to predict a larger portion of the channel bandwidth.31Referring to Fig. 3.3, knowledge of a larger channel bandwidth is requiredwithin the primary stream reconstruction pipeline where the Rummler channelis re-applied, and in the secondary stream linear equalizer. The straightforwardsolution to both of these problems is to send a set of training symbols over the fullbandwidth, while at a lower power to conform to the pulse shape requirements.The more novel approach is to use the information from the narrowband channelresponse to predict a larger portion of the channel bandwidth.Before discussing the novel channel estimation approach, we introduce an-other more simple method to obtain the Rummler channel response required forthe primary reconstruction stream. Referring to Fig. 3.3, the reconstruction streamonly requires the cascade of the Rummler channel and a single narrowband 1T1RRC filter. This is still a narrowband channel response, with a slightly less steeprolloff due to only one RRC filter being required. We obtain this single rolloffchannel response by removing one RRC from our estimated narrowband channelin the frequency domain.We begin by modelling the discrete-time representation of our overall channelasc[k] =∑lh[l]p′[k− l], (3.3)where h[l] denotes our discrete-time dispersive Rummler channel and p′[k] de-notes the discrete-time RC pulse shape where p[k] is a single RRC pulse. We canalso model our overall channel asc[k] =∑lc′[l]p[k− l], (3.4)where c′[k] denotes the cascade of our Rummler channel and a single RRC pulse.We then can remove a single RRC rolloff by modelling the overall channel inthe frequency domain asC[m] =C′[m] ·P[m] (3.5a)32C′[m] =C[m]/P[m] P[m]≥ ξ0 otherwise , (3.5b)where (C[m],C′[m],P[m]) represent the Discrete Fourier Transform (DFT) of theirrespective time-domain representations. The threshold ξ is used to consider theregion where we can reliably remove the RRC response. Typically ξ = 0.1 isused to ignore the frequency response region that is effectively zero. The DFTis calculated via the Fast Fourier Transform (FFT) operation. We cannot removeboth RRC filters via this method because of how they zero the channel response,an operation that is practically irreversible by a single division operation.The primary issue with this method is the inaccuracies introduced by eachDFT operation, and the numerical imprecision of being unable to remove the RRCrolloff effect at frequencies below the specified cutoff value.The other method for determining the Rummler channel response is to predictthe full bandwidth, required for the secondary stream equalizer and usable by theprimary reconstruction stream. We utilize a number of assumptions that have beenfound similar to other research ventures in sampling and reconstruction. Manysignals typically are limited by a finite number of degrees of freedom, specificallyin terms of a limited number of samples at particular units of time. These signalsthat exhibit a limited number of degrees of freedom are considered to have a finiterate of innovation and can be accurately reconstructed in the presence of noise[21]. The algorithm proposed to solve finite rate of innovation problems onlyrequires a non-aliased input stream, and knowledge of the pulse shape associatedwith the overall signal.Our Rummler channel model fits the description of having a finite rate of in-novation as it is limited to two primary taps separated by a constant time delta.We consider this finite stream of pulses asc(t) =L∑l=1cl p′(t− tl), (3.6)33where p′(t) is our known RC pulse shape, and {tl,cl}Ll=1 correspond to the un-known time delays and amplitudes. We assume that the number of pulses areknown L= 2 and the time delays are restricted to the finite sampling time intervalt ∈ [0,T ).We now consider the signal c(t) to be periodic with a sufficiently large intervalT so that its continuous-time Fourier series expansion is expressed asc(t) =∞∑k=−∞C[k]e− j2piT kt , (3.7)whereC[k] are the corresponding Fourier series coefficients. It can then be shownthat the coefficients C[k] satisfyC[k] =1TP′(2piTk)L∑l=1cle− j2piT ktl , (3.8)where P′( f ) represents the continuous-time Fourier transform of p′(t). By remov-ing the RC coefficients, the Rummler channel response can be expressed asX [k] =1TL∑l=1cle− j2piT ktl =1TL∑l=1clzkl , (3.9)where zl = e− j2piT tl represent the L= 2 complex exponentials we hope to find.We then utilize the subspace method to obtain these exponentials, outlined inthe following algorithm. This algorithm is explained in more detail in [21].34Algorithm: Subspace method for Rummler channel estimation1: Construct a M×N Hankel MatrixX=X [0] X [1] · · · X [N−1]X [1] X [2] · · · X [N]...X [M−1] X [M] · · · X [M+N−2] , (3.10)where M+N = K.2: Compute the singular-value decomposition X= USVH .3: Find the largest L = 2 largest singular values and the corresponding left andright singular vectors Us and Vs.4: Compute estimates of zˆl from (3.9) as the eigenvalues of the matrix Z=U+s ·U¯swhere the overbar and underbar symbols represent omitting the first and last rowof each matrix respectively.In order to practically obtain X [k], we calculate Ndft = 4K coefficients of thediscrete Fourier transform (DFT) instead of using the continuous-time Fouriertransform (3.9). We utilize only K of the available coefficients as we assume thatour known narrowband channel estimate C[k] is four-times oversampled.Given zˆl from the subspace method, we estimate the Rummler channel timedelays astˆl = NdftT∠zˆl2pi. (3.11)To obtain the channel coefficients, we transform (3.9) into a Vandermondematrix and solve the system of equations asP=[1 zˆ0 zˆ02 · · · zˆ0K−11 zˆ1 zˆ12 · · · zˆ1K−1](3.12)cˆl = P+ ·X [k]. (3.13)One modification we make to the original subspace algorithm is iterating overa number of M values to generate various unique X matrices (3.10). We then35select a final set of {tˆl, cˆl}Ll=1 coefficients that minimize the mean squared errorbetween the known narrowband channel c[k], and a reconstruction of the narrow-band channel cˆ[k] using such coefficients.Through the subspace method, we are able to obtain a wideband channel es-timate from the known narrowband channel that is suitable for primary streamreconstruction, and secondary stream equalization. However, we observe that anaccurate channel estimate is essential for the primary stream reconstruction. Whenperforming secondary stream detection, small errors in the primary reconstructionstream are amplified due to the large signal power difference. These effects andoverall improvements are illustrated in Chapter 5.3.3 Phase Noise EstimationAnother unique challenge that faces the superposition transmission scheme isthe necessity of precise phase noise estimation, especially for the reconstruc-tion of the primary stream in order to estimate the secondary stream. The phasenoise estimate is used in three locations of the receiver architecture displayed inFig. 3.3. While the initial primary stream phase noise compensator cannot be eas-ily improved, the phase noise re-application in the reconstruction phase is a muchgreater limit to system performance than the final phase noise compensator for thesecondary stream.Once the primary stream has been effectively detected and decoded, there ispotential for a second phase noise estimate. As long we using FEC such as anLDPC code, we could assume every symbol is a pilot in terms of a BCJR-likealgorithm, as long as the code has brought the BER to zero. This suggests that ifthis pilot-assumption method is utilized, the primary stream would have to be alow enough QAM order such that we could assume the BER would drop to zero.Similar to Sec. 2.8, the discrete-time baseband representation of our impairedchannel is expressed asr[k] = s[k]e jφ [k]+n[k], (3.14)36where n[k] denotes the discrete-time AWGN with variance σ2N , and φ [k] denotesa discrete-time representation of the phase noise. A Wiener process models thephase noise with zero-mean IID Gaussian variable steps with variance σ2φ . Themain change relative to Sec. 2.8 is that we now know the originally transmittedsymbol s[k].In order to estimate the phase noise, we use an alternative to the discretizedphase BCJR algorithm [22]. This method assumes the phase noise process is acomplex circularly symmetric Gauss-Markov process. This assumption results inforward and backward recursions in the form of a Kalman smoother. Similar tothe BCJR, we estimate the phase noise by utilizing the distribution P(s[k]) of thetransmitted symbol.The sum-product algorithm we present from [22] is expressed asP(s[k]) ∝∫ 2pi0p f (φ [k])pb(φ [k]) fk(s[k],φ [k])dφ [k] (3.15a)fk(s[k],φ [k]) = exp(1σ2NRe[r[k]s[k]∗e− jφ [k]]− |s[k]|22σ2N)(3.15b)∝ exp(− 12σ2N|r[k]− s[k]e jφ [k]|2),where p f (φ [k]) and pb(φ [k]) correspond to the forward and backward probabili-ties of the phase noise, and fk(s[k],φ [k]) corresponds to current stage’s probability.Note that the proportionality relationships used are allowed, since the algorithmallows scaling its messages by positive factors.In order to simplify the desired distribution P(s[k]), the forward messages areexpressed asp f (φ [k])'∫ 2pi0p(r[k] | φ [k])p f (φ [k−1])δ (φ [k]−φ [k−1])dφ [k−1] (3.16a)37p f (φ [k])'∫ 2pi0exp{r[k−1]s[k−1]∗e− jφ [k−1]σ2N}p f (φ [k−1])δ (φ [k]−φ [k−1])dφ [k−1](3.16b)p f (φ [k]) ∝ exp{Re[a f ,ke− jφ [k]]}, (3.16c)where we assume that the posterior distribution p(r[k] | φ [k]) follows a GaussianPDF of the previously decoded symbol, and that channel phase is slowly varyingfor σφ → 0 such that a simple delta δ (φ [k]−φ [k−1]) is incorporated into the finalrelation. The backward messages are simplified similarly.By using (3.15a) and (3.16c), the desired posterior distribution P(s[k]) takesthe form of a Tikhonov distribution expressed asP(s[k]) ∝ exp(−|s[k]|22σ2N)I0(∣∣∣∣a f ,k+ab,k+ r[k]s∗[k]σ2N∣∣∣∣) (3.17a)a f ,k = γ(σ2φ ,a f ,k−1+r[k−1]s∗[k−1]σ2N) (3.17b)ab,k = γ(σ2φ ,ab,k+1+r[k+1]s∗[k+1]σ2N) (3.17c)γ(x1,x2) =x21+ x1|x2| , (3.17d)where I0 represents the modified Bessel function. Fortunately, the desired pos-terior distribution is maximized at the location of the complex parameter of themodified Bessel function. This property is expressed asφˆ [k] = argmaxφP(s[k]) = ∠(a f ,k+ab,k+r[k]s∗[k]σ2N). (3.18)Therefore, with one forward and backward recursion of all received symbolsin a packet, the phase noise estimate can be improved. Similar to the channelre-estimation method, the phase noise estimate is essential for primary streamreconstruction. The overall improvements are illustrated in Chapter 5.38Chapter 4Multi-Carrier Transmission forUsing Spectrum SkirtsIn this chapter, we introduce the multi-carrier transmission scheme for efficientspectrum utilization through microwave links. This multi-carrier system was pri-marily developed by a colleague in our lab group. The chapter begins by de-scribing the system’s baseband transmission model and illustrating the generaltransmission and receive processes. We then describe the use of custom sidebandpulse shapes to improve overall data rates. Our primary contributions involve thefinal section, with the addition of dual-polarization transmission.4.1 System ModelThe multi-carrier spectrum utilization method transmits three pulses simultane-ously while remaining orthogonal in the frequency domain. This scheme is amethod similar to the frequency multiplexing technique known as Filter BankMulti-Carrier (FBMC) transmission. This technology sends multiple signals shiftedto adjacent frequency offsets, and relies on well designed transmitter and receiverfilters to neglect interference. It is commonly compared with Orthogonal Fre-quency Division Multiple Access (OFDM) but does not require a cyclic prefix or39suffer from high peak power.The continuous-time representation of our multi-carrier transmission model isexpressed ass(t) =∑kI1[k]p1(t− kT )+∑kI2[k]p2(t− kT )+∑kI3[k]p3(t− kT ), (4.1)where I1[k], I2[k], and I3[k] are the QAM symbols of the primary and secondarystreams scaled by power P1 and P2 respectively. The pulse shapes p1(t), p2(t), andp3(t) represent the pulse shapes of the single primary and two secondary streamstransmitted at symbol interval T . The frequency offsets for the secondary streamsare incorporated into each pulse shape.Regarding pulse shapes, Fig. 4.1 illustrates our primary pulse and one of thesecondary pulses that occupy the spectrum skirt. For this pulse shape design, weset the power of the secondary RC pulses to -45dB to ensure that a 30 MHz offsetfrequency fits within the spectral mask. Since these pulses are orthogonal in thefrequency domain, we have the option of using custom pulse shapes, which isdiscussed in a later section. While adding additional pulse shapes below the -50dB spectrum mask is possible, it is not feasible for reliable transmission for theSNR ranges we intend on using.The transmitter architecture in Fig. 4.2 highly resembles the other transmitterschemes with the addition of two secondary streams before analog up conver-sion. However, the main difference between the superposition scheme is that thesecondary pulses require a frequency offset, which does not require much moreadditional hardware complexity.The receiver architecture in Fig. 4.3 is more simple than the superpositionscheme as each pulse can be detected in parallel due to the minimal cross inter-ference. However, one optimization that can be made as discussed in the previoussection is using the channel and phase noise estimation of the primary stream toimprove achievable rates in the secondary streams.400 10 20 30 40 50Frequency Offset From Carrier (MHz)-60-50-40-30-20-10010Amplitude Frequency Response (dB)Multi-Carrier MaskIdeal RRCETSI Spectrum MaskFigure 4.1: Pulse shape for 51.2 MHz multi-carrier transmission scheme.FEC EncoderQAMMapperOffset Pulse 25.6 MHzAnalog Up-conv.Secondary Stream 1 Bits InFEC EncoderQAMMapperSecondary Stream 2 Bits InFEC EncoderQAMMapperPrimary Stream Bits InDACRRC Pulse 25.6 MHz DACOffset Pulse 25.6 MHz DACFigure 4.2: Transmitter architecture for multi-carrier scheme.4.2 Pulse Shape DesignAs mentioned earlier, the secondary pulses do not necessarily have to conformto the typical RRC shape seen in the other schemes. Instead, our colleagues de-sign a custom pulse to fill the spectrum mask. The problem may be formulatedas an optimization problem to match the spectrum mask as closely as possible.This translates to minimizing the weighted sum squared error between the desiredshape and the actual filter bank waveform. Note that these pulses are asymmetricand result in complex valued filter taps. Additionally, the filter coefficients are41FEC DecoderQAMDemapperLinear EQ + Phase Noise TrackingRRC Matched FilterAnalog Down-conv.T-SamplingPrimary Stream Bits OutFEC DecoderQAMDemapperLinear EQ + Phase Noise TrackingOffset Matched FilterAnalog Down-conv.T-SamplingSecondary Stream 2 Bits OutFEC DecoderQAMDemapperLinear EQ + Phase Noise TrackingOffset Matched FilterAnalog Down-conv.T-SamplingSecondary Stream 1 Bits OutFigure 4.3: Receiver architecture for multi-carrier scheme with linear equal-ization, phase noise tracking, and FEC coding.made to be conjugate-symmetric in order to limit the phase response as linear.The translation of these properties to a frequency response is expressed asP( f ) = e− j2piN f(v˜re( f )T p˜re+ v˜im( f )T p˜im)(4.2a)v˜re( f ) = [1,2cos(2pi f ),2cos(4pi f ), . . . ,2cos(2piN f )]T (4.2b)v˜im( f ) = [1,2sin(2pi f ),2sin(4pi f ), . . . ,2sin(2piN f )]T , (4.2c)where p˜re and p˜im denote the discrete-time filter coefficients and N denotes thenumber of filter coefficients we hope to use.Once the frequency responses are defined, the filter design optimization prob-lem can be formulated as the minimization of a weighted sum squared error asminp˜re,p˜im∫ Fs/2−Fs/2∣∣D( f )− (v˜re( f )T p˜re+ v˜im( f )T p˜im)∣∣2 d f (4.3)subject to∣∣v˜re( f )T p˜re+ v˜im( f )T p˜im∣∣≤ D( f ),∀ f ∈ [−Fs/2,Fs/2],where D( f ) denotes the amplitude response of the desired spectrum mask andFs denotes the sampling frequency of the desired spectrum mask. The optimizedpulse shape selected for simulations is illustrated in Fig. 4.4. Relative to the center420 10 20 30 40 50Frequency Offset From Carrier (MHz)-60-50-40-30-20-10010Amplitude Frequency Response (dB)Multi-Carrier MaskIdeal RRCETSI Spectrum MaskFigure 4.4: Modified pulse shape for 51.2 MHz multi-carrier transmissionscheme.frequency, the custom pulse spans from +5dB to -5dB in its active region, anddrops down to -50dB when exiting the bandwidth intended for usage.4.3 Dual-PolarizationWe again emphasize that we did not complete the preceding work, as it was notthe main focus of the thesis. The main focus of this thesis was the superpositionscheme, and how it compares to another modular spectrum utilization scheme.However, we contribute to the multi-carrier scheme by implementing an addi-tional technique known as Dual Polarization (DP), to significantly improve per-formance. While the superposition architecture has the option of supporting thismethod as well, the implementation is more straightforward with the separate non-overlapping pulse shapes within the multi-carrier scheme.Many practical state-of-the-art microwave systems utilize a horizontal and ver-tical polarization transmitted at the same carrier frequency in order to double thedata rate. However, these designs suffer from cross-talk between the two polar-43izations known as Cross-Polarization Interference (XPI). In order to combat thisimpairment, a synchronous approach may be taken after receiving time and fre-quency synchronized samples from both streams. By coordinating a XPI cancella-tion filter to remove interference simultaneously, the cross-talk can be effectivelycancelled [23].The continuous-time baseband model for DP transmission is expressed assi(t) =∑kIi[k]p(t− kT ), (4.4)where Ii[k] for i ∈ {1,2} denote the QAM symbols for the ith stream, while p(t)represents the transmission RRC pulse shape.The continuous-time baseband model for the received signal is expressed asri(t) = e jφri(t)2∑j=1∫ ∞−∞s j(τ)ejφt j (τ)hi j(t− τ)dτ+ni(t), (4.5)where hi j(t) denotes the effective cross-talk channel response, modelling the com-bined effects of multipath ISI and XPI. Similar to previous models, the noise niis AWGN, while φti and φri represent the transmitter and receiver phase noiseprocesses.This channel operation is also expressed in the block diagram of Fig. 4.5.Through this diagram, it can bee seen that each stream has an effect on the ad-jacent stream through the channel filter, and that the phase noise is applied bothat the transmitter and receiver. Previously, we assumed that the phase noise wascombined due to only having one dispersive channel. However, with the additionof cross-talk, the phase noise must be properly applied at the transmitter and re-ceiver. Nevertheless, the transmitter and receiver phase noise is treated as a singleprocess by the phase noise cancellation block.We utilize the BCJR algorithm to compensate for phase noise, but alternativemethods exist. One such option is a MMSE-based strategy that utilizes a Mas-ter/Slave phase synchronized phase lock loop in order to jointly track the phase44exp{jϕt1}s1s2n1n2Interference & Phase Noise Cancelation2DISI Channelh11h22h 21h12exp{jϕr1}exp{jϕr2}exp{jϕt2}Figure 4.5: Channel model for dual-polarization scheme.noise on each branch [24]. This method has the benefit of requiring no statisticalknowledge of the phase noise process. Another method is an adaptive decision-feedback structure with linear precoding that effectively cancels interference andtracks the carrier phase [23]. This method has the benefit of increased Faster-than-Nyquist (FTN) rates to improve spectral efficiency. However, we move for-ward with the original BCJR algorithm due to its reliability, and to stay consistentwithin our project.The addition of the dual channel also requires an increase of equalizer com-plexity. Instead of one time dispersive channel and one input stream, the equalizermust handle four channels and two input streams simultaneously. While many ofthe discussed joint phase noise and equalization techniques implement an adap-tive non-linear scheme, a linear approach is still possible. In a practical setting,the linear approach would be broken down into a training phase to learn the chan-nel, and operation phase for data transmission. However, in order to implementthe joint dual-polarization / equalization block, slight adjustments must be madeto our dispersive channel assumptions.Firstly, while performing each equalization operation separately is possible,performing the full operation concurrently allows the information of one streamto help decode the opposite stream. While many assumptions made by MMSElinear equalization still stand, the matrices must be formulated differently to allow45a dual convolution. Secondly, In order to allow the input of both streams and allfour channels in a single convolution operation, the data matrix interleaves thefirst stream data and the second stream data. The channel matrix is then groupedin 2×2 squares and simulate a Toeplitz Matrix convolution operation. Neglectingthe impact of phase noise, the resulting matrices are expressed asr =Cs, s=s1[0]s2[0]s1[1]s2[1]...s1[k−1]s2[k−1](4.6)C =c1,1[0] c1,2[0] 0 0 . . . 0 0c2,1[0] c2,2[0] 0 0 . . . 0 0c1,1[1] c1,2[1] c1,1[0] c1,2[0] . . . 0 0c2,1[1] c2,2[1] c2,1[0] c2,2[0] . . . 0 0............ . . . 0 0c1,1[L−1] c1,2[L−1] c1,1[L−2] c1,2[L−2] . . . c1,1[0] c1,2[0]c2,1[L−1] c2,2[L−1] c2,1[L−2] c2,2[L−2] . . . c2,1[0] c2,2[0],where ci, j correspond to the cascade of the transmitter and receiver filters, theRummler channel, and the cross-talk effects. Once the matrices are formed in thispattern, the equalizer coefficients may be found by using the previous equalizationtechniques discussed in Chapter 2.Dual polarization is possible to implement with the superposition scheme, butcross-channel talk would be difficult to reproduce for the reconstruction streamand would severely dampen performance. Additionally, the multi-carrier sec-ondary pulses are orthogonal in the frequency domain to the primary pulse, caus-ing minimal interference for the dual XPI and ISI filter. Instead, we keep dual-46polarization isolated to the multi-carrier method and illustrate results in the fol-lowing chapter.47Chapter 5Numerical Results and DiscussionThroughout this chapter, we present the numerical results for the spectrum utiliza-tion methods outlined throughout this thesis. We begin by presenting the effectsof each channel impairment on the superposition scheme, and then add the chan-nel extrapolation and phase noise re-estimation methods. We then compare thesuperposition scheme with the multi-carrier scheme, and then conclude with theanalysis of multi-carrier dual-polarization transmission.Throughout this chapter, we primarily use the AIR to predict the performanceof each system configuration. The AIR performance can be verified through sim-ulation by applying a strong FEC code and ensuring that the BER drops off withina predicted SNR range. For example, for a system using a 210-QAM constella-tion, when the simulated AIR reaches 5 bits per channel use, a 1/2 coding schemecould be applied to obtain a BER dropoff within a reasonable SNR range.We assume that the primary stream of our superposition model has been per-fectly detected when calculating the AIR for the secondary stream. This allowsfor the secondary stream to be detected with a primary stream reconstruction thatonly relies on the channel and phase noise estimates for strong performance. Wecan also validate this assumption by ensuring that the BER drops off within areasonable range against the predicted SNR location.We typically use a constellation size of [212,24]-QAM for the primary and48secondary streams of the superposition scheme, and [214,24]-QAM for the multi-carrier scheme. We also consider a baseline “RC” scheme throughout many sim-ulations, which utilizes a single RC pulse without making use of the spectrumskirts. This baseline RC method dictates the units of all of our AIR curves, bitsper RRC channel use, meaning how many bits could be sent relative to a trans-mission scheme with a single RC pulse. Whenever phase noise is present, we usethe BCJR algorithm with pilots sent every 50 symbols to compensate such phasenoise.5.1 Superposition Transmission with BCJR PhaseEstimationWe first consider the superposition transmission scheme with BCJR phase estima-tion. We assume that we have full wideband channel knowledge after performingsome pilot training phase. This section considers the transmission architecturebefore introducing improvements in Sec. 5.2 to illustrate a generalized overviewof channel impairments.We begin by comparing the pre-improvement superposition scheme againstvarious Rummler channels. Fig. 5.1 illustrates the results for two Rummler chan-nel instances with notch depths of 3.5dB and 7dB. A 214-QAM RC scheme isalso displayed to demonstrate that the superposition scheme is impacted by a se-vere notch depth by a similar amount. While the gaps between each simulationare slightly larger in the superposition case, the general shapes of the AIR curvesremain the same, and performance is only slightly impacted.The next set of results consider different levels of phase noise at the trans-mitter and receiver. Fig. 5.2 illustrates the AIR over an AWGN channel withlevels of phase noise at -90dBc/Hz and -85dBc/Hz. This phase noise is compen-sated with the BCJR algorithm without the Tikhonov phase re-estimation method.The superposition results are impacted by increased phase noise much more thanthe 214-QAM RC benchmarks. This is due to the necessity for accurate phasenoise estimates during primary stream reconstruction. However, the superposi-4930 35 40 45 50 55 60SNR [dB]05101520AIR [bits / RRC channel use]RC, No RummlerRC, 3.5dB NotchRC, 7dB NotchSP, No RummlerSP, 3.5dB NotchSP, 7dB NotchFigure 5.1: AIR for multiple Rummler channel instances with 214-QAM RCtransmission and [212,24]-QAM superposition transmission.tion scheme still outperforms the RC benchmark in each phase noise instance.5.2 Superposition Transmission withImprovementsWe now introduce channel extrapolation via the subspace method and Tikhonovphase re-estimation outlined in Chapter 3 to improve data rate performance. Westill use BCJR phase estimation for primary stream phase noise compensation,and also assume that the narrowband channel is known for channel extrapolation.We first begin with analyzing the channel extrapolation methods by observingsecondary stream AIR performance in Fig. 5.3. This simulation has no phasenoise effects and uses the QAM orders of 212 and 24 for the primary and secondarystream respectively. Two relatively severe Rummler channels with notch depthsof 7dB and 13dB are compared each with the RRC removal method, finite rate-of-innovation subspace method, and ideal channel knowledge. In each case tested,5030 35 40 45 50 55 60SNR [dB]05101520AIR [bits / RRC channel use]RC, No PNRC, PN with -90dBc/HzRC, PN with -85dBc/HzSP, No PNSP, PN with -90dBc/HzSP, PN with -85dBc/HzFigure 5.2: AIR for various phase noise levels with 214-QAM RC transmis-sion and [212,24]-QAM superposition transmission.the subspace method outperforms the RRC removal by some margin. While thesubspace approach does not reach perfect channel knowledge results, it is robustagainst moderately notched Rummler channel responses.Next, we observe the impact of phase noise re-estimation over a standardAWGN channel with no dispersive channel effects and -90dBc/Hz phase noise.The results are illustrated with the secondary 24-QAM AIRs in Fig. 5.4 withprimary streams of 212-QAM and 214-QAM. These results compare the origi-nal BCJR estimation, the new Tikhonov re-estimation, and a genie re-estimationwhich is analogous to no phase noise.We observe that regardless of QAM order, data rates can be improved withour new phase noise re-estimation method. Also, by observing the gaps betweenBCJR and Tikhonov phase estimation, we notice that an increased primary streamQAM order emphasizes the need for phase noise re-estimation. For clarification,we interpret that the two Tikhonov AIR curves align for 212-QAM and 214-QAMdue to a saturation of the best possible estimate below genie-aided results.5140 45 50 55 60SNR [dB]00.511.522.533.544.55AIR [bits / RRC channel use]7dB notch, RRC removal7dB notch, Subspace7dB notch, Ideal13dB notch, RRC removal13dB notch, Subspace13dB notch, IdealFigure 5.3: Secondary stream AIR for various Rummler channel reconstruc-tions with [212,24]-QAM superposition transmission.30 35 40 45 50 55 60 65 70SNR [dB]00.511.522.533.544.55AIR [bits / RRC channel use]BCJR, m=[12,4]Tikhonov, m=[12,4]Genie, m=[12,4]BCJR, m=[14,4]Tikhonov, m=[14,4]Genie, m=[14,4]Figure 5.4: Secondary stream AIR for various phase noise re-estimationmethods with [212,24] and [214,24]-QAM superposition transmissionwith phase noise at −90dBc/Hz.525.3 Comparing Superposition and Multi-CarrierTransmissionNext, we introduce the multi-carrier (MC) transmission scheme to compare withthe superposition (SP) scheme. In order to complete a fair comparison, we use thesame number of equalizer taps for Rummler channel equalization and the samenumber of states in the BCJR phase estimation state machine. We consistentlyapply a Rummler channel with a 5dB notch along with phase noise at -90 dBc/Hz.Fig. 5.5 shows the AIR comparison between the standard AWGN channel andimpaired channel for the standard RC and two modular schemes. We selected theQAM order configurations which yielded the strongest AIR results under our 5dBnotch Rummler channel instance and -90dBc/Hz phase noise level. The “DC”acronym represents a Rummler channel being present. While these QAM con-figurations performed best under the current impairments, different combinationsmay perform better at lower or higher SNR values. With this in mind, adaptivecoding and modulation could be applied based on pre-determined SNR thresh-olds. For instance, the secondary streams could use 23-QAM at low SNR values,and 24-QAM at high SNR values.Regardless of channel impairments, both modular schemes outperform thebaseline RC scheme. Under the standard AWGN channel, the multi-carrier schemeperforms the best at low SNRs while the superposition scheme reaches the highestmaximum data rate at high SNRs. However, with the introduction of a dispersivechannel and phase noise, the multi-carrier scheme outperforms the superpositionscheme at all SNR values. This is due to the difficulty of reproducing channelimpairments for the reconstructed primary stream for the superposition scheme.We then predict the dropoffs at particular code rates using the AIR results.The BERs shown in Fig. 5.6 demonstrate how accurate dropoff estimations are. ALDPC coding scheme with rate 0.75 and codeword length 64800 bits is used forchannel coding. The three code rates (Rc) are selected to attempt to fit the dropoffsnear 45dB.We first observe the non-steep dropoff of the RC scheme. The dropoffs of the5330 35 40 45 50 55 60SNR [dB]05101520AIR [bits / RRC channel use]RC, m=14, AWGNRC, m=14, DC & PNSP, m=[12,4], AWGNSP, m=[12,4], DC & PNMC, m=[14,4], AWGNMC, m=[14,4], DC & PNFigure 5.5: AIR for 214-QAM RC, [212,24]-QAM superposition, and[214,24]-QAM multi-carrier transmission with phase noise at−90dBc/Hz and a 5dB-notch Rummler channel.40 42 44 46 48 50SNR [dB]10 -410 -310 -210 -110 0Bit Error Rate (BER)Figure 5.6: BER for 214-QAM RC, [212,24]-QAM superposition, and[214,24]-QAM multi-carrier transmission with phase noise at−90dBc/Hz and a 5dB-notch Rummler channel.54superposition and multi-carrier scheme correspond to the secondary streams atlow 24-QAM orders. At these high SNR values, the primary streams already havepractically zero error-rates due to their strong code rates. However, the RC schemeuses a much higher code rate for its 214-QAM pulse, which results in the non-steepBER dropoff. We then observe how accurate the superposition dropoff estimatesare relative to the multi-carrier scheme. This is explained by the stronger phasenoise estimates that the superposition secondary stream has access to. While themulti-carrier scheme has a low QAM order, it also uses custom pulse shapes thatare slightly more difficult to equalize.Following these results, we wish to determine if the Rummler channel or phasenoise is the primary bottleneck for the superposition scheme. The schemes shownin Fig. 5.7 use 212-QAM for the primary streams of the superposition and multi-carrier schemes respectively, and 4 and 16-QAM for their secondary streams.Only the BER for the secondary streams are illustrated since the primary streamsundergo perfect detection at the SNRs used. As seen in the BER curves, the super-position scheme performs the strongest under only dispersive channel conditions,but the introduction of phase noise significantly decreases performance.5.4 Multi-Carrier Dual-Polarized TransmissionFinally, we implement dual-polarization alongside the multi-carrier architectureconsidering that it outperformed the superposition scheme under practical chan-nel conditions. While dual-polarization introduces cross-channel interference, wemay obtain a much higher data rate with sufficient cancellation methods.To illustrate the impact of cross-channel interference on multi-carrier perfor-mance, we first show results for a benchmark RC scheme. Fig. 5.8 shows theseresults under various levels of cross-channel interference with a 3.5dB notchedRummler channel and phase noise at -90dBc/Hz.The corresponding BERs are displayed in Fig. 5.9 under a 3/4 LDPC coderate. We notice that the cross talk curve takes much longer to dropoff relativeto the RC benchmark. We explain this by referring to Fig. 5.8, where the -12dB5540 45 50 55 60 65SNR [dB]10 -410 -310 -210 -110 0Bit Error Rate (BER)SP, DC, m=2SP, DC, m=4SP, DC & PN, m=2SP, DC & PN, m=4MC, DC, m=2MC, DC, m=4MC, DC & PN, m=2MC, DC & PN, m=4Figure 5.7: BER for [212,22/24]-QAM superposition, and [212,22/24]-QAM multi-carrier transmission with phase noise at −90dBc/Hz anda 5dB-notch Rummler channel with a 0.75 rate LDPC code.20 25 30 35 40 45 50SNR [dB]051015AIR [bits / RRC channel use]DP, no cross-talkDP, -15dB cross-talkDP, -12dB cross-talkDP, -10dB cross-talkFigure 5.8: AIR for 212-QAM RC dual-polarized transmission with phasenoise at −90dBc/Hz and a 3.5dB-notch Rummler channel.5626 28 30 32 34 36SNR [dB]10 -410 -310 -210 -110 0Bit Error Rate (BER)Figure 5.9: BER for 212-QAM RC dual-polarized transmission with phasenoise at −90dBc/Hz and a 3.5dB-notch Rummler channel.cross-talk curve saturates at 10.5 bits. By using a 3/4 code rate at 212-QAM, thepredicted dropoff is located at 9 bits, which is close to the maximum data rate. Byusing a stronger code rate to obtain a predicted dropoff at a lower SNR, a steeperdropoff would be observed.We finally introduce dual-polarization to the multi-carrier scheme. The multi-carrier scheme originally used 214-QAM for its primary pulse, but must be re-duced to 212-QAM due to the cross-channel talk introduced by dual-polarization.Fig. 5.10 shows the results for our original multi-carrier and RC benchmark, alongwith a 212-QAM dual-polarization RC transmission scheme and a 212-QAM dual-polarization multi-carrier scheme with 24-QAM sideband usage. We observe thatthe application of dual-polarization outperforms all previous results discussedwithin this thesis. While this transmission system requires a more complex ISIand cross-channel interference cancellation block, and the transmitter and receivermust be capable of receiving dual-polarized signals, the achievable data-rates canbe significantly improved by implementing this technology.5720 25 30 35 40 45 50 55 60SNR (dB)051015202530AIR [bits / RRC channel use]RC, m=14MC, m=[14,4]DP, m=12DP & MC, m=[12,4]Figure 5.10: AIR for 212-QAM RC and [212,24]-QAM multi-carrier dual-polarized transmission with phase noise at −90dBc/Hz and a 3.5dB-notch Rummler channel.58Chapter 6ConclusionsIn this thesis, we outlined two modular microwave transmission methods that uti-lize spectrum skirts to improve data-rate performance. We began by introducinga generalized microwave link transmission model that does not use the spectrumskirts, in order to establish a benchmark system. We also discussed system impair-ments such as multipath fading and phase noise, that would be present in practicalmicrowave communication systems.We then proposed a superposition transmission model that added a high-powernarrowband and low-power wideband signal at the transmitter, and sequentiallydetected the signals at the receiver. We then introduced a novel channel estimationmethod which made use of the narrowband channel in order to extrapolate thewideband channel response to reduce equalization overhead. In order to detectthe low-power secondary signal, the primary stream needed to be reconstructedfor cancellation purposes. We improved this cancellation accuracy by utilizingFEC-aided symbol estimates to re-estimate the phase noise.Next, we outlined a multi-carrier transmission model developed by a colleaguethat sent two low power secondary pulses orthogonal to the primary pulse in thefrequency domain. These secondary streams were able to use custom pulse shapesdue to their minimal interference from the high power primary stream. Our con-tributions included adding dual-polarization transmitter and receiver to improve59data-rates further. We finally compared these two modular methods via numericalresults in our final section.Both spectrum utilization methods allowed for easy modular implementa-tion due to how their secondary streams could be simply enabled or disabled.While the superposition scheme offered more novel techniques such as Tikhonovphase re-estimation and channel extrapolation, the multi-carrier approach hadthe best performance under our selected channel impairments. Additionally, theease of implementing dual-polarization for the primary stream of multi-carrierwas another added benefit. Reconstructing a dual-polarized superposition pri-mary stream would likely be too difficult and still under-perform the multi-carrierscheme. However, superposition did not require custom pulse shapes and out-performed the other scheme without phase noise, which would be useful in someapplications.Future work could include the pursuit of a single-carrier scheme with a singlecustom pulse shape. While this would require advanced equalization techniquesto handle the ISI caused by the custom pulse shape, it could utilize more of theavailable bandwidth. Additionally, we made use of linear equalization to handleall dispersive channel impairments. An adaptive-equalization method could beimplemented in order to test the effects of time varying dispersive channels, andthe actual overhead required for a practical equalization architecture. Finally, oneprimary assumption made at the beginning of this thesis was to assume that thesidebands would go unused through the duration of a transmission. 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Thesis/Dissertation
eng
Electrical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Modular spectrum utilization for next-generation fixed transmission networks
Text