A thesis outline submitted in partial fulfillment of the requirement of Nazarbayev University for the degree of Doctor of Philosophy

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Performance analysis of future communications systems under residual hardware impairments

Leila Tlebaldiyeva

A thesis outline submitted in partial fulfillment of the requirement of Nazarbayev University for the degree of Doctor of Philosophy

April, 2020

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Dated:

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Abstract

Cognitive radio (CR) and millimeter wave (mmWave) communication are two potential technologies for future wireless communication systems to meet ever-increasing consumer data demand. The significant advantage of CR is its ability to improve spectrum utilization by introducing spectrum management paradigms between primary and cognitive users. An even more significant enabling technology for future communications is mmWave communication that offers enormous bandwidth at mmWave frequency bands.

Low-grade transceiver hardware is often utilized in modern communication systems to lower the cost of potential networks. The residual hardware distortion noise originating from high rate and low-grade transceiver hardware is a vital parameter to consider while designing reliable systems. This dissertation work pursues to model residual transceiver hardware impairments by using the statistical additive Gaussian model, which is mathematically tractable and can be embedded in complex system configurations.

In this thesis, we first develop a system model for a dual-hop decode-and-forward underlay CR relay network operating under residual hardware impairments and derive a closed-form expression for the outage probability performance. Moreover, this work provides useful discussions on the design aspects of wireless communication systems in terms of the outage probability given residual transceiver noise level and fading parameters of channel.

Secondly, we study the spectrum sensing technique by employing an improved energy detector (ED) under residual hardware constraints. We present a novel test statistic for improved ED that accounts for residual distortion noise when the fading statistics of the received signal follows theα−µdistribution. Moreover, we derive closed-form expressions for theprobabilities of detection and false alarmand thearea under the receiver operating characteristic curve (AUC)for additive white Gaussian and Nakagami-mfading channels. Our work proposes a new diversity concept ofp-order-law combiningand p-order-law selectingschemes to combat the adverse effect of residual hardware impairments.

Thirdly, our study develops an analytical framework for analog beamforming device- to-device mmWave communication constrained by residual hardware impairments and other random impairments such as multi-user interference, inter-beam radio frequency (RF) power leakage, and imperfect channel state information (CSI). We perform in-depth outage probability and ergodic capacity analysis for the proposed system model.

Finally, we propose to implement a maximum sub-array transmission (MST) scheme built on a hybrid beamforming structure that enables multi-user communication and high outage probability and ergodic capacity performance. The MST diversity suffers from RF power leakage and transceiver distortion noise that are addressed in this work.

The hardware impaired communication systems transmit at considerably lower rates than the ideal ones, and, therefore, our research emphasizes the importance of residual distortion modeling.

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Acknowledgments

During my Ph.D. program, I had this rare opportunity working with three well- established researchers in the field of wireless communications. I feel enormously fortu- nate and proud for being supervised by ProfessorCorbett ROWELL, ProfessorTheodoros A. TSIFTSIS, and ProfessorBehrouz MAHAM. During the first year of the Ph.D. program, ProfessorCorbett ROWELLtaught us the most interesting courses in advanced communications that enlightened me and increased my knowledge in the area of wireless communications. I want to thank ProfessorCorbett ROWELL for sharing his unique experience working in the telecom industry and designing RF circuits.

Starting from March 2016 I began working with ProfessorTheodoros A. TSIFTSIS. He proposed the main title of the dissertation work and helped me to acquire important research skills and methods. Besides, I was closely working with Professor Theodoros A. TSIFTSISuntil completion of my Ph.D. program through videoconferencing and email communication. Beginning from March2018, I started working with ProfessorBehrouz MAHAM, who has broadened and enriched my research area to the millimeter wave communications, which is a popular research direction today. Additionally, I still communi- cate with I want to express my greatest gratitude to ProfessorTheodoros A. TSIFTSISand Professor Behrouz MAHAM for dedicating their mentorship, delightful collegiality, and sharing valuable knowledge and time during my Ph.D. studies.

Besides, I would like to thank my co-supervisor, ProfessorRefik Caglar KIZILIRMAK

for his valuable comments and professional advice.

Besides my supervisors, I would like to distinguish and thank ProfessorLuis R. Rojas- SOLÓRZANOfor his positive attitude, trust, and genius support during my Ph.D. journey.

My highest appreciation goes to my family members for their patience, love, and prayers. Mainly, I would like to thank our grandmother - Bakhyt, for her sincere dedica- tion to taking care of her two young grandchildren (my children) Alimzhan and Rayana.

Finally, my thanks go to all my friends and colleagues who have supported me to complete this research work.

Leila TLEBALDIYEVA

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Preface

Leila TLEBALDIYEVA received the B.Sc. (with Distinction) degree in Communications Engineering from Carleton University, Ottawa, Canada, in June 2010. She got M.Sc.

(with Merit) degree in Wireless and Optical Communications Engineering fromUniver- sity College Londonin September2012. From August2010to March2011, she worked as a broadcast liaison manager in IT and TV broadcast department of Organizing Committee for the 7th Winter Asian Games in Astana-Almaty, and then as a laboratory assistant at Nazarbayev Universityfrom April2011to September2011. Then after pursuing an MSc degree, she continued working as a laboratory assistant from October 2012 to Jan 2015.

Then, from May 2012 till January 2017, she worked as a teacher assistant atNazarbayev University. Since January2015, she started a Ph.D. degree in Science, Engineering, and Technology with the research topic on Performance analysis of future communications systems under residual hardware impairments at the School of Engineering and Digital Sciences, Nazarbayev University.

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List of Figures

1.1 Worldwide mobile subscribers (in millions) in2007−2018years. . . 2

1.2 Global mobile data traffic (exabytes per month) in2017−2022years. . . 2

2.1 Cognitive radio network scheme. . . 8

2.2 Major cognitive user functionalities. . . 9

2.3 Overview of CR paradigms: underlay, overlay, and interweave. . . 9

2.4 5G deployment map in the World. . . 11

2.5 A typical direct conversion radio receiver architecture. . . 12

2.6 Representation of the EVM vector. . . 16

3.1 System and signal model for underlay dual-ho DF relay network under hardware impairments. . . 21

3.2 Outage probability versusP/N₀ at differentI/N₀ = 0,10,15,20(dB). . 26

3.3 Outage Probability at different fading parameters simulated forκ = 0.1 andκ= 0.4. . . 27

3.4 The outage probability plots forx= 3; 16dB andκ= 0.1; 0.65. . . 27

3.5 Evaluatedκ₁ values atm_sp =m_rp = 3,m_sr =m_rd=1:6. . . 29

3.6 Calculated results forκ₂, whenm_sp =m_rp = 3,m_sr =m_rd=1 : 6. . . 29

4.1 System model for the improved ED for non-diversity SU receiver. . . 35

4.2 ThepLC andpLS diversity reception schemes for the improved ED. . . . 45

4.3 Error plot forP¯_{DN ak}^id,appr whenj = [ 0 : 40] andn = [0 : 50], m = 2, p = 10,γ¯ = 0.1. . . 50

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4.4 Total error rate for diversity receivers and non-diversity receiver versus SNR over AWGN channels. . . 51 4.5 The ROC curves at varyingγ values over AWGN channel. . . 52 4.6 The ROC curves for diversity and non-diversity receivers over Rayleigh

fading channels. . . 52 4.7 The average AUC versus average SNR forp= 4; 6; 10over AWGN channel. 53 5.1 System model for the beamformed D2D assisted communication network

with interfering nodes. . . 57 5.2 The outage probability versus average SNR at distancesL = 100; 150; 350

m forκ = 0; 0.2; 0.3.. . . 70 5.3 The outage probability versus rate for high and low interference fading

parameters. . . 71 5.4 Normalized ergodic capacity for the D2D assisted communication net-

work under the presence of interfering nodes given L = 70,300 m and κ= 0.1,0.2,0.3. . . 71 5.5 Normalized ergodic capacity for D2D network givenN = 0; 5; 10; 30; 50,

κ= 0,L0 = 70m, and ideal CSI. . . 72 5.6 Normalized ergodic capacity versusλforN = 5,10,30,κ = 0; 0.3, and

SNR= 0; 20dB. . . 72 5.7 Normalized ergodic capacity with its upper and lower bounds for the pro-

posed system model with L = 70 m, N = 30, κ = 0; 0.3, and ideal CSI. . . 73 6.1 Hybrid beamforming mmWave network model under RF power leakage

constraint by using SDMA to separate users. . . 78 6.2 Hybrid beamforming network with maximum sub-array transmission di-

versity technique towards UE1. . . 80 6.3 Outage probability curves versus receive SNR for different levels of transceiver

distortion noise and UE2average power. . . 84

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6.4 Outage probability for a hybrid beamforming mmWave network model forL= 50m and different levels of transceiver distortion noise. . . 84 6.5 Ergodic capacity for a hybrid beamforming mmWave network model un-

der RF power leakage constraint and transceiver distortion parameters κ= 0.01; 0.2; 0.3. . . 85

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List of Tables

3.1 The fading parameter values for Fig. 3.3 . . . 26 3.2 Calculatedκ₂values form_sp =m_rp = 3,m_sr=m_rd = 1 : 6 . . . 30 4.1 Total error rate for non-diversity and diversity receivers atγ =−2dB. . . 51 5.1 Network parameters for outage probability simulations. . . 69 5.2 Network parameters and their numerical values. . . 71 6.1 System parameters of the proposed system model . . . 85

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List of Abbreviations

1G first generation

2G second generation

3G third generation

3GPP third generation partnership project

4G fourth generation

5G fifth generation

ACI adjacent channel interference ADC analog-to-digital converter

AUC area under the receiver operating characteristic curve AWGN additive white Gaussian noise

BPSK binary phase shift keying CDF cumulative distribution function

CR cognitive radio

CSI channel state information

CU cognitive user

DAC digital-to-analog converter

DARPA Defence Advanced Research Projects Agency

dB decibel

DF decode-and-forward

D2D device-to-device

ED energy detector

EVM error vector magnitude

I/Q in-phase (I) and quadrature (Q)

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I.I.D. (i.i.d.) independent and identically distributed I.N.I.D. (i.n.i.d.) independent and not identically distributed

LOS line-of-sight

LTE long term evolution

MST maximum sub-array transmission MIMO multiple-input multiple-output MmWave millimeter wave

NLOS non line-of-sight

OFDM orthogonal frequency-division multiplexing OSA opportunistic spectrum access

PDF probability density function

PU primary user

QAM quadrature amplitude modulation QPSK quadrature phase-shift keying

RF radio frequency

ROC receiver operating characteristic

RV random variable

SNDR signal-to-noise-distortion ratio

SNDIR signal-to-noise-distortion-interference ratio SRDNR signal-to-RF leakage-distortion-noise ratio SNR signal-to-noise ratio

SU secondary user

UE user equipment

UHF ultra-high frequency

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List of Symbols

CN(a, b) complex normal distribution withamean andbvariance f_X(x) probability density function of random variableX F_X(x) cumulative distribution function of random variableX Γ(·) Gamma function

Γ(a, b) upper incomplete Gamma function γ(a, b) lower incomplete Gamma function E(·) statistical expectation operator

κ EVM level

λ wavelength

N₀ noise power at the receive node γ_th predefined SNR threshold x lower bold case denotes vector

|x| absolute value ofx kxk Euclidean norm ofx γ nominal transmit SNR D secondary destination Pr(A) probability of the eventA P_out(·) outage probability

P average signal power P R primary receiver

S secondary source

R secondary relay

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Chapter 1

Introduction

"Wireless is coming to mankind... Some day there will be, say, six great wireless tele- phone stations in a world system connecting all the inhabitants on this earth to one another, not only by voice but by sight" said Nicola Tesla [1] back in1905 by predicting mainstream wireless communication that empowers both voice and video communication. Tesla’s prediction came true in the twenty first century and Fig. 1.1 from [2] and Fig. 1.2from [3] demonstrate the scale of modern communication. In Fig. 1.1, the fore- cast of active mobile users between 2017 to 2022 is presented by Cisco Systems. The number of global mobile users has enormously emerged over the last decade. Based on Fig. 1.2, we see that global mobile data traffic annually increases by around average to 50% from2017 to2022. Alternatively, monthly data demand will increment6.73times over 5years [4]. A high market demand for wide bandwidth as well as competition for a high revenue among mobile vendors and technological development of semiconductor technology accelerated development of wireless communication networks from1G with 2 kb/s data rate in 1980 to 5G with 1 Gb/s data rate in 2020. In this work, we investigate the practical future wireless communications systems that aim to meet consumer requirements.

1.1 Problem statement

Ever-increasing data demand and bandwidth limitation in the ultra-high frequency (UHF) range create a performance bottleneck in modern communication systems. Spectrum

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Chapter 1. Introduction 2

Figure 1.1.Worldwide mobile subscribers (in millions) in2007−2018 years.

Figure 1.2.Global mobile data traffic (exabytes per month) in 2017−2022years.

sensing/sharing techniques and millimeter wave (mmWave) communication with massive multiple-input multiple-out (MIMO) antennas are two popular, promising technologies to meet high bandwidth demand. On the one hand, cognitive radio (CR) technology [5], [6]

solves the spectrum scarcity problem by managing spectrum sharing between primary and

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Chapter 1. Introduction 3 secondary users. On the other hand, mmWave frequencies along with massive MIMO antenna systems [7], [8] began a new era in wireless communications, called5G and beyond, that aims to resolve the technological limitation of the UHF range and explore enormous bandwidth between3−300GHz. Practical transceivers used in high rate systems are not ideal and add residual distortion noise to the system [9]. The impact of distortion noise is even more profound in mmWave systems due to complications in high frequencies [10].

Other performance degradation factors in wireless communication are interference and RF power leakage [11], [12] from neighboring user equipment (UE) nodes.

1.2 Motivation

Residual transceiver distortion noise always exists in wireless communications systems;

however, it is often ignored in the analysis of modern communication systems. In this work, we aim to fill this gap by studying recently introduced technologies for5G, such as cognitive spectrum sensing/sharing networks and mmWave communication technologies under transceiver distortion noise constraints. The advantage of residual distortion noise modelling is the ability to design more reliable modern communication systems. This work suggests using comprehensive transceiver distortion noise modelling that also facilitates analysis of other system constraints such as interference, RF power leakage, and imperfect CSI.

1.2.1 Key contributions

This section demonstrates the key findings of dissertation work:

• Decode-and-forward (DF) dual-hop cognitive relay system under the presence of transceiver hardware impairments and interference temperature constraint is presented in this chapter, and the performance of the system is evaluated by deriving a closed-form expression for an outage probability. Nakagami-mfading channels are considered for all primary and cognitive links. Besides, this chapter discusses the design aspects of achieving a certain outage probability based on fading parameters

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Chapter 1. Introduction 4 of the channel and hardware impairment level, which is inversely proportional to the transmission rate. Calculation results reveal that by measuring fading parameters of the channel, one could choose the proper threshold to meet the desired outage probability.

• Moreover, we investigate a non-blind spectrum sensing by utilizing an improved ED under the presence of transceiver distortion noise over Nakagami-mfading channel.

We propose a novel method of evaluating the improved ED statistics forN signal samples with α −µ distribution. We present closed-form analytical formulas to find probabilities of detection and false alarm of the improved ED over additive white Gaussian noise (AWGN) channel. We extend our analysis to evaluate closed- form formulas for the average detection probability over fading channels. Also, the asymptotic analysis of the improved ED is studied over the fading channel when the average Signal-to-Noise Ratio (SNR) approaches to zero. The AUC analysis evaluates the quality of the detector over AWGN channel. Our numerical results show the detrimental effect of distortion noise. Therefore, we propose to apply diversity techniques such as p-order law combining and p-order law selecting to enhance the improved ED accuracy.

• Furthermore, we study device-to-device (D2D) communication for a finite number of D2D users overlaying the mmWave network by considering residual transceiver distortion noise and interference fromN device nodes. Simultaneous spectrum and time sharing among D2D pairs create interference that degrades the performance of a wireless system. We formulate signal-to-distortion-interference-noise-ratio and evaluate its probability density function (PDF) and cumulative density function (CDF). Besides, closed-form expressions are derived for the outage probability and ergodic capacity performance metrics, including lower/upper ergodic capacity bounds for the mmWave network co-existed by D2D nodes.

• A hybrid beamforming based mmWave network is developed where a base station simultaneously communicates with multiple UEs. We consider that the proposed

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Chapter 1. Introduction 5 system model is impaired by RF power leakage from neighboring UEs as well as hardware residual distortion noise. To mitigate RF power leakage and distortion noise a MST diversity technique is implemented based on hybrid beamforming structure. Multiple and independent beams from the base station are combined by using MST diversity technique at a receiver UE. The performance of the mmWave system is evaluated through outage probability and ergodic capacity analysis.

1.2.2 List of Publications

The results of this dissertation work have yielded the following journal and conference publications.

Published journal papers

• L. Tlebaldiyeva, T. A. Tsiftsis and B. Maham, "Performance Analysis of Improved Energy Detector With Hardware Impairments for Accurate Spectrum Sensing," in IEEE Access, vol. 7, pp. 13927-13938, 2019.

• L. Tlebaldiyeva, B. Maham, and T. A. Tsiftsis, "Device-to-Device mmWave Com- munication in the Presence of Interference and Hardware Distortion Noises" in IEEE Communications Letters, 17 June 2019.

• L. Tlebaldiyeva, B. Maham and T. A. Tsiftsis, "Capacity Analysis of Device-to- Device mmWave Networks under Transceiver Distortion Noise and Imperfect CSI,"

in IEEE Transactions on Vehicular Technology.

Published conference papers

• L. Tlebaldiyeva and T.A. Tsiftsis, "Underlay Cognitive Radio with Imperfect Transceiver Electronics under Nakagami-m Fading," 2018 International Conference on Com- puting and Network Communications (CoCoNet), Astana, 2018, pp. 58-63. IEEE best paper award.

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Chapter 1. Introduction 6

• L. Tlebaldiyeva, T. A. Tsiftsis and B. Maham, "Spectrum Sensing using Improved Energy Detector under Transceiver Hardware Impairments," 2018 IEEE Interna- tional Symposium on Dynamic Spectrum Access Networks (DySPAN), Seoul, 2018, pp. 1-5.

• L. Tlebaldiyeva, B. Maham, O. Tirkkonen, "Maximum Sub-array Transmission Di- versity for mmWave Network under RF Power Leakage and Distortion Noises", 2020 IEEE WCNC, Seoul. Accepted.

1.2.3 Thesis Outline

This dissertation work is sub-categorized into three parts. The first part consists of Chap- ter 1, 2. Chapter 1introduces the subject of the dissertation work, including a problem statement, the motivation of the research, and presents key contributions with the list of publications. Chapter2discusses background information about CR technology, massive MIMO mmWave communication as well as the major sources of transceiver hardware impairments. Moreover, this chapter introduces a residual transceiver distortion noise model studied in this work.

The second part of the thesis consists of Chapters3and4, where research findings on the cognitive relay network and improved ED for spectrum sensing are studied under the presence of transceiver distortion noise.

The third part of the thesis is comprised of Chapter 5 and Chapter6that focuses on issues in D2D assisted mmWave communication and multi-user mmWave communication considering interference modelling, imperfect CSI, and inter-beam RF power leakage from nearby nodes as well as transceiver distortion noise. A maximum sub-array transmission diversity technique is proposed to mitigate the imperfections mentioned above.

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Chapter 2

Literature Review

2.1 Future Communication Systems

2.1.1 Cognitive Radio Technology

The RF spectrum is a scarce resource owned and arbitrated by government agencies of each state, e.g., Federal Communications Commission in the US and the Committee of Communications, Informatization, and Information in Kazakhstan. Voracious demand on the RF spectrum leads to a looming scarcity of RF spectrum in cm wave range around the globe. For instance, the number of active mobile subscribers has increased from268 million in2007year to5286million in2018year [3], which means that mobile subscrip- tions have incremented nearly 20times in 11years. Besides, 1 trillion wireless devices are expected by2020[13] from cell phones to wearable devices in the civilian sector and underwater sensors to satellites in the military sector. Traditionally, the RF spectrum is sub-divided between licensed users over a large geographical region. Although exclusive spectrum usage guarantees interference-free communication, the spectrum below3GHz is not fully utilized between 15−85 % of the time in practice [13]. The US Defence Advanced Research Projects Agency (DARPA) perceived the significance of CR systems in military and personnel applications and organized the DARPA Spectrum Collaboration Challenge that was held in October 2019 to bring new ideas and experiments on stage from academia and industry.

CR is an intelligent system that facilitates the detection of primary and secondary

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Chapter 2. Literature Review 8

Figure 2.1.Cognitive radio network scheme.

users and arbitrates unused bandwidth between them by adjusting bandwidth, modulation type, as well as frequency based on transmission and reception. Fig. 2.1 illustrates the basic concept of a CR system: a primary base station network owns the frequency, and a secondary user (SU) is granted access based on the chosen CR paradigm that will be further discussed in this section. CR spectrum management concepts work despite the type of network generation (e.g.,2G,3G,4G, and5G and beyond). CR spectrum management is either called Dynamic Spectrum Access, Flexible Spectrum Use, or Opportunistic Spectrum Access (OSA). Spectrum awareness, analysis and decision, and spectrum ex- ploitation are three main cycles in spectrum sensing [14]. Spectrum sensing uses time, frequency, space, and polarization domains to check the bandwidth occupancy. The OSA poses some challenges to the transceiver since it must sense the spectrum over the wide range and give a quick decision response [15]. According to [13], each cognitive user (CU) possesses the following functionalities: spectrum sensing, spectrum decision, spectrum sharing, and spectrum mobility.

2.1.2 Cognitive Radio Paradigms

Three major spectrum sharing paradigms that describe the interaction between primary and secondary users such as underlay, overlay, and interweave are shown in Fig. 2.3and summarized as well.

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Figure 2.2.Major cognitive user functionalities.

Figure 2.3.Overview of CR paradigms: underlay, overlay, and interweave.

• Underlay paradigm

Cognitive transmitter is aware about its interference to the PU. Cognitive trans- mitters can concurrently transmit data along with PUs as long as the interference level from CUs is under a certain threshold. Therefore, the power of the cognitive transmitter is limited to interference temperature constraint (harmful interference), which is approximated by the channel sounding or cooperative sensing.

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• Overlay paradigm

CUs are aware of PUs essential information such as channel gain and encoding information. This paradigm allows transmission to both cognitive and primary users simultaneously. However, CU’s power is relayed to the PU’s data to offset the interference. Therefore, CUs do not have a limit on transmit power level. The disadvantage of this paradigm is that encoding and decoding processes are more complex in comparison to the other two paradigms.

• Interweave paradigm

CUs sense the environment on the absence of PUs in space, time, and frequency.

Simultaneous data transmission occurs only during the misdetection of a PU. The CU transmit power is limited to the radius of PU activity.

2.2 MmWave Communication with Massive MIMO An- tennas

MmWave wavelength massive MIMO antennas are promising technologies for high spectrum utilization and energy efficiency for future mobile networks [7], [8]. Commercial 5G networks operating on mmWave frequency and employing massive MIMO antennas are already being implemented in the World. Fig. 2.4 presents 5G coverage map with commercial, limited, and pre-release5G networks. China demonstrated the first remote robotic surgery on an animal in January 2019, where Huawei’s5G network technology was used for control and video links at both ends [16].

Accommodation of a large number of antennas and RF blocks is a challenge for base stations and handsets in the conventional RF range. Inter element antenna spacing should be at leastλ/2 apart from each other, whereλ is antenna wavelength. MmWave antennas have small physical size, therefore, it is possible to decrease the spacing between antenna elements and install up to 64 to 512 antennas at a base station [17] and up to 32 MIMO antennas at UE nodes. A large number of antennas create more degree of

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Chapter 2. Literature Review 11 freedom, which results in increased data rate and reduced outage probability. Another advantage of massive MIMO technology is spectrum reuse due to high free space loss and high attenuation [18]. The authors in [19] summarized the challenges of massive MIMO as hardware impairments of low-cost components, performance measurement, the physical size of massive MIMO antennas, pilot contamination, internal power consumption, channel characterization, fast digital signal processing hardware, propagation models and deployment of the mmWave standard. Multi-user massive MIMO network deployment targets low cost and power-efficient hardware implementation at base station [20]; both of these factors are a significant concern for network providers. Large scale antennas for multi-user communication require fast digital processing hardware operating in real-time.

Signal processing algorithms should be linear or nearly linear. According to [19], massive MIMO antennas could be modeled by the law of large numbers, meaning that noise, interference, and fading is averaged out. Array antennas of an order of 100s require inexpensive components such as direct conversion radio receivers. Bjornson et al. suggested that transceiver distortion noise limits the channel estimation accuracy and channel capacity of massive MIMO systems [21].

Figure 2.4.5G deployment map in the World.

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2.3 Transceiver Hardware Impairments

2.3.1 Sources of transceiver hardware impairments

Modern communication systems require low power, inexpensive, and high data rate transceivers. As was discussed in the previous subsection, low-grade transceiver equipment is often used for massive MIMO systems. For instance, direct-conversion radio receivers are frequently considered in the technical literature for spectrum sensing/sharing [22–24] due to low power consumption and ease of circuit integration. A typical direct conversion radio receiver architecture is shown in Fig. 2.5presented in [9]. At the transmitter side, a modulated digital signal from the digital baseband part passes through digital-to-analog-converter (DAC), then it up-converts to RF and gets amplified. Exter- nal intermediate frequency filters and image rejection filters are not required for direct conversion radio receivers as it is required for superheterodyne receivers. Although most of the digital processing is performed at the digital side, RF front-end requires careful consideration [9]. Analog front-end contains power amplifiers, converters, filters, mixers, oscillators, and each of those components adds imperfections to the system.

Figure 2.5.A typical direct conversion radio receiver architecture.

2.3.1.1 Power Amplifier Non-Linearity

A power amplifier is a main component of the transceiver that accounts for most of the power consumption and cost of the entire RF circuit. For example, power amplifiers at

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Chapter 2. Literature Review 13 base station terminals use around 50−80% of total power [25]. When power amplifier operates at a saturation region, nonlinear effects of power amplifier increases and creates nonlinear interference, these nonlinear distortions vary based on bandwidth and operating frequency [26]. Adjacent channel interference (ACI) is a result of spectral re- growth of power amplifier output at nonlinear operation region [27]. Power allocation in CR networks in the presence of nonlinear effects of a power amplifier is investigated in [14]. Secondary receiver average SNR is studied under the peak, and average ACI, closed-form equations for the power allocation are derived under peak and average ACI constraints. The theoretical and simulation results of this work show that the average ACI demonstrates better performance rather than peak ACI. The authors in [14] presents a sub-optimal power allocation method. This method uses a bisection search method for nonlinear power amplifiers based on the orthogonal frequency-division multiplexing (OFDM) CR network. Linear and nonlinear power amplifiers are simulated and com- pared in [14]. As a result, it was proven that energy efficiency is severely degraded while using a nonlinear power amplifier. Contemporary linearization methods including digital post/pre-distortion, feed-forward, and feedback are used now to mitigate the effect of non- linearity. Digital pre-distortion technique fixes the nonlinear signal before transmission.

Feedback path that contains analog-to-digital converters (ADCs) and mixers is required after power amplifier. The feedback path delivers an analysis of the signal image to eliminate non-linearities. The disadvantage of this method is the consumption of additional power [25]. The digital post-distortion method compensates amplifier non-linearities at the baseband side of the receiver. This way, no feedback path is required at the transmitter, which reduces digital signal processing calculations at the cognitive transmitter side.

2.3.1.2 I/Q imbalance

Direct conversion radio receivers do not require image rejection filters and external intermediate frequency. Alternatively, image rejection is done in by in-phase (I) and quadrature (Q) arms [9]. I/Q imbalance of direct conversion radio receivers degrade the spectrum sensing capability. Single-channel and multi-channel direct-conversion receivers with I/Q

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Chapter 2. Literature Review 14 imbalance are studied in [25]. Closed-form expressions for the probability of detection and false alarm are evaluated, and following conclusions are drawn: 1) Single channel receivers are tolerant to I/Q imbalance, however, multiple-channel receivers are susceptible to I/Q imbalance; 2) false alarm probability significantly increases when non-ideal receivers with I/Q imbalance are used. The authors in [25] proposed a waveform level interference cancellation method for compensation of I/Q imbalance effect. It was done by clearing the primary channel signal from the image channel signal.

2.3.1.3 ADC/DAC Quantization Noise

The ADC/DACs transform the analog RF signal into the digital domain by quantizing con- tinuous analog signal into its discrete domain. Quantization error and clipping errors are the two main sources of quantization noise [14]. For OFDM waveform clipping error is more problematic, since it may pose a difficulty in detecting low SNR PU signal. Practical next generation networks apply low-grade components, including low cost ADCs/DACs with a low resolution level. Simulation results from [28] claimed that the system works correctly with a quantization level of2and3bits at1decibel (dB) SNR loss. According to [14], glitch energy is a major source of non-linearity for high-performance ADC/DAC.

2.3.1.4 Phase Noise

Phase noise is the frequency deviation in a local oscillator that brings sudden changes in local oscillator frequency and timing. Therefore, phase noise is considered as a major limitation in communication systems. More about phase noise measurement and estimation are given in [29–31]. Oscillator phase noise in direct-conversion radio receivers creates crosstalk while multi-channel energy detection [23].

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2.3.2 Gaussian Model for Aggregate Residual Transceiver Impair- ments

Practical transceivers are not ideal and add inevitable distortion noise to the system, as was described in Section 2.3.1. Calibration and pre-distortion techniques are applied at the transmitter side, and complex algorithms are used at the receiver side to mitigate hardware impairment noise [9]. However, in practice, it is not possible to filter out all transceiver imperfections, and residual distortion noise remains in the system. The main reasons for distortion noise are a deviation in parameter estimation, a mismatch between a practical transceiver and compensated model, as well as complex implementation of compensation algorithm [32].

The sources of aggregate residual distortion noise that we consider in this dissertation work originate from I/Q imbalance, phase noise, and non-linear amplifier discussed in Section2.3.2. The aggregate residual distortion noise is distributed as a circular symmetric complex Gaussian variate, which is proportional to average signal power multiplied to an error vector magnitude (EVM) parameter that is discussed in Section2.3.2.1. Ac- cording to theoretical and measurement results, [32–36] statistical Gaussian model provides an accurate approximation of aggregate residual impairments. Besides, the Gaus- sian model is mathematically tractable while incorporating residual distortion noise into more complex system analysis. According to [21], hardware impairments at UE mainly limit capacity as the number of antennas increases at UE, whereas impairments dimin- ish asymptotically at massive MIMO base stations. Also, it was analytically proved that hardware impairment creates uplink and downlink capacity ceiling regardless of SNR and the number of antennas.

Let us consider a simple point-to-point system that is constrained by a transmitter and receiver residual distortion noise. A complex signals with an average signal power P = E{|s|²}is transmitted through complex fading channelhand additive white Gaus- sian noise n is added to the signal. The received signal ywith residual transmit Tx/Rx

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Chapter 2. Literature Review 16 impairments could be expressed as

y=h(s+ν_t) +ν_r+n, (2.1)

whereν_tandν_r are corresponding transmit and receive residual impairments modeled as ν_t ∼ CN(0, κ²_tP)and ν_r ∼ CN(0, κ²_rP h). The EVM parametersκ_t > 0and κ_r > 0 determines the level of distortion noise, alternatively κt = 0 and κr = 0 is for ideal system model. Similar to [21], we could express the general expression for the joint Tx/Rx residual impairments as

Eνt,νr{|hν_t+ν_r|²}=P|h|²(κ²_t +κ²_r) =P|h|²(κ²_t +κ²_r) = P|h|²κ², (2.2)

whereκ=p

κ²_t +κ²_r. Numerical value ofκis a protocol specific number.

Figure 2.6.Representation of the EVM vector.

2.3.2.1 Error Vector Magnitude

The EVM is a Figure of Merit that measures the physical transceiver quality and modulation performance. The general schematic that represents the EVM is shown in Fig.

2.6. An error vector represents a difference between an actual vector and a reference vector. Hence, it is evaluated as logarithmic function with ratio of amplitude of error signal, P_error, to amplitude of reference signal, P_ref, as EVM (dB)= 10 log₁₀

Perror

Pref

or EVM(%) = 10 log₁₀

Perror

P_ref

∗ 100%. The EVM describes the combination of all

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Chapter 2. Literature Review 17 impairments that influence signal constellation in an additive way [37]. A low EVM value indicates less distortion noise presence. Hence, low EVM values are desired for a high rate and reliable communication. There are specifications on the EVM level for a given modulation type. For instance, for wideband code division multiple access that uses quadrature phase-shit keying (QPSK) EVM level should be no more than 17.5%, 3GPP LTE requirement for EVM is 8%,17.5%. The authors in [38] discusses the individual impact of each source of transceiver impairments on EVM including I/Q imbalance, nonlinear power amplifier, local oscillator phase noise, as wellas local oscillator leakage. The overall EVM is expressed as a summation of all sub-EVMs from each source of circuit nonideality.

2.3.2.2 Transceiver Distortion Noise in MmWave Communication

The primary sources of transceiver hardware impairments in mmWave communication were listed as ADC/DAC resolution, I/Q imbalance in quadrature modulators, phase noise in phase-locked loops, and non-linearity in power amplifiers in [39]. The achievable rate of massive MIMO antennas considering hardware impairment noise over Rician fading channel was studied in [10]. The multipair massive MIMO system assisted by relay network evaluated spectral efficiency of the system by taking into account residual transceiver distortion noise. Transceiver distortion noise was deeply investigated in CR systems [40–42]. A cell-free massive MIMO network with transceiver distortion noise was analyzed in [43] where spectral and energy efficiencies of the system were exten- sively studied.

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18

Chapter 3

Cognitive Relay Networks

In this chapter, the performance analysis of the dual-hop DF underlay CR network under residual transceiver distortion noise and interference power constraints is presented.

Closed-form analytical calculations for the outage probability over independent and non- identical distributed (i.i.d.) Nakagami-m fading channels. Moreover, closed-form expressions for the outage probability asymptotic analysis are derived as well. We found a relation between hardware impairment level and possible transmission rate through numerical simulations. We have investigated different fading severity parameters of the fading channel given the fixed source node power and desired outage probability level.

This chapter was written based on the author’s work published in [44].

3.1 Introduction

CR networks contain many secondary nodes that could be used as relay nodes to facilitate cooperative communication between source-destination nodes to increase the throughput and coverage of the network by minimizing the factor of path loss between source- destination link. The relay assisted networks have been popular among researchers and industry due to increased coverage, high reliability, and improved quality of service. The secondary relay system contains the source (S), relay (R), and destination nodes (D). The secondary relay system operates at the same frequency as a primary one. The source node sends its signal to the relay node at the first time-slot. Depending on the relaying protocol, it could be either amplified and forwarded to the destination node, decoded

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Chapter 3. Cognitive Relay Networks 19 and forwarded or compressed, and forwarded. Hence, the major relaying protocols are amplify-and-forward (AF), DF, and compress-and-forward (CF).

3.1.1 Related work

One of the practical applications of the dual-hop network is an ad-hoc wireless network.

The work in [45] integrated 3G Wireless Wide Area Network and802.11Wireless Lo- cal Area Network. A typical dual-hop relay network have an S, R, and D nodes that are assembled by non-ideal RF chains and communication blocks. Authors investigated dual-hop relay networks with non-ideal hardware in [46–49]. Moreover, the works in [40]

and [50] studied the multiple relay CR networks under transceiver distortion noises over Rayleigh fading channels. Initially, a generalized system and signal model for a dual-hop relay network with aggregate distortion noises were introduced in [46]; this study models aggregate distortion noises as additive Gaussian noise as in [9]. The work in [40]- [47]

applied the generalized non-ideal hardware impairment signal described in [46]. The authors in [47] evaluated closed-form formulas for the outage performance of a DF CR network non-ideal transceiver electronics by using practical 3GPP LTE EVM parameters for Rayleigh fading channel. According to this study, the system with a high data rate is more affected by distortion noises. The work in [48] analyzed the outage probability and throughput of a dual-hop relay network with distortion noises under Rayleigh fading channel. This study also demonstrated that the DF protocol is less susceptible to distortion noises in comparison to AF protocol. Multiple relay CR network with transceiver hardware impairments was analyzed in [50] over Rayleigh fading channel. Moreover, a partial relay selection and opportunistic techniques were studied in [40], and closed-form expressions for the outage probability were derived over Rayleigh fading channels. The authors in [51] studied the combined effect of distortion noise and channel estimation error for dual-hop CR network given ideal hardware over Nakagami-mfading channel. According to these studies, the outage probability saturates at high interference temperature values.

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Chapter 3. Cognitive Relay Networks 20 Based on the literature survey analysis, majority of the researchers analyzed dual- hop CR networks for non-ideal hardware under Rayleigh fading channel for analytical tractability purposes.

3.1.2 Contributions

The principal contributions of this chapter are listed as:

• Presentation of a system and signal model for the underlay dual-hop DF cognitive relay system with transceiver imperfections and interference constraints under Nakagami-mfading channel;

• Derivation of the analytical expression for the outage probability given dual-hop DF network under aggregate transceiver imperfections and interference constraints;

• Verification of the analytical outage probability expressions with Monte-Carlo simulations for N = 10⁶ iterations at various interference temperature constraints, fading parameters, and hardware impairments levels;

• Delivering design aspects on the maximum hardware impairments level to meet the desired outage probability threshold for varying fading parameters.

3.1.3 Organization

3.2 System and Signal Model

We present a dual-hop CR relay network in Fig. 3.1where a cognitive network consists of a S node that communicates to D node through relay R node. We consider the absence of the direct link betweenSandDnodes caused by a far distance. Cognitive relay system operates in a half-duplex mode: at the first time-slot the message is sent fromS to R and at the second time-slot the signal gets forwarded from R to D nodes. Cross- channel information is required for underlay paradigm to enable coexistence of PU and SUs. Secondary/cognitive network imposes interference to the primary receiver (PR).

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Chapter 3. Cognitive Relay Networks 21

Figure 3.1.System and signal model for underlay dual-hop DF relay network under hardware impairments.

Power control of underlay paradigm assists to handle this interference. We consider i.i.d.

Nakagami-mfading channel coefficients between primary and interference links, denoted ashsr,hrd, hspandhrp with corresponding channel gain amplitudes|hsr|², |hrd|², |hsr|², and|h_rp|²that follow Gamma distribution. Due to power control in a secondary network, a transmit power ofSandRnodes are selected as a minimum value between interference temperature constraint,I, as well as a maximum available power at theSandRnodesP₁ andP₂, respectively, to eliminate the interference with primary network as in [51].

P1 ≤min I

|h_sp|², P

, (3.1)

P₂ ≤min I

|h_rp|², P

. (3.2)

In Fig. 3.1, we present signal path from the S to Dnodes. The original signals s₁ and s₂ originating from the S and R nodes are deteriorated by aggregate distortion noises µj ∼ CN 0, κ²_jP

, whereP = E{|sj|²}is an average power of the signal. In addition, κ_j ≥ 0, j = 1,2 represents an aggregate transceiver distortion noise level measured by the EVM. Moreover, µ_j represents circularly-symmetric complex Gaussian distributed variable that describes aggregate distortion noise from the transmitter and receiver nodes.

A residual transceiver distortion noise model from a transmitter side is given as µ_t ∼ CN(0, κ²_rP|h|²). Similarly, µ_r ∼ CN(0, κ²_rP|h|²) stands for the aggregate distortion

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Chapter 3. Cognitive Relay Networks 22 noise from the receiver node. The summation of aggregate distortion noises from the transmitter and receiver nodes could be represented asEµ{|hµ_t +µ_r|²} = P|h|²(κ²_t + κ²_r) = P|h|²κ². Authors in [46] stated that the hardware impairment level parameter,κis inverse proportional to the outage probability threshold as,κ≤ 1

x, wherexis a predefined threshold on signal-to-noise-distortion ratio (SNDR). We denoteκ₁parameter betweenS and R nodes and κ₂ parameter between R and D nodes, respectively. In addition to distortion noises circularly-symmetric complex Gaussian distributed receiver noise ν_i is also added to the signal s_i, ν_i ∼ CN(0, N_i). Next, the generalized received signal for non-ideal system is formulated as

y_i =p

P_ih_i(s_i+µ_i) +ν_i i= 1,2. (3.3)

3.3 Outage Probability

This section presents closed-form expressions for the outage probability under the presence of transceiver distortion noises. The outage probability finds the probability of faded end-to-end SNDR to fall below a defined threshold,xas

P_out(x) = Pr(γ ≤x), (3.4)

whereγ is the SNDR.

3.3.1 Signal-to-Noise-Distortion Ratio for underlay dual-hop DF net- work

The end-to-end SNDR for underlay dual-hop DF secondary relay network is evaluated as

γ = min

P₁|h_sr|²

P₁|h_sr|²κ²₁+N₁, P₂|h_rd|² P₂|h_rd|²κ²₂ +N₂

. (3.5)

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Chapter 3. Cognitive Relay Networks 23 We represent end-to-end SNDR per each hop asT₁andT₂for hop1and2, respectively.

T1 =

min(_|h^I

sp|², P)|h_sr|² min(_|h^I

sp|², P)|h_sr|²κ²₁+N₁, and

T₂ =

min(_|h^I

rp|², P)|h_rd|² min(_|h^I

rp|², P)|h_rd|²κ²₂+N₂,

(3.6)

respectively.

3.3.2 Outage Probability

The outage probability for the underlay dual-hop DF secondary network is calculated by making use of (3.4) and independence of SNDRs for the hops1and2as follows

P_out(x) = Pr(min(T₁, T₂)< x) =1−Pr(T₁ > x) Pr(T₂ > x)

= 1−(1−F_T₁(x))(1−F_T₂(x)),

(3.7)

whereF_T₁ andF_T₂are CDFs of the SNDR for the hop1and2, respectively. The derivation of CDFs forT₁andT₂random variables (RVs) are presented in Lemma1.

Lemma 1 Let us consider|h_xy|² is a non-negative RV andβ_i, i ∈ 1,2withm_i,i ∈ 1,2 are positive constants. The CDF of RVT is expressed as

F_T_j(x) = γ

m₁, β1xNj

P_j −xP_jκ²_j

Γ(m₁)

γ

m2,β₂I P_j

Γ(m₂) + Γ

m₂,^Iβ_P²

j

Γ(m₂) − β₂^m² Γ(m₂)

m1−1

X

t=0

_xβ

1Nj2

I(1−xκ²_j)

t

t!

×Γ

m₂+t,

β₂+ xβ₁N_j² I(1−xκ²_j)

I Pj

β₂+ xβ₁N_j² I(1−xκ²_j)

^−m2−t

,

(3.8) wherei= 1stands for channel parameters betweenS-RandR-Dnodes, whereas,i= 2 indicates channel parametes betweenS-P RandR−P Rnodes. Moreover, m_i,i ∈1,2 andβ_i,i∈1,2represent fading and scale parameters of the corresponding channels.

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Proof: The proof is given in AppendixA.

By using Lemma 1, we formulate the outage probability for the dual-hop relay network with transceiver hardware impairment noise and interference constraints.

Lemma 2 Let suppose that T_i is an independent non-negative RV with CDF F_T(·) for i= 1,2. The outage probability for dual-hop DF cognitive relay network under distortion noise and interference temperature constraints is

P_out(x) =











1− 1−F_T₁(_P ^N¹^x

1(1−κ²₁x))

1−F_T₂(_P ^N²^x

2(1−κ²₂x))

, x < ¹_δ, 1, x≥ ¹_δ,

(3.9)

where _σ¹ = max(κ²₁, κ²₂)By substituting (3.8) to (3.9), we obtain the analytical formula for the outage probability over Nakagami-mfading channel.

3.3.3 Asymptotic Analysis for the Outage Probability

We analyze the asymptotic outage probability given two extreme conditions: 1) a source power approaches infinity and 2) interference temperature constraint approaches to zero.

3.3.3.1 Outage probability whenP → ∞

We evaluate the outage probability given an infinite source power

P_out(x) = 1−(1− lim

P→∞F_T₁(x))(1− lim

P→∞F_T₂(x))), (3.10)

Plim→∞F_T_j(x) = 2 + β_j2^m^j2 Γ(m_j2)

mj1−1

X

i=0

( ^xβ^j1^N

2 j

I(1−xκ²_i))ⁱ i!

×Γ(mj2+i)(βj2+ xβ_j1N_j²

I(1−xκ²))^−m^j2⁻ⁱ.

(3.11)

From (3.10) one could notice interference temperature constraint limits the secondary network operation despite infinite power available at the transmitter. Hence, the outage probability of the secondary network is dependent onI.

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3.3.3.2 Outage Probability whenI →0

Let us consider that interference temperature constraint value approaches to zero, then the CDF of SNDR approximates to one shown as

I→0limF_T(x)≈1, (3.12)

Therefore, the outage probability atI →0is evaluated as

P_out(x) = 1−(1−lim

I→0F_T₁(x))(1−lim

I→0F_T₂(x))), (3.13)

P_out(x)≈1. (3.14)

The outage probability approximates to one whenI approaches to zero and primary network does not allow any communication in secondary network.

3.4 Simulation Results

In this section, the theoretical closed-form expression for the outage probability is val- idated through MATLAB Monte-Carlo simulations. We emphasize on the influence of interference temperature constraints, fading parameter values, and aggregate distortion noise level on the performance of the outage probability. We plot the outage probability versusP/N₀in Fig.3.2given a set of interference temperature constraintsI/N₀=0; 10; 15; 20 dB for κ = 0.1. In addition, we analyze the outage probability at interference temperature constraint at zero; as expected, the secondary network is at idle state and the outage probability is equal to one. Notice that the outage probability performance enhances asI value increases.

In Fig. 3.3, the outage probability is displayed as an element ofP/N₀ forI/N₀=15 dB and x = 3 dB. Note that, dotted plots represent the outage probability at κ = 0.4 and the solid plots denote outage probability atκ = 0.1. Moreover, we simultaneously differ two major parameters: 1) hardware impairment level, κ, at low and high values

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Figure 3.2.Outage probability versusP/N₀at differentI/N₀= 0,10, 15,20(dB).

Table 3.1. The fading parameter values for Fig.3.3 Case msr msp mrd mrp κ2 κ2

a) 2 2 2 2 0.1 0.4

b) 2 10 2 10 0.1 0.4

c) 5 5 5 5 0.1 0.4

and 2)Nakagami-mfading parametersm_sr (S −R),m_rd(R−D), m_sp (S −P R), m_rp (R−P R) at a) identical low fading parameters of both cognitive and interference links; b) at low cognitive fading parameters and high interference fading parameters; c) at identical medium fading parameters of cognitive and interference links. Table 3.1 above summa- rizes fading parameters of three cases that are used to plot Fig. 3. The plot (c) with mediumm_xy fading parameters of both cognitive and interference links demonstrated the best outage probability performance. The plot (a) with identically low m_xy parameters shows the second high outage probability performance. The plot (b) shows the worst outage probability performance. This figure justifies that residual transceiver distortion noise level plays a crucial role in evaluating the outage probability. Moreover, fading parameter values of both primary and secondary links substantially affect the outage probability performance.

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Figure 3.3.Outage Probability at different fading parameters simulated forκ= 0.1andκ= 0.4.

In Fig. 3.4, we analyze the relationship between SNDR threshold, x and hardware imapirment levelκ. According to [46], κ² < 1/x. Alternatively, we could express the threshold by using the rate asκ <1/2^2∆−1, where∆is a transmission rate [bits/s]. More- over, rate could be written as∆ =aR_s, wherearepresents a number of bits per each modulated symbol andRs indicates symbol rate [symbol/s]. Since high rate systems require

Figure 3.4.The outage probability plots forx= 3; 16dB and κ= 0.1; 0.65.

A thesis outline submitted in partial fulfillment of the requirement of Nazarbayev University for the degree of Doctor of Philosophy

Performance analysis of future communications systems under residual hardware impairments

Leila Tlebaldiyeva