On Multiantenna Cellular Communications: FromTheory to Practice

NIMA NAJARI MOGHADAM

Doctoral ThesisStockholm, Sweden 2017

TRITA-EE 2017:050ISSN 1653-5146ISBN 978-91-7729-435-1

KTH Royal Institute of TechnologySchool of Electrical Engineering

SE-100 44 StockholmSWEDEN

Akademisk avhandling som med tillstand av Kungl Tekniska hogskolan framlaggestill offentlig granskning for avlaggande av teknologie doktorsexamen i electro- ochsystemteknik fredag den 9 juni 2017 klockan 14.00 i Kollegiesalen, Brinellvagen 8,Stockholm.

© 2017 Nima Najari Moghadam, unless otherwise noted.

Tryck: Universitetsservice US AB

To my parents

iii

v

Abstract

Today, wireless communications are an essential part of our everydaylife. Both the number of users and their demands for wireless data have in-creased tremendously during the last decade. Multiantenna communicationsis a promising solution to meet this ever-growing traffic demands. However,impairments that exist in most practical communication networks may sub-stantially limit the performance of a multiantenna system. The characteri-zation of such a performance loss and how to minimize that are still largelyopen problems. The present thesis addresses this important research gap. Inparticular, we focus on three major impairments of a multiantenna cellularnetwork: impairment in the channel state information (CSI), interference andimpairment in the transceiver hardware components.

To fully realize the benefits of multiantenna communications, the usersneed to acquire a certain level of information about their propagation envi-ronment; that is, their corresponding CSI. In practice, the CSI is not known bythe users and should be acquired by allocating part of the network resourcesfor pilot transmission. This problem is mainly important in the systems witha large number of antennas, as in general the required network resourcesfor CSI acquisition scales with the number of transmitting antennas. Theproblem of CSI acquisition in a single-cell multiuser multiple-input multiple-output (MIMO) system is addressed in this thesis. A linear spatial precodingand combining scheme for pilot transmission is proposed. This scheme re-quires less number of network resources for channel estimation compared tothe conventional schemes. The gains of the proposed scheme is characterizedby finding an upper-bound and a lower-bound on the channel estimation er-ror. Moreover, as an ultimate performance metric, an achievable sum-rate ofthe network is formulated and analyzed numerically.

Due to the broadcast nature of the wireless channels, the performanceof the users in a network is intertwined; the desired signal of one user mayinterfere other users. Hence, the interference is another major impairment inwireless communication systems. In this thesis, the practical challenges of aninterference management technique, namely MIMO interference alignment isinvestigated by implementation on a multiuser MIMO testbed. Then, in thecontext of interference alignment, the problem of optimal power allocation forpilot and data transmission is studied and verified by the measurements.

The impairment in the hardware components of the transceivers, that is,any deviation of the components from their ideal behavior, degrades the per-formance of a communication system. In particular, the impact of nonlineartransmitter power amplifiers (PA)s is investigated in this thesis. First, con-sidering a memoryless third-order polynomial model for the PAs, a model forthe transmitted nonlinear distortion signal from a multiantenna transmitter isproposed and validated by measurements. This model implies that the spatialdirection of the transmitted distortion is dependent on the spatial directionof the desired signal. Then, this model is extended for a general arbitrary or-der polynomial model. Exploiting the developed distortion model, the energyefficiency of a multiantenna system operating at millimeter wave frequenciesis studied.

vii

Sammanfattning

Numera ar tradlos kommunikation en vasentlig del av var vardag. Badeantalet anvandare och deras behov av tradlos data har okat enormt underdet senaste decenniet. For att mote detta standigt okande behov, mastenya teknologier utvecklas. Flerantennkommunikation har setts som en ny-ckelteknologi for framtida kommunikationssystem. Dock sa ar vinsterna avfleranvandarsystem med multipla antenner i praktiken begransade pga flerabrister. Denna avhandling behandlar problemen med flerantennbaserade mo-bilnat. Specifikt sa undersoks tre problemomraden, brister i kanalkannedom(CSI), interferens samt ickeideal radiohardvara.

For att fullt ut na vinsterna med flerantennkommunikation, maste anvand-arna samla in en viss niva av information om radioutbredningsmiljon, dvsmotsvarande CSI. I praktiken astadkoms detta genom att en viss del av ra-dioresurserna reserveras for att sanda traningssignaler. Detta ar primart ettproblem i system med ett stort antal antenner, eftersom kravet pa natverksres-urser for traning i allmanhet skalar linjart med antalet antenner. Problemetmed CSI-skattning for multiple input multiple output-system (MIMO-system)med flera anvandare inom en cell, behandlas i denna avhandling. En prin-cip for linjar forkodning och kombinering av traningssignaler foreslas. Dennametod kraver mindre natverksresurser for kanalskattning jamfort med tradi-tionella losningar. Vinsterna med den foreslagna metoden karaktariseras mhaovre och lagre granser for kanalskattningsfelen. Dessutom, som ett fundamen-talt prestandamatt, formuleras och analyseras den uppnaeliga summadatatak-ten for natverket.

Eftersom en radiosignal sprids till alla mottagare, sa kopplar prestan-dan samman for alla anvandare; en signal avsedd for en mottagare kommeratt orsaka storning for ovriga anvandare. Darfor ar interferens en avgorandebegransning i tradlosa kommunikationssystem. I denna avhandling undersoksde praktiska utmaningarna for en interferenshanteringsteknik, MIMO interfer-ence alignment, genom implementation pa en testbed for fleranvandar-MIMO.Problemet med optimal effektallokering for tranings- och datasandning stud-eras, for interference alignment, och verifieras med matningar.

Brister i sandarnas och mottagarnas hardvarukomponenter, dvs alla avvik-elser fran deras ideala beteende, forsamrar prestandan i kommunikationssys-tem. Speciellt analyseras paverkan av ickelineariteter i effektforstarkarna, idenna avhandling. Forst, utgaende fran en tredje ordningens polynomiskmodel for effektforstarkarna, foreslas en modell for resulterande storning franen multiantennsandare, och valideras med matningar. Denna modell visar attden spatiella riktningen for den utsanda storningen beror pa den spatiellariktningen for den onskade signalen. Darefter utokas denna modell till engenerell polynomisk modell med godtyckligt gradtal. Med hjalp av dennastorningsmodell, studeras energieffektiviteten for multiantennsystem i mil-limetervagsomradet.

List of Papers

The thesis is based on the following papers:

[A] N. N. Moghadam, H. Shokri-Ghadikolaei, G. Fodor, M. Bengtsson and C.Fischione, “Pilot Precoding and Combining in Multiuser MIMO Networks,”in IEEE J. Sel. Areas Commun. , vol. 35, no. 6.

[B] N. N. Moghadam, H. Farhadi, P. Zetterberg and M. Skoglund, “Test-bed im-plementation of iterative interference alignment and power control for wirelessMIMO interference networks,” in Proc. 15th IEEE Int. Workshop on SignalProcess. Adv. Wireless Commun. (SPAWC), Jun. 2014, pp. 239-243.

[C] N. N. Moghadam, H. Farhadi and P. Zetterberg, “Optimal power allocationfor pilot-assisted interference alignment in MIMO interference networks: Test-bed results,” in Proc. 20th IEEE Int. Conf. Digit. Signal Process. (DSP), Jul.2015, pp. 585-589.

[D] N. N. Moghadam, P. Zetterberg, P. Handel and H. Hjalmarsson, “Correlationof distortion noise between the branches of MIMO transmit antennas,” inProc. IEEE 23rd Int. Symp. Pers. Indoor Mobile Radio Commun. (PIMRC),Sep. 2012, pp. 2079-2084.

[E] N. N. Moghadam, G. Fodor, M. Bengtsson and D. J. Love, “On the energyefficiency of MIMO hybrid beamforming for millimeter wave systems withnonlinear power amplifiers,” IEEE Trans. Wireless Commun., to be submit-ted for publication.

ix

x

In addition to papers A-E, the following book chapter and papers have also been(co)-authored by the author of this thesis:

[1] N. N. Moghadam, H. Farhadi, P. Zetterberg, M. Khormuji and M. Skoglund,“Interference alignment: Practical challenges and test-bed implementation,book chapter in Contemporary Issues in Wireless Communications, INTECHOpen Access Publisher, Nov. 2014.

[2] C. M. Yetis, N. N. Moghadam, J. Fanjul, H. Farhadi and J. A. Garcia-Naya,“Interference alignment testbed,” submitted to IEEE Commun. Mag., underrevision (minor).

[3] P. Zetterberg and N. N. Moghadam, “An experimental investigation of SIMO,MIMO, interference-alignment (IA) and coordinated multi-point (CoMP),”in Proc. IEEE 19th Int. Conf. Syst., Signals Image Process. (IWSSIP), Apr.2012, pp. 211-216.

[4] N. N. Moghadam, H. Farhadi and M. Bengtsson, “An energy efficient commu-nication technique for medical implants/micro robots,” in Proc. IEEE 10thInt. Symp. Medical Inform. Commun. Technol. (ISMICT), Mar. 2016, pp.1-5.

[5] N. N. Moghadam, H. Shokri-Ghadikolaei, G. Fodor, M. Bengtsson, and C.Fischione, “Pilot precoding and combining in multiuser MIMO networks,” inProc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Mar. 2017.

[6] E. Olfat, H. Shokri-Ghadikolaei, N. N. Moghadam, M. Bengtsson, and C. Fis-chione, “Learning-Based Pilot Precoding for Wideband mmWave Networks,”2017 IEEE Int. Workshop Computational Advances in Multi-Sensor AdaptiveProcess. (CAMSAP), submitted.

xi

Acknowledgements

First and foremost, I would like to thank my main advisor Prof. MatsBengtsson for all of his guidance and support during the second half of myPh.D. studies. His office door was always open for technical discussions andhis insightful comments highly impacted my research. I appreciate all hiscontributions of time and ideas to make my Ph.D. experience productive andstimulating.

Besides my main advisor, I would also like to thank Dr. Per Zetterbergfor introducing me to the world of software-defined radio and testbeds andproviding me with help and guidance during the first half of my Ph.D. stud-ies. I also wish to thank my co-advisor Dr. Gabor Fodor for all the fruitfulmeetings and discussions.

I would like to acknowledge Prof. Peter Handel for giving me the oppor-tunity for pursuing my Ph.D. studies in Signal Processing department, KTH.I am also thankful to Prof. Mikael Skoglund, Prof. Hakan Hjalmarsson, andProf. Carlo Fischione for our scientific collaborations. I am indebted to myformer colleagues, co-authors and distinguished researchers Hossein Shokri-Ghadikolaei for his willingness and enthusiasm to discuss and share knowl-edge, Dr. Hamed Farhadi for the informative and long discussions, and Dr.Majid Nasiri Khormuji for his helps and guidance from the first days that Istarted my M.Sc. at KTH. I would also like to thank Dr. Rami Mochaourab,Dr. Satyam Dwivedi for the instructive discussions and collaborations. I amalso thankful to Prof. Lars Kildehøj for acting as quality reviewer of this the-sis and Prof. David J. Love for giving me the opportunity to visit his groupat Purdue University.

I am thankful to Hossein Shokri-Ghadikolaei, Ehsan Olfat, and ArashOwrang for proofreading of my thesis and also for scientific discussions thatindeed highly impacted my research. It has been an honor to share office withDr. Alla Tarighati, who showed me how a researcher can be both hardworkingand fun. I would also like to acknowledge Dr. Shoaib Amin, for answeringmy never ending questions regarding power amplifiers and also providing mewith measurement results which I have used in the first part of this thesis.Tove Schwartz should be thanked for taking care of administrative issues, herSwedish lessons and teaching me about Swedish tax system.

I wish to thank Dr. Federico Boccardi for taking time to act as opponentfor this thesis, and also Prof. Nuria González-Prelcic, Prof. Fredrik Tufvesson,and Dr. George Jongren for participating in the evaluation committee.

I would like to thank all my past and present colleagues for their un-flinching support and encouragement and for bringing out the potential inme. I really appreciate all the good times we shared together in the work-place. You are all the best: Alla, Amirpasha, Arash, Arun, Ehsan, Farshad,Hadi, Hamed, Hossein, Klas, M. Reza Gholami, Majid Gerami, Majid NasiriKhormuji, Marie, Martin, Nafiseh, Rasmus, Senay, Serveh, Shahab, Shoaib,and VJ.

I am also deeply thankful to my friends for their support and encourage-ments Shahab, Roonak, Shervin, Behnoush, Pouya, Niloofar, Roody, Mohsen,

xii

Golshid and above all Sara for believing in me and her unconditional love andsupport.

Finally, my deep and sincere gratitude to my family for their continuousand unparalleled love, help and support. I am forever indebted to my parents,Reza and Sousan, for giving me the opportunities and experiences that havemade me who I am. They selflessly encouraged me to explore new directionsin life and seek my own destiny. This journey would not have been possible ifnot for them, and I dedicate this milestone to them. I am grateful to my sister,Shadi, who compassionately has taken care of my parents all these years that Ihave been away. I am grateful to my brother, Omid, whose high ambition andcuriosity inspired me in many ways. I am grateful to my sister-in-law, Asaland the youngest member of our family Dario for bringing joy and happinessto my life.

Nima Najari MoghadamStockholm, June 2017

Contents

Abstract v

Sammanfattning vii

List of Papers ix

Acknowledgements xii

Contents xiii

List of Acronyms xvii

I Thesis Overview

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1.1 Wireless Channel . . . . . . . . . . . . . . . . . . . . . . . 41.1.2 Multiantenna Communication . . . . . . . . . . . . . . . . 51.1.3 Multiantenna Networks . . . . . . . . . . . . . . . . . . . 61.1.4 Pilot-based Channel State Information Acquisition . . . . 71.1.5 Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . 81.1.6 Interference Management . . . . . . . . . . . . . . . . . . 91.1.7 Hardware Impairments . . . . . . . . . . . . . . . . . . . . 131.1.8 KTH Fourmulti Testbed . . . . . . . . . . . . . . . . . . . 16

1.2 Our Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 201.2.1 Problem I: Acquiring CSI in Multiantenna Cellular Sys-

tems with a Large Number of Antennas . . . . . . . . . . 201.2.2 Problem II: Interference Management in Practical Multi-

antenna Cellular Systems . . . . . . . . . . . . . . . . . . 241.2.3 Problem III: Hardware Impairments in Multiantenna Cel-

lular Systems . . . . . . . . . . . . . . . . . . . . . . . . . 281.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

xiii

xiv Contents

References 37

II Included Papers

A Pilot Precoding and Combining in Multiuser MIMO NetworksA.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A.2.1 Channel Model . . . . . . . . . . . . . . . . . . . . . . . .A.2.2 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . .

A.3 Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . .A.3.1 Non-precoded and Uncombined Pilot Transmission (nPuC)A.3.2 Precoded and Uncombined Pilot Transmission (PuC) . . .A.3.3 Precoded and Combined Pilot Transmission (PC) . . . . .A.3.4 Implementation of Pilot Precoding and Combining Filters

A.4 Data Transmission . . . . . . . . . . . . . . . . . . . . . . . . . .A.4.1 Performance Metric . . . . . . . . . . . . . . . . . . . . .A.4.2 Data Precoding . . . . . . . . . . . . . . . . . . . . . . . .

A.5 Further Discussions . . . . . . . . . . . . . . . . . . . . . . . . . .A.6 Concluding Remarks and Outlook . . . . . . . . . . . . . . . . .A.7 Appendix A: Preliminaries . . . . . . . . . . . . . . . . . . . . . .A.8 Appendix B: Proofs . . . . . . . . . . . . . . . . . . . . . . . . .

References

B Test-Bed Implementation of Iterative Interference Alignmentand Power Control for Wireless MIMO Interference NetworksB.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B.2 Multi-user MIMO Interference Network . . . . . . . . . . . . . .B.3 Transmitted Frame Structure . . . . . . . . . . . . . . . . . . . .B.4 Transmitter and Receiver Structure . . . . . . . . . . . . . . . . .B.5 Test-bed Implementation . . . . . . . . . . . . . . . . . . . . . .

B.5.1 Hardware Platform . . . . . . . . . . . . . . . . . . . . . .B.5.2 Software Platform . . . . . . . . . . . . . . . . . . . . . .

B.6 Measurement Campaign . . . . . . . . . . . . . . . . . . . . . . .B.7 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . .

B.7.1 Comparison of the PC and noPC schemes . . . . . . . . .B.7.2 Practical Limitations . . . . . . . . . . . . . . . . . . . . .

References

C Optimal Power Allocation for Pilot-Assisted Interference Align-ment in MIMO Interference Networks: Test-bed ResultsC.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Contents xv

C.2 Signal and System Model . . . . . . . . . . . . . . . . . . . . . .C.2.1 Data Transmission . . . . . . . . . . . . . . . . . . . . . .C.2.2 Pilot Transmission and Channel Estimation . . . . . . . .C.2.3 Interference Alignment . . . . . . . . . . . . . . . . . . . .

C.3 Optimal Power Allocation . . . . . . . . . . . . . . . . . . . . . .C.4 Test-bed Implementation . . . . . . . . . . . . . . . . . . . . . .

C.4.1 Hardware Platform . . . . . . . . . . . . . . . . . . . . . .C.4.2 Software Platform . . . . . . . . . . . . . . . . . . . . . .C.4.3 Frame Structure . . . . . . . . . . . . . . . . . . . . . . .

C.5 Measurement Methodology . . . . . . . . . . . . . . . . . . . . .C.6 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . .

References

D Correlation of Distortion Noise Between the Branches of MIMOTransmit AntennasD.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D.2 Analytical analysis of 3rd order impairment . . . . . . . . . . . .

D.2.1 Memoryless Transmitters . . . . . . . . . . . . . . . . . .D.2.2 Transmitters with Memory . . . . . . . . . . . . . . . . .

D.3 Cross Correlation of the Distortion Noises . . . . . . . . . . . . .D.4 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D.6 Appendix: : Proofs . . . . . . . . . . . . . . . . . . . . . . . . . .

References

E On the Energy Efficiency of MIMO Hybrid Beamforming forMillimeter Wave Systems with Nonlinear Power AmplifiersE.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .E.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E.2.1 Papers Analysing the Combined Effects of Hardware Im-pairments . . . . . . . . . . . . . . . . . . . . . . . . . . .

E.2.2 Papers Focusing on Dominant Impairment Effect . . . . .E.2.3 Papers Dealing with mmWave Systems . . . . . . . . . . .E.2.4 Papers Related to Power Minimization and Energy Effi-

ciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . .E.3 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E.3.1 Channel Model . . . . . . . . . . . . . . . . . . . . . . . .E.4 Nonlinear Power Amplification . . . . . . . . . . . . . . . . . . .E.5 Spectral Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . .E.6 Energy Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . .E.7 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . .E.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xvi Contents

E.9 Appendix: Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . .

References

List of Acronyms

3GPP 3rd Generation Partnership Project

AoA angle of arrival

AoD angle of departure

BER bit error rate

BF beamforming

BS base station

CSI channel state information

ULA uniform linear array

FDD frequency division duplexing

MIMO multiple-input multiple-output

MMSE minimum mean square error

MU-MIMO multiuser multi-input multi-output

mmWave millimeter-wave

MRC maximum ratio combining

MRT maximum ratio transmission

MSE mean square error

RF radio frequency

SINR signal-to-noise-plus-interference ratio

SNR signal-to-noise ratio

TDD time division duplexing

UE user equipment

xvii

xviii List of Acronyms

RF radio frequency

FCC federal communications commission

PA power amplifier

PSD positive semi-definite

NMSE normalized mean square error

LS least square

ADC analog-to-digital converter

DAC digital-to-analog converter

LNA low-noise amplifier

TDMA time division multiple access

FDMA frequency division multiple access

AM-AM amplitude-to-amplitude

AM-PM amplitude-to-phase

PAPR peak-to-average-power ratio

DPD digital predistorter

SISO single-input single-output

EVM error vector magnitude

CoMP coordinated multipoint

FER frame error rate

CDF cumulative distribution function

AWGN additive white Gaussian noise

PPS pulse-per-second

LS-MIMO Large scale multiple input multiple output

HPA high-power amplifier

OFDM Orthogonal Frequency Division Multiplexing

Part I

Thesis Overview

1

Introduction

It is not a long time since the first commercial mobile phone service was imple-mented by AT&T in 1946. Since then, the demand for wireless data traffic hasbeen increased tremendously. The number of subscribers has already exceeded thepopulation of the earth and is constantly growing. The application areas span alarge range of applications including smartphone users, connected cars, personalwearable, smart grids, sensor networks and IoT devices. Global mobile data traf-fic is expected to reach 49 exabytes per month by 2021, which shows a seven-foldincrease from 2016 [1, 2]. At the same time, the number of mobile-connected de-vices are expected to exceed 11.6 billion by 2021, i.e., 1.5 devices per capita [1, 2].Using the current technologies, it will be increasingly difficult to sustain with thisever-increasing demand. In fact, many of the requirement envisioned for the fifthgeneration (5G) of the cellular systems look already formidable [3].

One of the central performance metrics that reflects the capacity of a networkfor supporting the wireless demands of its users is the network throughput which isdefined as

Throughput[bitssec

]= Bandwidth [Hz]× Spectral Efficiency

[bits

sec Hz

].

This definition indicates that to increase the wireless throughput, we should usecommunication technologies that operate in wide band and/or improves the spec-tral efficiency. Currently, most of the commercial wireless applications are operatedin parts of the electromagnetic spectrum which lie below 6 GHz, leading to a se-rious spectrum scarcity. To address this problem, various technologies have beendeveloped in order to increase the spectral efficiency. One core technology thathas attracted lots of attentions due to its capability for increasing the spectral ef-ficiency is multiantenna communications, where the transmitters and/or receiversare equipped with multiple antenna elements. Having multiple antennas, togetherwith advanced signal processing techniques, enables changing the pattern of the ra-diated signal so as to reduce the interference to unwanted receivers while increasingthe transmission rate toward the intended one.

With the advances in the radio frequency (RF) technologies, commercial appli-

1

2 Introduction

cations at higher frequencies are enabled [4, 5]. In the recent years, many researchstudies have confirmed the potentials of the so-called millimeter-wave (mmWave)frequencies1 for wireless cellular communications. Moreover, federal communica-tions commission (FCC) has already adopted a notice of inquiry to examine thepotential for the provision of mobile radio services in bands above 24 GHz [6]. Com-munications at mmWave frequencies are characterized by large bandwidth and shortrange due to high penetration loss and high atmospheric absorption [5]. Therefore,although the bandwidth is not the bottleneck in the mmWave communications butthe intrinsic characteristics of the electromagnetic waves at the mmWave frequen-cies can limit the spectral efficiency and consequently the achievable throughput.Recent studies suggest that these intrinsic limitations can be mitigated by exploit-ing multiple antennas both at the transmitter and at the receiver [7]. Therefore,multiantenna communications has been considered as an essential enabler to realizemmWave cellular network.

A large body of research has been conducted to investigate the technologiesassociated with multiantenna communication and their potentials for future wirelesscommunication networks. To fully leverage the potentials of multiantenna systems,we need to address the following challenges:

• Acquiring accurate channel state information (CSI): The knowledge aboutthe propagation environment, a.k.a. channel state information (CSI), plays apivotal role in the multiantenna communications. When the CSI is known,several signal processing techniques can be used to enhance the quality ofcommunication. For instance, the transmitted signals from different antennascan be designed in a way that they add coherently at the intended receivers toprovide a gain in the received power or add destructively at unintended onesto reduce the interference. This technique is called transmit beamforming [8].

A widely-used approach to acquire the CSI is to allocate a part of the networkresources (such as time, frequency and power) for transmitting symbols thatare known by the receivers a priori. Then, the received symbols can be utilizedto estimate the channel responses. Intuitively, the more resources allocatedfor channel estimation the better the quality of the acquired CSI, and therebythe resulting beamforming, will be. However, network resources are limitedand extremely valuable. Therefore, allocating more resources for channel es-timations leaves fewer resources for the actual data transmission leading to awell-known pilot-data trade-off [9]. Seeking optimal approaches for allocatingthe optimal amount of resources for acquiring CSI has been a line of researchfor a long time [10–12]. Addressing this trade-off becomes more challenging asthe number of antennas grows, which happens in future multiantenna systemslike massive MIMO and mmWave cellular systems.

1Radio frequencies in the electromagnetic spectrum from 30 GHz to 300 GHz are usuallydefined as mmWave band.

Introduction 3

• Practical Interference Management: As the number of users who share thenetwork resources increases, the problem of interference between them be-comes more important. Conventionally, to manage the interference in thewireless networks, resources are allocated orthogonally to users. For instanceby employing approaches such as time division multiple access (TDMA) andfrequency division multiple access (FDMA), users are communicating in non-overlapping time slots or frequency bands, respectively. Therefore, by increas-ing the number of users in the network, the share of each user from the re-sources and subsequently its throughput decreases.A decade ago, a revolutionary approach was introduced in [13, 14] to com-pletely cancel the received interference at the users while still, everyone canenjoy half of the network resources. This approach is called interference align-ment and specifically refers to “a construction of signals in such a mannerthat they cast overlapping shadows at the receivers where they constituteinterference while they remain distinguishable at the receivers where theyare desired” [14]. Although this approach attracted lots of attentions at thebeginning but soon, due to the associated practical problems, its feasibil-ity was under question. Therefore, real-world implementation of interferencealignment can pave the way to carefully investigate and subsequently allevi-ate these practical challenges. This will take us one step closer to world ofubiquitously connected mobile devices.

• Compensating for Hardware Impairments: Each antenna branch of a transceiv-er device consists of several RF hardware components such as power amplifier(PA), low-noise amplifier (LNA), mixer, digital-to-analog converter (DAC),and analog-to-digital converter (ADC) which especially at high frequenciescan be expensive. Consequently, the implementation cost of the multiantennasystems increases proportional to the number of transceiver antenna elements.However, the practical implementation of future cellular systems, where largeantenna arrays are employed at the transceivers, is feasible only if each an-tenna element consists of inexpensive hardware. Inexpensive hardware com-ponents are prone to variety of hardware impairments including nonlineardistortion, IQ imbalance and phase noise [15] which can greatly degrade theperformance of the system.

Inspired by the above discussion, in this thesis, we mainly investigate these threeproblems in multiantenna cellular systems using theoretical and numerical analysisas well as measurement on a real-world testbed.

In the sequel, a brief review of several fundamental concepts which will be usedthroughout this thesis is give in Section 1.1. In this section we also introduce thetestbed that we have used for implementation and measurement of our algorithms.In Section 1.2, we will list the specific contributions of this thesis together with ashort description of the system model and the central results of the included paper.The conclusions of the thesis are discussed in Section 1.3.

4 Introduction

1.1 Background

In this section, we will briefly review some of the concepts and definitions which arerequired for the presentation of the materials used in the next part of this thesis.

The contributions of this section are in part based on

• [16] N. N. Moghadam, H. Farhadi, P. Zetterberg, M. Khormuji and M.Skoglund, “Interference alignment: Practical challenges and test-bed imple-mentation, book chapter in Contemporary Issues in Wireless Communica-tions, INTECH Open Access Publisher, Nov. 2014.

• [17] C. M. Yetis, N. N. Moghadam, J. Fanjul, H. Farhadi and J. A. Garcia-Naya, “Interference alignment testbed,”submitted to IEEE Commun. Mag.,under revision (minor).

1.1.1 Wireless ChannelThe signal transmitted from a wireless transmitter goes through a physical mediumbefore reaching its destination. This physical medium is called wireless channel orin short channel. When the signal passes through a wireless channel, unlike thewired channels, it will be spread in different (and sometimes unwanted) directions.Therefore, by traveling through the channel, the signal’s power decays. This decayis called the channel path loss and is an increasing function of the distance betweenthe transmitter and the receiver.

In addition to the path loss, there are several other random phenomena whichaffect a signal transmitted through a wireless channel. These random phenomenainclude

• multi-path fading: which happens when the superposition of multiple copiesof the signal reflected from the obstacles in the medium are received withdifferent delays at the destination.

• shadowing: which happens when the signal is blocked by some large obstaclesin the medium. The shadowing leads to a loss in the signal’s power which ismuch larger than the channel path loss.

• interference: which is an additive disturbance due to the transmitted signalsfrom the interfering transmitters in the medium. Like the desired signal, theinterference is not known at the receiver and is considered to be random.

• receiver thermal noise (a.k.a. Jannson noise): which is an additive noise gen-erated by the electronic circuitry of the receiver due to the thermal agitationof charge carriers.

In linear systems, the combined effects of these random phenomena is math-ematically modelled using a random multiplicative gain and an additive random

1.1. Background 5

disturbance. In this case, when a symbol x is transmitted from a transmitting an-tenna, the actual received symbol at the receiving antenna is

y = hx+ n , (1.1.1)

where h represents the channel gain and contains the effects such as path loss,multi-path fading and shadowing, while n models the interference and the receivernoise.

Although in a real communication system, the channel gain is continuously andgradually changing, it is a common practice to assume that it remains constant fora certain period, known as coherence time of the channel, and suddenly changesto a new value, independent from the previous one, at the beginning of the nextcoherence time. This model is referred to as block-fading.

1.1.2 Multiantenna CommunicationThe use of wireless systems equipped with multiple transmit and receive antennashas gained an overwhelming attention during the last two decades since the pio-neering works by [18, 19]. In general, multiple antennas in a system are used inorder to enhance the bit rate, decrease the bit error rate, and improve the receivedsignal-to-noise-plus-interference ratio (SINR).

In the following, we characterize the gains of multiantenna communication -with respect to the single-antenna case - within four different categories.

• Array gain: It is a gain in the transmitted or received power achieved by co-herently transmitting or combining the signals at different antenna elements2,respectively. In a uniform linear array (ULA) antenna, where antenna ele-ments are equally spaced and are located on a straight line, it is shown thatthe array gain increases linearly with the array length [20].

• Diversity gain: When the antenna elements are placed far enough from eachother, they see uncorrelated channels. It means that the channels betweendifferent transmit-receive antenna pairs, affect the signal in an uncorrelatedway. The provided diversity, through the uncorrelated channels, can be usedto increase the reliability of communication; loosely speaking, if one channelpath is in a deep fading, there is a high probability that the other paths havea good quality. Therefore, by transmitting the same data stream through allthe channel paths a robustness against fading is gained.The correlation between different paths of a channel depends on both thephysical channel between transmitter and receiver, and the structure of thetransmitting and receiving antenna arrays. Namely, poor- or rich-scatteringcharacteristic of the channel as well as the space between the antenna elementsaffect the diversity gain of the channel. For instance, to enjoy the full diversity

2 Precisely speaking, an antenna may contain one or several antenna elements. However, inthis thesis antenna and antenna element are interchangeably used to refer to the same concept.

6 Introduction

BS UE

Figure 1.1: Point-to-point MIMO network.

using ULAs in a rich-scattering environment, where the signal is reflectedfrom many scatterers, the antenna elements should be spaced at least half awavelength (of the carrier waveform) from each other [20].

• Multiplexing gain: The uncorrelated channels between the transmitter andreceiver can also be used for conveying several independent streams of datainstead of transmitting the same data stream through different channel paths.

• Interference management: When the transmitter or receiver is equipped withan array of antennas, signal processing techniques can be used to design thetransmit or receive gain of the array in different spatial directions, respec-tively [21]. Therefore when the terminals are located at different locations,this approach can be utilized to reduce the interference between differentlinks.

1.1.3 Multiantenna Networks

Point-to-Point MIMO

A point-to-point multiple-input multiple-output (MIMO) is the simplest MIMOnetwork where a multiantenna transmitter serves a multiantenna receiver (see Fig-ure 1.1). To mathematically model this network, the channel gains between all thetransmit-receive antenna pairs are collectively represented by the channel matrixH. In this case, the vector of received symbols at the receiver is

y = Hx + n, (1.1.2)

where x and n represent the vector of transmitted symbols and noise at differentreceiving antennas, respectively.

Single-Cell Multiuser MIMO

In a MU-MIMO cellular network setup, multiantenna base station (BS)s locatedat different cells communicate with their allocated multiantenna user equipment(UE)s. However, the shared nature of the wireless links causes the nearby trans-mitters to interfere with each other. In this case, depending on the direction of thecommunication the model of the network can be different. In the uplink, where the

1.1. Background 7

BS

UE

UE

Figure 1.2: Single-cell Multiuser MIMO.

BS

UE

UE

BS

UE

UE

Figure 1.3: Multi-cell Multiuser MIMO.

BS is receiving while UE k transmits message xk, the receive signal is the receivedsignal

yul =K∑k=1

Hulk xk + n, (1.1.3)

where Hulk is the channel between UE k and the BS. In a similar way, in the downlink

the received signal by UE k can be written as

ydlk = HH

k xdl + nk, (1.1.4)

where Hdlk represents the channel between the BS and UE k.

Multi-Cell Multiuser MIMO

Several cells in a network form, a multi-cell multiuser MIMO. Figure 1.3 schemati-cally shows a multi-user MIMO network with two neighboring cells. As it is shownin the figure, the neighboring cells in a network can make interference to each other.Moreover, the BSs can cooperate through the backhaul link to improve the overallperformance of the network.

1.1.4 Pilot-based Channel State Information AcquisitionIn order to harvest the gains of a multiantenna system, mentioned earlier in Sec-tion 1.1.2, the instantaneous CSI needs to be acquired. In pilot-based channel esti-mation approaches, part of the network resources (such as time and frequency) are

8 Introduction

allocated for transmitting pilot symbols, i.e., symbols that - unlike the data symbols- are a priori known at the receiver. The received symbols reflect the impacts of thechannel on the transmitted signals and can be utilized for acquiring CSI.

1.1.5 BeamformingBeamforming is a versatile and powerful signal processing technique that can beused in multiantenna systems to transmit or receive signals in a spatially selectiveway [22]. When the receiver is equipped with multiple antennas, receive beam-forming can be applied to combine the received signal vector in a way that someperformance metric (such as received signal-to-noise ratio (SNR) or minimum meansquare error (MMSE) of the received symbols) is optimized. In contrast, transmitbeamforming can be used when the transmitter is equipped with multiple antennasto optimize the same performance metrics as in receive beamforming. In this case,the data streams intended for one or several receivers in the network are precodedin a way that the transmitted signal from each antenna is a combination of thedifferent data streams 3.

Beamforming filters are usually designed based on the estimated instantaneousCSI and are not linear in general. However, it is shown that when the number ofantennas is large the linear filters, despite their low complexity, have a near-optimalperformance [23,24]. Therefore, we only focus on the linear beamforming strategiesin this thesis. Some of the most popular transmit beamforming strategies are listedbelow:

• maximum ratio transmission (MRT) precoder: MRT is a linear precoder im-plemented at the transmitter, whose goal is to maximize the delivered powerto an intended receiver.

• Zero-forcing precoder: In contrast with the MRT precoder, with zero-forcingthe focus is on the interference instead of the desired signal. In fact the zero-forcing precoder is designed in a way that the received interference at unin-tended receivers is nulled.

• MMSE precoder: MMSE precoder takes both the intended signal power andthe interference power into account and optimizes the received SINR at anintended receiver. However, the implementation of MMSE is more complicatedcompared to MRT and zero-forcing.

There are equivalent combiners to the the aforementioned precoders, namely max-imum ratio combining (MRC), zero-forcing and MMSE combiner respectively, thathave the same properties and operational meaning, which instead of the transmitterare implemented at the receiver side.

3 Throughout this thesis, the receive and transmit beamforming filters are sometimes referredto as combiner and precoder, respectively.

1.1. Background 9

1.1.6 Interference Management

Due to the broadcast nature of the wireless communication channels, when thereis more than one transmitter in a network, in addition to the desired signal, theunintended signals are also overheard by the receivers. Hence, the signal receivedat each receiver is a noisy combination of the desired signal and the interferencefrom the interfering transmitters weighted by the corresponding channel gains. Ingeneral, three main strategies are considered for managing the interference in anetwork. These strategies are illustrated in Figure 1.4 and are briefly describedbelow.

When the received interference is weak the desired signal can be extracted fromthe noisy signal by treating the interference as noise. In this case, each transmittercan precode its message independent from the other transmitters. This strategy, isschematically presented in Figure 1.4a for a network with three transmitter-receiverpairs. As the figure shows, each message (represented by color-coded squares) spansthe whole signal space and therefore interference is inevitable.

In high-SNR regime, where the inter-user interference is strong and the inter-ference is dominating, some cooperations among the transmitters is necessary toimprove the quality of the communication links. Conventionally, to avoid interfer-ence at the receivers, orthogonal signal transmission schemes, such as TDMA andFDMA, have been used where the network resources (i.e., time and frequency, re-spectively) are allocated orthogonally to different users. Figure 1.4b illustrates theorthogonal signal transmission strategy. As the figure shows, although the receiversdo not suffer from the inter-user interference, but the signal space has not beenused efficiently in this case. This issue is more highlighted in the networks with alarge number of users as by increasing the number of users the share of each userfrom the network resources decreases.

A more efficient scheme for managing the inter-user interference based on coop-eration among the users proposed in [13,14]. In this scheme, the transmitted signalsare precoded in a way that at each receiver the interfering signals are aligned in asubspace of the signal space referred to as interference subspace while leave the restof the signal space, i.e., desired signal subspace free of interference. Therefore thisstrategy is called interference alignment. The concept of interference alignment isschematically presented in Figure 1.4b. Interference alignment can be performed indifferent domains such as time [25,26], frequency [14,27], space (across different an-tennas in multiantenna systems) [13,14], and also any combination of these domains(for interference alignment over a combination of space and frequency see [28]).

Practical Interference Alignment

The structure of a canonical transmitter and receiver for the implementation ofinterference alignment is shown in Figure 1.5. At the transmitter side, there is anencoder which encodes the messages to the corresponding codewords suitable fortransmission over the channel. The transmission can be enhanced by the adaptation

10 Introduction

BS1

BS2

BS3

UE1

UE2

UE3

H11

H21

H31

H13

H23

H33

H12

H22

H32

(a) Non-orthogonal signal transmission.

BS1

BS2

BS3

UE1

UE2

UE3

H11

H21

H31

H13

H23

H33

H12

H22

H32

(b) Orthogonal signal transmission.

BS1

BS2

BS3

UE1

UE2

UE3

H11

H21

H31

H13

H23

H33

H12

H22

H32

(c) Interference alignment.

Figure 1.4: Major interference management strategies.

1.1. Background 11

Source

Encode

rPo

wer

Con

trol

Precod

erCha

nnel

+

Interferen

ce

Com

bine

rDecod

erDestin

ation

Synch

Cha

nnel

Estim

ation

Feed

back

Cha

nnel

RateAda

ptation

Ana

log

feed

back

digital

feed

back

Figu

re1.5:

Can

onical

structureof

tran

smitt

eran

dreceiver

ininterferen

cealignm

entsche

me.

12 Introduction

of the transmitted signal according to the received CSI feedback. Specifically, in aclass of communication systems that transmission powers are fixed and a maximumthroughput is desired, the encoder may adapt transmission rate according to theestimate of the mutual information of the channel (computed by the rate adaptationmodule). On the other hand, in another class of systems which desire fixed-ratetransmission, power control module should adjust transmitted power according tothe channel state feedback to maintain mutual information of the channel largerthan a certain level. Each transmitter has a precoder which compute the propersignal for transmission over the channel according to the interference alignmentconcept.

At the receiver side, channel estimation module computes the estimation ofincoming channel gains. These channel estimations can be used for recovering thetransmitted message and computing the channel state information feedback signal.The filter module exploits estimated channel gains to recover the desired signal frominterference signals according to the interference alignment concept. The decodermodule decodes the message using an estimate of the incoming channel gain. Thefeedback encoder module computes the feedback signal according to the estimatedchannel gains. Also, there is a synchronizer module to synchronize the receiver andthe transmitter.

The significant gain of interference alignment relies on challenging requirementssuch as availability of global perfect CSI, large amount of network resources (suchas power and bandwidth), and perfect synchronization. These requirements alongwith the solutions for relaxing them in the practical interference alignment systemsare discussed below.

• Globally available perfect CSI : In the original interference alignment techniqueall terminals need to know CSI perfectly in order to design their precodersand filters. In practice, additional radio resources are allocated for channeltraining and only a noisy CSI estimate can be provided. Receivers can estimate(locally) CSI through a pilot-based channel training scheme (see e.g. [29] and[30]). In time division duplexing (TDD) systems, channel reciprocity can beexploited to acquire CSI at the transmitters, although a precise calibration ofthe RF equipment is needed as shown in [31]. In frequency division duplexing(FDD) systems, transmitters can obtain CSI using feedback channels, i.e.,each receiver sends its estimated CSI to the transmitters via analog or digitalfeedback signals. However, the feedback CSI suffers from additive noise (inanalog feedback), quantization noise (in digital feedback) or delay (in bothcases). Although perfect feedback is often assumed in the experiments (seee.g. [30] and [32]), realistic analog wireless feedback has been also reportedin [33]. Also, the overhead due to the feedback can be alleviated by means ofcompression as shown in [34].

• Unlimited network resources: The second requirement for implementing a per-fect interference alignment scheme is the availability of a large amount ofnetwork resources such as time, frequency, number of antennas and power.

1.1. Background 13

Limited resources in practical networks will naturally degrade the interferencealignment performance. As the number of users increases, larger signal spacedimensions are required to perfectly align the interference signals at the re-ceivers. It has been shown that the number of dimensions grows exponentiallywith the number of users when interference alignment is implemented overfrequency or time. Hence, the scalability of interference alignment testbeds isan important issue.

The finite received SNR is another limitation for achieving the optimal DoFpromised by interference alignment. However, testbed implementations showthat despite the imperfections in CSI acquisition and radio hardware, interfer-ence alignment still can outperform the conventional communication schemessuch as TDMA and greedy interference avoidance in the mid to high SNRregime [32].

Accurate CSI estimations at the transmitters can guarantee the outstandingperformance of interference alignment. On the other hand, as more radioresources are allocated for CSI acquisition and feedback, less resources areavailable for user data transmissions. This trade-off has been investigated inthe literature (e.g. see [35] and [29]). As the network size increases, moreresources should be allocated for CSI acquisition and feedback to maximizethe throughput [29].

• Perfect synchronization Perfect synchronization among network users is an-other important requirement in the interference alignment implementation.Imperfect synchronization in interference alignment, similar to other coher-ent multi-user approaches, causes additional errors at receivers due to inter-symbol and inter-carrier interference. To increase the practicality of inter-ference alignment, some solutions have been suggested and implemented ontestbeds. Perfect synchronization can be achieved when the beamformers aredesigned at a single baseband processing unit and then distributed to thecorresponding nodes, which are synchronized through cabling or making syn-chronization reference signals available at all nodes. Reference signals typicallyconsist in a pulse-per-second (PPS) signal and a 10 MHz reference signal,found in Rubidium- and/or GPS-based frequency standards. On the otherhand, fully distributed systems may use wireless synchronization protocols(e.g. see [31], [33]), which typically require additional network resources.

1.1.7 Hardware Impairments

So far, we have only discussed the ideal communication systems, where the linkbetween each transmit and receive antenna pair can be described using a math-ematical model as in (1.1.1). The linear modeling facilitates the analysis of com-munication systems and the deign of the associated signal processing techniques.Therefore the techniques, such as channel estimation, beamforming, power control

14 Introduction

-1 -0.5 0 0.5 1In-Phase

-1

-0.5

0

0.5

1

Qua

drat

ure

(a) Phase Noise

-1 -0.5 0 0.5 1In-Phase

-1

-0.5

0

0.5

1

Qua

drat

ure

(b) IQ imbalance

Figure 1.6: Influence of phase noise and IQ imbalance on 16-QAM OFDM symbols.

and interference management, are usually designed based on ideal system assump-tion. However in practice, this assumption does not hold in general. Specially, asthe communication systems are moving toward operation at higher frequencies andimplementation using low-cost devices, the effect of hardware imperfections on thesystem performance is more severe.

Below, we discuss the effects of three major hardware impairments in wirelesscommunication systems, namely phase noise, IQ imbalance and nonlinearity.

Phase Noise

Imperfection in the oscillators of a wireless transceiver, which is originated fromthermal noise, leads to a random deviation of the carrier frequency from the ex-pected one. This imperfection is usually modeled as an excess random phase addedto the signal and therefore called phase noise. Figure 1.6a shows 16-QAMmodulatedsymbols influenced by phase noise imperfection.

IQ imbalance

The radio transceivers built based on in-phase and quadrature (IQ) signal process-ing architecture are of great values for the low-cost and flexible applications. Inan ideal architecture, the local oscillators at I- and Q-branches, which are used forup- or down-conversion of the I and Q signals, respectively, have the same ampli-tude and 90° phase difference. However, any deviation from the ideal phase andamplitude leads to imbalance between the I and Q signals. The influence of the IQimbalance on the 16-QAM modulated symbols is illustrated in Figure 1.6b.

1.1. Background 15

(a) AM-AM (b) AM-PM

Figure 1.7: Measured AM-AM and AM-PM characteristics of a GaN class-A am-plifier (Cree CGH40006-P).

Nonlinearity

In a wireless transceiver front-end, several RF components such as ADCs, DACs,mixers, LNAs and PAs can exhibit a nonlinear behavior. Nevertheless, the nonlinearbehavior of a front-end is mainly caused by the PAs operating close to the saturationdue to the power efficiency considerations [36]. The highly nonlinear behavior of PAstogether with the fact that they are the most power-consuming analog componentsof the transmitters, motivates the study of the impact of PAs on the performanceof a communication system in particular.

A PA is a circuit which converts the DC power of the biased signal to the ACpower of the communication signal [37]. When the communication signals are con-stant modulus or have low peak-to-average-power ratio (PAPR), the influence ofthe PA nonlinearities on the performance of the system is negligible. In these cases,the linear model still gives a good approximation of the system’s behavior. How-ever, to increase the spectral efficiency, exploitation of high-order constellation andmultiple access techniques such as OFDM which lead to high PAPR is inevitable.The signals with high PAPR are more prone to distortion by the PAs working closeto the saturation region.

The PA nonlinearity can distort the amplitude and the phase of the signal whichgoes through it. The nonlinear distortion depend on the amplitude of the inputsignal and is characterized by amplitude-to-amplitude (AM-AM) and amplitude-to-phase (AM-PM) transfer functions of the PA. Figure 1.7 shows the AM-AM andAM-PM characteristics of a class-A amplifier.

In general, several solutions and techniques have been proposed to reduce thenonlinearity effects in a wireless system. When the number of RF-chains is notlarge, it is possible to prevent the distortion at the cost of expensive highly-linearRF components. However, this solution increases the total cost of the system sig-

16 Introduction

-1 -0.5 0 0.5 1In-Phase

-1

-0.5

0

0.5

1

Qua

drat

ure

(a) No input back-off.

-1 -0.5 0 0.5 1In-Phase

-1

-0.5

0

0.5

1

Qua

drat

ure

(b) 3 dB input back-off

-1 -0.5 0 0.5 1In-Phase

-1

-0.5

0

0.5

1

Qua

drat

ure

(c) 10 dB input back-off

Figure 1.8: Influence of PA nonlinearities on 16-QAM OFDM symbols. By increas-ing input back-off, the nonlinear distortion decreases.

nificantly, specially when the number of RF-chains is large and when the operatingfrequency of the chains is high.

Another alternative technique for reducing the PA distortion is to apply a largeinput back-off from the saturation point and instead bias the PA at the linearoperating region. Figure 1.8 illustrates how the input back-off can improve theerror vector magnitude (EVM) of 16QAM OFDM symbols distorted by a nonlinearPA. However, although applying input power back-off causes less distortion, but italso leads to a lower power efficiency [38].

Another technique to relax the linearity requirement of a PA is to use digitalpredistorter (DPD), in which the signal is predistorted prior to passing through thePA using the complementary transfer function of the PA. It means that the pre-distorter transfer function is designed in a way that the concatenation of the DPDand the associated PA gives a linear transfer. The performance of this techniqueis highly dependent to the accuracy of the available model for the PA. Moreover,considering the varying behavior of the PAs due to signal characteristics such asaverage power and bandwidth and also the environment effects such as temperatureadds to the complications of this technique.

1.1.8 KTH Fourmulti Testbed

KTH four-multi is a USRP-based wireless communication testbed consisting ofseveral stationary and movable multi-antenna nodes. A software framework ac-companies the hardware setup of the test-bed which facilitates the rapid testingof multi-antenna schemes (see http://fourmulti.sourceforge.net/). In the fol-lowing, the hardware and software structure of the test-bed is described.

1.1. Background 17

(a) Baseband processing unit.

(b) Mobile Station.

(c) Base Station.

Figure 1.9: KTH fourmulti testbed.

Hardware Setup

The current version of the test-bed consists of six nodes where three of them arefixed and take the role of transmitting sources while the other three are movable re-ceiving destinations. All the nodes are equipped with two vertically polarized dipoleantennas spaced 20 cm apart which is 1.6 times of the carrier’s wavelength. TwelveEttus Research USRP N210 (see www.ettus.com) are used to govern the twelveantennas in the network. The source USRPs are equipped with the standard EttusXCVR2450 RF dautherboards while the destination USRPs use custom boards toachieve sufficient noise figure and dynamic range. The output signal of each sourceUSRP is amplified by a ZRL-2400LN power amplifier. Two Linux computers con-trol all the USRPs in the network. The network structure of four-multi test-bed isillustrated in Figure 1.10.

The network is designed to work at 2.49 GHz center frequency with 12 MHzbandwidth. Synchronization of the network is performed in three levels, namelytime, frequency and transmit-receive synchronizations. The time and transmit-receive synchronizations are done by means of a pulse-per-second (PPS) signal(0-5 V, 1 Hz square wave) and a national marine electronics association (NMEA)

18 Introduction

USRP

USRP

USRP

USRP

USRP

USRP

BS3

BS2

BS1

master node

USRP

USRP

USRP

USRP

USRP

USRP

UE3

UE2

UE1feedback

backhaul

CLK

CLK

CLK

CLK

TX

Baseb

and

Processin

gUnit R

XBaseband

ProcessingUnit

TCP/IP TCP/IP

GPS

PPSPPSNMEANMEA

Figure 1.10: KTH Fourmulti testbed.

signal (an ASCII protocol that provides hour-minute-second time), respectively.Both signals are generated by an EM406A GPS module and distributed throughthe network. The frequency synchronization is also performed by helps of 10 MHzreference clocks (CLK). All the source’s local oscillators are locked to the sameclock while a separate clock is provided for each of the destinations. In a real imple-mentation the same synchronization would be achieved using common control andsynchronization channels (cellular systems) or from the burst preambles (wirelesslocal area networks). In a system with interference alignment, transmitter will inany case need some kind of back-haul to provide a common time reference anddisperse scheduling decisions.

Software Setup

The four-multi software framework has been developed in C++ (see http://fourmulti.sourceforge.net/). It run on two Linux computers separately. One of thecomputers controls the three source nodes while the other one controls the threedestination nodes connected to them via Ethernet connections. The sources’ com-puter generates the transmitted frames and feeds them to the source nodes whilethe destinations’ computer process the received frames at the destination nodes.A TCP/IP connection between the source and the destination computers providesthe feedback links. Backhaul communication among the source nodes is also imple-mented by the help of TCP/IP connections between the source computer and the

1.1. Background 19

Table 1.1: KTH four-multi modulation and coding toolbox specifications.

OFDM1 AMCFFT length 80 Coding rates 1

2 ,58 ,

34

Cyclic prefix length 12 Codeword length 1520Number of null subcarriers 42 QAM modulation orders 4, 16, 64, 256Subcarrier spacing (KHz) 312.5

source nodes.The framework contains a toolbox for coding and modulation (AMC and OFDM1)

which was used in the implementations of the next two sections. The modulationand coding toolbox includes an LDPC channel encoder/decoder, a QAM modu-lator/demodulator and an OFDM modulator/demodulator. The specifications ofthese built-in functions is summarized in Table 1.1.

20 Introduction

1.2 Our Contributions

In this section, we will discuss our contributions in the study of practical limita-tions and impairments in multiantenna cellular communication systems. In the firstpart of this section, we will investigate the problem of CSI acquisition in the mul-tiantenna cellular systems with a large number of antennas. We have studied thisproblem in [39] which is labeled as Paper A in this thesis. In the second part, wewill investigate the problem of practical interference management in multiantennasystems. We have studied this problem in [40,41] labeled as Papers B-C throughoutthis thesis. Finally, we will deal with the problem of signal distortion due to thenonlinear RF hardware in multiantenna transmitters. We have studied this prob-lem in [42, 43] labeled as Papers D-E in this thesis. For each paper, we will brieflydiscuss the previous works and the system model used in the paper and present thecentral results.

Contributions by the author

The contributions of this thesis’ author on the included papers are the outcome ofthe author’s own work, in collaboration with the list of co-authors. The order ofthe author names reflects the contribution levels in each paper. The author of thisthesis, when being the first author of the paper, has been giving the substantialand the vast majority of the contributions, especially regarding theoretical analysis,computer simulations, testbed implementations, measurements and paper writing.

1.2.1 Problem I: Acquiring CSI in Multiantenna CellularSystems with a Large Number of Antennas

Paper A: Pilot Precoding and Combining in Multiuser MIMONetworks [39]

In this paper, we investigate pilot precoding and combining in the uplink of a single-cell network. The main idea behind this work is to utilize the a priori availableknowledge about the long-term statistics of the channel in a multiantenna networkto improve the channel estimation quality. Using the pilot precoders and combiners,significantly reduces the number of network resources needed for channel trainingand leaves more resources for the actual data transmission. Hence the networkthroughput can be improved significantly.

Background

When the perfect instantaneous CSI is available, it has been shown that the spec-tral efficiency of the multiantenna systems increases rapidly with the number ofantennas [19, 44]. However, in practice, the CSI needs to be estimated in each co-herence time of the channel by transmitting pilot symbols. In traditional channel

1.2. Problem I 21

training approaches, network resources, such as time and frequency, are allocatedorthogonally to the UEs for pilot transmission. It means that no interference isallowed between the UEs during the channel training phase.

By allocating orthogonal resources to the UEs in the large networks, wherethe number of UEs is comparable with the number of resource elements, a largeportion of the network resources need to be allocated for channel training. Themore resources allocated for channel training, the fewer resources remain for theactual data transmission. This problem is particularly important in massive MIMOsystems, where a large number of UEs are served within one cell. Another areathat this problem arises is in the context of mmWave cellular networks [45], wherethe UEs are equipped with a large array of antennas and the channel coherenceinterval is shorter than the conventional cellular networks operating at sub 6 GHzfrequencies.

Since the network resources are scarce, reusing them throughout the network isinevitable. Reusing the resource elements leads to a well-known problem called pilotcontamination [46], where the received pilots are contaminated by the pilot symbolstransmitted from the neighboring cells. Despite the large number of resources thatneed to be allocated for training in massive MIMO systems, the single-antennaUEs might suffer from low SNR during pilot transmission phase, especially theones located close to the cell edges. Moreover, the lack of antenna array gain atsingle-antenna UEs will lead to the imbalanced coverage range for pilot and datatransmission [47, 48].

In the case of multiantenna UEs, even more resources are needed for channeltraining; in a point-to-point MIMO scenario, [9] showed that the optimal numberof required resource elements for channel training is equal to or larger than thenumber of transmit antennas. However, when the channel gains are correlated, thelong-term statistics of the channel can be used to design shorter training sequencesfor optimal CSI estimation [11].

Contributions

In this paper, we suggest that utilizing multiple antennas at the UEs along withusing simple spatial precoding and combining filters at the UEs and the BS, respec-tively, improves the performance of the network significantly. We also characterizethis performance improvement in terms of both the channel estimation quality andthe achievable sum-rate of the network.

Three uplink pilot transmission scenarios in combination with MMSE chan-nel estimation at the BS have been studied in this paper. The pilot transmissionscenarios are briefly described below:

1. Non-precoded and uncombined pilot transmission (nPuC): In this scenario,which is used as a benchmark, orthogonal pilot sequences are transmittedfrom each UEs’ antenna. Pilot sequences are neither precoded at the UEs norcombined at the BS.

22 Introduction

2. Precoded but uncombined pilot transmission (PuC): In this scenario, orthog-onal resources are allocated for pilot transmission from each UE. However,the pilot sequences transmitted from different antennas of a particular UEare not necessarily orthogonal. Although the orthogonality constraint on theantennas of each UE is relaxed, a simple spatial linear precoding filter is pro-posed to improve the quality of the estimated CSI at the BS. By relaxingthe orthogonality constraint on the pilot sequences, the amount of necessaryresources for the channel training decreases significantly. This leaves more re-source elements for data transmission and consequently increases the spectralefficiency of the network.

3. Precoded and combined pilot transmission (PC): In the third pilot transmissionscenario, the orthogonality constraint on the pilot sequences transmitted fromall the transmitting antennas in the network is relaxed. Therefore, in PC notonly different antennas of one UE can make interference to each other butalso the pilot sequences transmitted from different UEs are allowed to interferewith each other. In this scenario similar to PuC, a linear spatial filter is used toprecode the transmitted pilots while the inter-UE interference is rejected usinga spatial combining filter at the BS. Again, non-orthogonal pilot transmissiondramatically reduces the amount of necessary resources for channel trainingand leads to higher spectral efficiency.

In Figure 1.11, the channel estimation performance of the different pilot trans-mission scenarios, in the normalized mean square error (NMSE) sense, are comparedfor a network with two UEs. In this figure, tτ represents the number of resource el-ements allocated for channel training. In addition to the aforementioned scenarios,the NMSE of two additional pilot transmission and channel estimation scenarios,denoted by LS and Heu, are also plotted in this figure for benchmarking. For theLS curve, similar to [10], orthogonal pilot transmission and least square (LS) chan-nel estimation is used, while for Heu a heuristic pilot design suggested in [11] andMMSE channel estimation is implemented.

As Figure 1.11, shows in this setup, PuC can achieve the same estimation erroras nPuC with almost 5 dB less energy. Alternatively, for a given pilot transmissionenergy, pilot precoding can improve the estimation error by 6 dB compared withthe conventional nPuC. Another observation from the figure is that the performanceof PC with only 4 orthogonal resource elements is almost identical to that of PuCwith 64 orthogonal resource elements.

As an indicator for the channel spectral efficiency, lower bounds on the achiev-able sum-rates for the pilot transmission scenarios discussed before, are plotted inFigure 1.12. In this figure, ρτ represents the energy allocated for pilot transmissionnormalized to the total energy budget of each UE for transmission within one co-herence block. This figure shows that PuC and PC always lead to higher spectralefficiency compared to the conventional nPuC. Moreover, the maximum spectralefficiency that PC can reach is higher than PuC, though PuC has a better channelestimation performance; see Figure 1.11. Another observation from Figure 1.12 is

1.2. Problem I 23

−20 −15 −10 −5 0 5 10 15 20−50

−40

−30

−20

−10

0

10

Pilot transmition energy ρτ (dB)

Aver

age

norm

aliz

edM

SE(d

B)

nPuC,tτ=64LS,tτ=64 PC,tτ=4PuC,tτ=8 PC,tτ=2Heu,tτ=8 PC,tτ=1

Figure 1.11: The impact of pilot energy and number of transmitted pilot symbolson the channel estimation performance.

that the optimal pilot energy of PuC and PC are substantially smaller than that ofnPuC.

In this paper, we also analyze the performance of the network in the asymptoticregime, where either the UEs or the BS or both are equipped with the large array ofantennas. Ultimately, we show that using the pilot precoding and combining, whenboth the UEs and the BS have large number of antennas, the interference betweenUEs as well as the interference between the antennas of each UE vanishes.

The following Corollary summarizes the contributions of this paper regardingthe large antenna regime.

Corollary 1.2.1. In a cellular network, suppose that there are a limited numberof paths between each UE and its serving BS and that the second-order statisticsare perfectly known. Let either the number of BS antennas or the number of UEantennas tends to infinity, then

1. the pilot contamination problem disappears,

2. a multi-cell network can be modeled by multiple uncoordinated single-cell net-works with no performance loss, and

3. channel training in the entire network can be done with a single pilot symbol.

24 Introduction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

Normalized pilot energy ρτ

Spectral

effic

iency(bits

/use)

nPuCPuCPC, tτ = 1

Figure 1.12: Spectral efficiency as a function of normalized pilot energy. The max-imum point of the curves are marked by circles.

1.2.2 Problem II: Interference Management in PracticalMultiantenna Cellular Systems

Paper B: Test-bed implementation of iterative interferencealignment and power control for wireless MIMO interferencenetworks [40]

In this paper, a practical implementation of interference alignment in the down-link of a MIMO multi-cell cellular system is investigated. To alleviate the impact ofhardware impairments and CSI estimation error an iterative power control is imple-mented jointly with an iterative interference alignment algorithm. The implementedpower control algorithm helps to maintain the fixed rate of the communication linkbetween each BS and its corresponding UE.

Background

Interference alignment was introduced as a promising approach to improve thespectral efficiency of the interference networks [13,14]. However, the successful per-formance of this approach depends on some theoretical assumptions, which arechallenging to fulfill in practice. Providing perfect CSI at all the terminals, per-fect synchronization throughout the network and ideal hardware are among thesechallenges, which have been discussed with more detail in [16,49].

In the practical scenarios, where the aforementioned assumptions do not hold,

1.2. Problem II 25

the interference signals can not be aligned perfectly at the receivers. As a result,the leakage of the interference into the signal subspace is inevitable. Therefore,several research attempts have been made for designing the algorithms based onthe interference alignment concept to relax the perfect alignment constraint andyet achieve a good spectral efficiency in the network. In [50], two iterative and dis-tributed approaches have been proposed to either minimize the interference leakageor maximize the received SINR, where each terminal only needs to know its localCSI (i.e., the CSI corresponding to the channels which the terminal is transmittingto or receiving from). Another iterative approach has been suggested in [51] whichfocuses on optimizing the weighted sum-rate of the network by taking the residualhardware impairments of the transceivers into account. The iterative interferencealignment approach is used in combination with a power control algorithm in [52,53]to guarantee a fixed rate reception by the receivers when the acquired local CSI atthe terminals is perfect or noisy, respectively.

Contributions

Based on [52, Algorithm 1], we have implemented a joint iterative interference align-ment and power control beamforming strategy (PC) on KTH fourmulti testbed (seeSection 1.1.8). As a benchmark, we have also implemented the iterative interferencealignment (noPC), as proposed in [50], on the same testbed.

The implemented interference alignment algorithm pushes the received interfer-ence from all the BSs to a subspace of the signal space, referred to as interferencesubspace, at each UE while tries to keep the desired signal subspace free of in-terference. However in practice, due to the imperfections in the network and thetransceivers such as imperfect RF hardware and noisy CSI the leakage of the in-terference to the signal subspace is inevitable. This makes the quality of each link,represented by SINR, dependent to the inter-user interference signals. Moreover,considering the time varying nature of the channel gains, the received SINRs fluc-tuate in practical environments. To ensure the quality of the links remains constantduring the communication period, a power control algorithm is implemented jointlywith interference alignment.

Figure 1.13 shows the empirical cumulative distribution function (CDF) of thereceived SINR for the two implemented strategies on the testbed, namely PC andnoPC. In the measurements corresponding to PC the target SINR for all links wereset to 18 dB while noPC was measured with four different average transmit powers.As the figure illustrates, the measured SINR values in PC are concentrated aroundthe target SINR, while in the other measured scenarios, the SINR values span alarger range.

Table 1.2 also compares the performance of PC and noPC in terms of bit errorrate (BER), frame error rate (FER), the average received SINR and the averagetransmitted power. As the measurement results in the table suggest PC can achievethe best BER and FER performance with a comparably low power transmission.

26 Introduction

−5 0 5 10 15 20 25 30 350

0.2

0.4

0.6

0.8

1

SINR (dB)

PC,SINRtr = 18 dBnoPC,Ptr=7.1 dBmnoPC,Ptr=1.1 dBmnoPC,Ptr=-3.4 dBmnoPC,Ptr=-12.9 dBm

Figure 1.13: CDF of the received SINR.

Table 1.2: Measurement results.

scheme noPC PC

Average power (dBm) -12.9 -3.4 1.1 7.1 -1FER 0.6856 0.1700 0.0528 0.0561 0.0071BER 0.0815 0.0124 0.0020 0.0030 2.2× 10−4

Average SINR (dB) 10.9 20 24.3 26.7 18.5

Paper C: Optimal power allocation for pilot-assisted interferencealignment in MIMO interference networks: Test-bed results [41]In this paper, we investigate the problem of optimal power allocation for trainingand data symbols in an OFDM-MIMO interference network, where spatial inter-ference alignment is used to manage the inter-user interference. Then, we use KTHfourmulti testbed (see section 1.1.8) to experimentally validate our theoretical re-sults.

Background

In an interference network, several transmitters communicate with their intendedreceivers while at the same time they may cause interference to the non-intendedreceivers. Therefore the transmitters need to coordinate their transmissions in orderto provide a reliable communication link. Interference alignment has been proposed

1.2. Problem II 27

as an interference management technique [54] where by using a linear precoder ateach transmitter, the received interferences are aligned into a subspace indepen-dent from the desired signal subspace. Hence, the interference-free signals can beextracted using linear filters at the receivers.

The successful performance of interference alignment depends heavily on thequality of the available instantaneous CSI at the terminals. The terminals transmitpilot symbols within each coherence time of the channel to acquire the CSI. How-ever, in practice due to the varying nature of channels and the limited availableresources in the network, only a noisy version of CSI can be estimated. The impactof the noisy CSI on the performance of interference alignment in a narrow-bandMIMO interference network has been studied in [55,56] where a large performancegap due to uncertainty in the CSI has been reported.

In the pilot-assisted interference alignment, part of the network resources, i.e.,time, frequency and power, are allocated for CSI acquisition. However, in practicalscenarios, the amount of resources in a network is limited and therefore there isa trade-off between the amount of resources used for pilot transmission and theones exploited for data transmission. The problem of finding the optimal resourceallocation scheme for interference alignment has been investigated in a narrow-bandsingle-input single-output (SISO) network in [29] and in a narrow-band MIMOnetwork in [35,57].

Countributions

In this paper, we have adapted OFDM modulation, where the pilot symbols andthe data symbols are embedded in different subcarriers of the transmitted OFDMsymbols. In the downlink, the CSI is estimated at the pilot subcarriers (i.e., thesubcarriers which are filled with the pilot symbols) and interpolated for the rest ofsubcarriers. Then the estimated CSI is fed back to the BSs using error-free feedbacklinks.

The interference alignment filters are designed in each subcarrier independentlyfrom the other subcarriers. However, to study the average performance, interferencealignment in one particular subcarrier with average channel estimation error (av-eraged over all the subcarriers) are considered. Then, by fixing the average powerbudget per OFDM symbol, we derive the optimal power allocation scheme to max-imize the achievable sum-rate of the network.

In order to validate our theoretical results, we have implemented a pilot-basedinterference alignment on KTH fourmulti testbed, where OFDM symbols with 38subcarriers are used for pilot and data transmission (2 pilot subcarriers per OFDMsymbol). In this implementation we have used an iterative approach called MinILalgorithm [50] to design the precoders and combiners. In addition to that we havealso implemented MaxSINR algorithm [50] for the sake of comparison.

Figure 1.14 represents simulation results as well as the results of measurementsperformed on KTH fourmulti. In this figure, β is the power of a data subcarriernormalized to the average power of a subcarrier. As the performance metric, we

28 Introduction

0 0.2 0.4 0.6 0.8 10

50

100

150

200

β

EVM

(%)

SimulationMinILMax-SINR

Figure 1.14: The EVM measurements for different power allocation schemes.

measure EVM at the receivers which is inversely proportional to the square root ofSINR. All the three curves plotted in the figure, are minimized at β ≈ 0.8 whichconfirms the theoretical results of this paper.

1.2.3 Problem III: Hardware Impairments in MultiantennaCellular Systems

Paper D: Correlation of Distortion Noise Between the Branchesof MIMO Transmit Antennas [42]

A multiantenna transmitter with hardware impairments is considered in this pa-per. In particular, the distortion of the transmitted signal due to the nonlinearcharacteristics of the transmit RF-chains is investigated. Moreover, the spatial cor-relation of the distortion noise generated in different antennas of the transmitter ischaracterized as a function of spatial correlation of the desired transmitted signals.

Background

The widely-used signal processing techniques for the multiantenna systems are de-signed based on the assumption of ideal and linear behavior of the RF components.However, this assumption does not hold in general. Specially, as the future commu-nication systems will be equipped with a large number of antennas [58] and work

1.2. Problem III 29

at high frequencies [3], the performance of the communication systems will be moreaffected by the hardware impairments.

The nonlinear distortion at transmitter is mainly caused by the PAs workingclose to saturation [36]. Conventionally, applying a large back-off from the satura-tion power of a PA has been considered as a solution for decreasing the nonlineardistortion. However, a disadvantage of this solution is that by moving away fromthe saturation, the PAs will work less energy efficiently. The low energy efficiency ofthe PAs not only leads to the waste of power but also increases the heat dissipationin the communication circuits which in turn necessitates spending more energy inthe cooling systems.

When the PAs are biased close to the saturation, the signals with high PAPRare more prone to distortion. Nevertheless, to have a high spectral efficiency, the useof signals with high PAPR in modern communication systems is inevitable. Thisimplies that there will be a trade-off between the energy and spectral efficiency onone side and the distortion generated at the transmitter on the other side. Thistrade-off has been investigated in [38].

The impact of nonlinear PAs on the spectrally efficient OFDM signals have beenstudied in single antenna systems in [59–61] and in multiantenna systems in [15,62].In [15], a general model is proposed for the overall behavior of the residual hard-ware impairments, including phase noise, IQ imbalance and nonlinear distortion inMIMO systems. In this model, the distortion is considered as an additive whitenoise whose power is an increasing function of the desired signal power. Moreover,it is assumed that the distortion noise is Gaussian and independently distributedacross the different antennas of a multiantenna transmitter. This model for the dis-tortion noise has been adopted by several papers to analyze the effects of hardwareimpairments on the spectral efficiency of the wireless networks [62–66], due to itsgenerality and mathematical tractability. However, one major disadvantage of thismodel is that when a particular hardware impairment is dominant in the system,it loses its accuracy.

Contributions

In [62] the independence of the distortion noise across the different antennas of amultiantenna transmitter was concluded based on an assumption that the desiredsignals fed to the transmit antennas are independent. However, the multiplexing anddiversity gains in a multiantenna system are achieved using linear precoders whichlead to the transmission of correlated signals from different antennas. Furthermore,the spectrally efficient signal processing techniques used in multiantenna networks,such as interference alignment and coordinated multipoint (CoMP), work based onintroducing correlation between the signals transmitted from different antennas.

In this paper, we show that in general the assumption on the independence ofthe distortion signals transmitted from different antenna branches of multiantennatransmitter does not hold. Specifically, we derive the correlation of the distortionsignals transmitted from two arbitrary antennas as a function of the desired signals

30 Introduction

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

correlation coefficient of desired signals

correlationcoeffic

ient

ofdistortio

nsig

nals

TheoryMeasured

Figure 1.15: Correlation coefficient of the distortion signals vs. correlation coeffi-cient of the desired signals fed to two arbitrary antenna branches of a multiantennatransmitter.

fed to the corresponding antennas when the PAs in the two branches are follow-ing a third-order polynomial model. Furthermore, we have tested our theoreticalresults by measurements on an antenna branch of KTH fourmulti testbed (see Sec-tion 1.1.8). Figure 1.15 shows the measurement results as well as the simulation ofthe theoretical findings. As the figure suggests there is a good match between themeasurements and our theoretical results.

Paper E: On the Energy Efficiency of MIMO HybridBeamforming for Millimeter Wave Systems with NonlinearPower Amplifiers [43]

In this paper, we study the trade-off between spectral and energy efficiency ina MIMO mmWave system employing nonlinear PAs at the transmitter. We showthat the spatial direction of the distortion signal is affected by beamforming andsubsequently a part of its power will be aligned with the desired signal. Therefore,even in systems equipped with large antenna arrays, where narrow beams can begenerated, distortion is still a limiting factor.

1.2. Problem III 31

Background

A large body of research efforts have been conducted to investigate the impactsof RF hardware impairments on the performance of MIMO systems. While insome of the works, the combined effect of residual hardware impairments is con-sidered [15,51,62–66], some others focus on a particular impairment effect, such asPA nonlinearity [67–69].

A widely-used approach to model the distortion due to the residual hardwareimpairments is to use additive white Gaussian noise (AWGN) signals at differentantenna elements. In this model, it is assumed that the distortion signals are inde-pendent across the different antenna elements. Moreover, the distortion power ateach antenna element is considered to be a (convex) function of the signal power fedto the corresponding antenna branch. This model includes a wide range of hardwareimpairments and yet it is mathematically tractable. Hence it can be used to driveintuitions on the performance of MIMO systems in general. However, the maindisadvantage of this model is that in cases where one of the impairments is domi-nating, the intuitions derived using this model might not be accurate. In particular,this model does not reflect all the characteristics of the distortion generated by thetransmitter’s PAs working close to the saturation due to energy efficiency consid-erations. As [42] implies the spatial direction of the transmitted distortion dependson the spatial direction of the transmitted signal, while in the AWGN model fordistortions, this dependency is not reflected.

In [68–70], the effect of memoryless nonlinear hardware on the system perfor-mance is analyzed. Using a general nonlinearity model for the transmitter RF-chains, [68] suggests an optimal transmit beamforming strategy for MIMO sys-tems. However, the suggested strategy is not practical as the precoders depend onthe transmitted signal and hence need to be designed prior to each channel use.Furthermore, an accurate knowledge about the nonlinearity model of the trans-mitters is needed which makes the design of the precoders even more complicated.In [70], an information theoretic approach is used in order to bound the capacityof a point-to-point single-antenna system, with nonlinearities at both transmittingand receiving sides. In [69], using a polynomial model for the transmitter PAs andfollowing the approach in [15] for modeling the nonlinear distortion, an ergodic ratefor a MIMO system was derived.

Specifically, in the framework of mmWave communications, [71–73] have studiedthe effect of hardware impairments on the performance of a MIMO system. Whilein [71,72], the impact of the hardware impairments is studied mainly using numer-ical simulations, in [73] the distortion signals transmitted in the same direction asthe desired signal are completely ignored for the sake of mathematical tractability.

Contributions

In this paper, we have developed a statistical model for the signal transmittedfrom a multiantenna transmitter with nonlinear RF hardware. This model is de-

32 Introduction

−20 −15 −10 −5 0 5 10 15

20

40

60

Input Power P (dBm)

No.

ofTr

ansm

itan

tenn

asNt

0

0.2

0.4

0.6

0.8

1

Figure 1.16: Energy efficiency of the system in (Gbit/Joul).

rived based on a memoryless polynomial model of arbitrary order for the PAs inthe transmitter and therefore can be considered as a generalization of the modeldeveloped in Paper D. Using the developed model, we found the covariance matrixof the desired signal (i.e., part of the transmitted signal which is linearly amplifiedby the power amplification stage) as well as the one’s of the distortion signal (i.e.,part of the transmitted signal which is uncorrelated with the desired signal). Us-ing the covariance matrices of the signals, we showed that the spatial direction ofthe distortion signal is dependent to the spatial direction of the desired signal andtherefore is affected by the spatial precoding filter.

Using our proposed impairment model, we studied the impact of nonlinear PAson the performance of a mmWave MIMO system, where a hybrid beamformingstructure is exploited for data transmission. By treating the received distortion asnoise, the spectral efficiency of such a system is derived.

Furthermore, we used a realistic model for the power consumption of the PAsto compute the overall energy efficiency of the system, i.e., the amount of energyneeded for conveying one bit of information to the receiver. Although on one handthe distortion power generated by the transmitter increases by pushing the PAstoward their saturation regions, but on the other hand the PAs are operating moreefficiently when they are close to saturation. Figure 1.16 shows the impact of theinput power, P , and the number of transmit antennas, Nt, on the energy efficiencyof the system. As the figure implies when Nt is large, increasing P degrades theenergy efficiency of the system, while with the small Nt, by increasing the powerwe can still achieve a good performance.

The trade-off between the spectral and energy efficiency for the transmitter

1.2. Problem III 33

0 1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

1.2

Spectral Efficiency (bits/sec/Hz)

Energy

Effic

ienc

y(G

bits/J

oul) Nt = 4

Nt = 8Nt = 16Nt = 32Nt = 64

Figure 1.17: Energy efficiency vs. spectral efficiency. The input power, P , increasesin the direction of arrows.

with various number of antennas is also illustrated in Figure 1.17. This figure showsthat although the maximum spectral efficiency increases by increasing Nt but themaximum energy efficiency of the system remains unaffected.

34 Introduction

1.3 Conclusions

Multiantenna communications as enabler of the future cellular systems, which needto support a large number of users with a high wireless data demand, are subject toseveral impairments and practical challenges. The aim of this thesis is to investigatethese practical challenges and analyze the impact of these impairments on theperformance of the multiantenna systems. Specifically, three major challenges areaddressed in this thesis: 1) acquiring CSI in systems with large number of antennas,2) interference management in practical multiantenna systems, and 3) performancedegradation due to imperfect RF hardware.

In a single-cell multiuser MIMO system, we showed that the potentials of mul-tiantenna UEs, compliant with existing and emerging wireless standards, can beexploited to improve the overall performance of the system significantly. In partic-ular, a simple spatial pilot precoding and combining approach was suggested. Usingthis approach, it was shown that the problems associated with massive MIMO sys-tems such as scalability, pilot contamination, FDD transmission, poor pilot SNR inthe uplink, and imbalance coverage of pilot and data signals can be resolved. Byformulating bounds on the normalized channel estimation error, the gains of pilotprecoding and pilot combining were characterized. Moreover, using numerical anal-ysis, the sum-rate performance of the proposed approach was studied and shown tosignificantly outperform the conventional approach where neither pilot precodingnor combining was employed.

To investigate the practicality of the theoretically outstanding interference align-ment technique, we implemented several iterative interference management algo-rithms in the context of interference alignment on a multiuser MIMO testbed. Byperforming measurements on the testbed, we showed that joint interference align-ment and power control can be used to guarantee fixed rate communication betweenthe BSs and UEs in a multicell system. Moreover, we showed that by fixing the tar-get received SINR at each user, a large gain in the transmit power can be obtainedwhile the BER is kept at an acceptable level. Furthermore, we found the optimalpower allocation scheme for data and pilot symbols for a MIMO cellular systememploying interference alignment. Then, we verified our suggested scheme usingmeasurements on the testbed.

Finally, we propose a novel statistical model for the nonlinear distortion signalgenerated in a multiantenna transmitter due to the RF hardware impairments.This model shows that the spatial direction of the distortion signal is dependentto the spatial direction of the desired signal and consequently will be affected bybeamforming. Then, we verify this model by measurements on a transmit antennabranch. Using the proposed model, we investigate the spectral efficiency and energyefficiency of a MIMO mmWave system. Furthermore, we formulate an optimizationproblem for finding the optimal beamforming scheme in a hybrid beamformingscenario. We also formulate an equivalent problem for the case when only analogbeamforming is applied and find its closed-form solution. We conclude that in thissetup, increasing the number of transmit antennas not always reduces the impact of

1.3. Conclusions 35

hardware impairments but might also lead to lower energy efficiency of the system.

References

[1] Cisco, “Cisco visual networking index: Global mobile data traffic forecast up-date,” Tech. Rep., 2017.

[2] Ericsson, “Traffic and market data report,” Tech. Rep., 2016.

[3] S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter-wave cellular wirelessnetworks: Potentials and challenges,” Proc. IEEE, vol. 102, no. 3, pp. 366–385,Mar. 2014.

[4] T. S. Rappaport, J. N. Murdock, and F. Gutierrez, “State of the art in 60-GHz integrated circuits and systems for wireless communications,” Proc. IEEE,vol. 99, no. 8, pp. 1390–1436, Aug 2011.

[5] Z. Pi and F. Khan, “An introduction to millimeter-wave mobile broadbandsystems,” IEEE Commun. Mag., vol. 49, no. 6, pp. 101–107, Jun. 2011.

[6] (2014, Oct.) Use of spectrum bands above 24 GHz for mobile radio services.Federal Communications Commission. [Online]. Available: https://www.fcc.gov/document/noi-examine-use-bands-above-24-ghz-mobile-broadband

[7] A. L. Swindlehurst, E. Ayanoglu, P. Heydari, and F. Capolino, “Millimeter-wave massive MIMO: the next wireless revolution?” IEEE CommunicationsMagazine, vol. 52, no. 9, pp. 56–62, Sep. 2014.

[8] E. Bjornson, M. Bengtsson, and B. Ottersten, “Optimal multiuser transmitbeamforming: A difficult problem with a simple solution structure [lecturenotes],” IEEE Signal. Proc. Mag., vol. 31, no. 4, pp. 142–148, July 2014.

[9] B. Hassibi and B. Hochwald, “How much training is needed in multiple-antennawireless links?” IEEE Trans. Inf. Theory, vol. 49, no. 4, pp. 951–963, Apr. 2003.

[10] M. Biguesh and A. B. Gershman, “Training-based MIMO channel estimation: astudy of estimator tradeoffs and optimal training signals,” IEEE Trans. SignalProcess., vol. 54, no. 3, pp. 884–893, March 2006.

[11] E. Bjornson and B. Ottersten, “A framework for training-based estimation inarbitrarily correlated Rician MIMO channels with rician disturbance,” IEEETrans. Signal Process., vol. 58, no. 3, pp. 1807–1820, Mar. 2010.

37

38 References

[12] G. Fodor, P. D. Marco, and M. Telek, “On the impact of antenna correla-tion and CSI errors on the pilot-to-data power ratio,” IEEE Trans. Commun.,vol. 64, no. 6, pp. 2622–2633, Jun. 2016.

[13] M. A. Maddah-Ali, A. S. Motahari, and A. K. Khandani, “Communication overMIMO X channels: Interference alignment, decomposition, and performanceanalysis,” IEEE Trans. Inf. Theory, vol. 54, no. 8, pp. 3457–3470, Aug. 2008.

[14] V. R. Cadambe and S. A. Jafar, “Interference alignment and degrees of freedomof the K-user interference channel,” IEEE Trans. Inf. Theory, vol. 54, no. 8,pp. 3425–3441, Aug. 2008.

[15] T. Schenk, RF imperfections in high-rate wireless systems: impact and digitalcompensation. Springer Science & Business Media, 2008.

[16] N. N. Moghadam, H. Farhadi, P. Zetterberg, M. N. Khormuji, andM. Skoglund, Interference Alignment — Practical Challenges and Test-bed Im-plementation. INTECH Open Access Publisher, Nov. 2014, ch. InterferenceAlignment — Practical Challenges and Test-bed Implementation.

[17] C. M. Yetis, N. N. Moghadam, J. Fanjul, H. Farhadi, and J. A. Garcia-Naya,“Interference alignment testbed,” submitted to IEEE Commun. Mag., underrevision (minor).

[18] G. J. Foschini, “Layered space-time architecture for wireless communication ina fading environment when using multi-element antennas,” Bell Labs TechnicalJournal, vol. 1, no. 2, pp. 41–59, Autumn 1996.

[19] E. Telatar, “Capacity of multi-antenna gaussian channels,” European Trans-actions on Telecommunications, vol. 10, no. 6, pp. 585–595, 1999.

[20] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cam-bridge University Press, 2005.

[21] H. Krim and M. Viberg, “Two decades of array signal processing research: theparametric approach,” IEEE Signal. Proc. Mag., vol. 13, no. 4, pp. 67–94, Jul.1996.

[22] A. B. Gershman, N. D. Sidiropoulos, S. Shahbazpanahi, M. Bengtsson, andB. Ottersten, “Convex optimization-based beamforming,” IEEE Signal. Proc.Mag., vol. 27, no. 3, pp. 62–75, May 2010.

[23] T. L. Marzetta, “Noncooperative cellular wireless with unlimited numbers ofbase station antennas,” IEEE Trans. Wireless Commun., vol. 9, no. 11, pp.3590–3600, Nov. 2010.

[24] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors,and F. Tufvesson, “Scaling up MIMO: Opportunities and challenges with verylarge arrays,” IEEE Signal. Proc. Mag., vol. 30, no. 1, pp. 40–60, Jan. 2013.

References 39

[25] H. Maleki, S. A. Jafar, and S. Shamai, “Retrospective interference alignmentover interference networks,” IEEE J. Sel. Top. Signal Process., vol. 6, no. 3,pp. 228–240, June 2012.

[26] M. A. Maddah-Ali and D. Tse, “Completely stale transmitter channel stateinformation is still very useful,” IEEE Trans. Inf. Theory, vol. 58, no. 7, pp.4418–4431, July 2012.

[27] M. Shen, A. Host-Madsen, and J. Vidal, “An improved interference alignmentscheme for frequency selective channels,” in Proc. 2008 IEEE InternationalSymposium on Information Theory, July 2008, pp. 559–563.

[28] R. Brandt, P. Zetterberg, and M. Bengtsson, “Interference alignment over acombination of space and frequency,” in Proc. 2013 IEEE International Con-ference on Communications Workshops (ICC), June 2013, pp. 149–153.

[29] H. Farhadi, M. N. Khormuji, and M. Skoglund, “Pilot-assisted ergodic inter-ference alignment for wireless networks,” in Proc. Speech and Signal Processing(ICASSP) 2014 IEEE Int. Conf. Acoustics, May 2014, pp. 6186–6190.

[30] C. Lameiro, s. González, J. A. García-Naya, I. Santamaría, and L. Castedo,“Experimental evaluation of interference alignment for broadband WLAN sys-tems,” EURASIP Journal on Wireless Communications and Networking, vol.2015, no. 1, p. 1, Jun. 2015.

[31] S. Gollakota, S. D. Perli, and D. Katabi, “Interference alignment and cancel-lation,” SIGCOMM Comput. Commun. Rev., vol. 39, no. 4, pp. 159–170, Aug.2009.

[32] J. Fanjul, C. Lameiro, I. Santamaria, J. A. García-Naya, and L. Castedo, “Anexperimental evaluation of broadband spatial IA for uncoordinated MIMO-OFDM systems,” in 2015 IEEE International Conference on Digital SignalProcessing (DSP), July 2015, pp. 570–574.

[33] S. Lee, A. Gerstlauer, and R. W. Heath, “Distributed real-time implementationof interference alignment with analog feedback,” IEEE Trans. Veh. Technol.,vol. 64, no. 8, pp. 3513–3525, Aug 2015.

[34] P. Zetterberg, “Interference alignment (IA) and coordinated multi-point(CoMP) with IEEE802.11AC feedback compression: Testbed results,” in Proc.2014 IEEE International Conference on Acoustics, Speech and Signal Process-ing (ICASSP), May 2014, pp. 6176–6180.

[35] O. E. Ayach, A. Lozano, and R. W. Heath, “On the overhead of interferencealignment: Training, feedback, and cooperation,” IEEE Trans. Wireless Com-mun., vol. 11, no. 11, pp. 4192–4203, Nov. 2012.

40 References

[36] F. M. Ghannouchi and O. Hammi, “Behavioral modeling and predistortion,”IEEE Microwave Mag., vol. 10, no. 7, pp. 52–64, Dec. 2009.

[37] F. H. Raab, P. Asbeck, S. Cripps, P. B. Kenington, Z. B. Popovic, N. Pothecary,J. F. Sevic, and N. O. Sokal, “Power amplifiers and transmitters for RF andmicrowave,” IEEE Trans. Microwave Theory Tech., vol. 50, no. 3, pp. 814–826,Mar. 2002.

[38] H. Ochiai, “An analysis of band-limited communication systems from amplifierefficiency and distortion perspective,” IEEE Trans. Commun., vol. 61, no. 4,pp. 1460–1472, Apr. 2013.

[39] N. N. Moghadam, H. Shokri-Ghadikolaei, G. Fodor, M. Bengtsson, and C. Fis-chione, “Pilot precoding and combining in multiuser MIMO networks,” IEEEJ. Sel. Areas Commun., vol. 35, no. 6, June 2017.

[40] N. N. Moghadam, H. Farhadi, P. Zetterberg, and M. Skoglund, “Test-bedimplementation of iterative interference alignment and power control for wire-less MIMO interference networks,” in Proc. IEEE 15th Int. Workshop SignalProcessing Advances in Wireless Communications (SPAWC), Jun. 2014, pp.239–243.

[41] N. N. Moghadam, H. Farhadi, and P. Zetterberg, “Optimal power allocationfor pilot-assisted interference alignment in MIMO interference networks: Test-bed results,” in Proc. IEEE Int. Conf. Digital Signal Processing (DSP), Jul.2015, pp. 585–589.

[42] N. N. Moghadam, P. Zetterberg, P. Handel, and H. Hjalmarsson, “Correlationof distortion noise between the branches of MIMO transmit antennas,” in Proc.Indoor and Mobile Radio Communications - (PIMRC) 2012 IEEE 23rd Int.Symp. Personal, Sep. 2012, pp. 2079–2084.

[43] N. N. Moghadam, G. Fodor, M. Bengtsson, and D. J. Love, “On the energyefficiency of MIMO hybrid beamforming for millimeter wave systems withnonlinear power amplifiers,” to be submitted to IEEE Trans. Wireless Commun.

[44] G. Foschini and M. Gans, “On limits of wireless communications in a fading en-vironment when using multiple antennas,” Wireless personal communications,vol. 6, no. 3, pp. 311–335, 1998.

[45] H. Shokri-Ghadikolaei, L. Gkatzikis, and C. Fischione, “Beam-searching andtransmission scheduling in millimeter wave communications,” in Proc. IEEEInt. Conf. Communications (ICC), Jun. 2015, pp. 1292–1297.

[46] J. Jose, A. Ashikhmin, T. L. Marzetta, and S. Vishwanath, “Pilot contamina-tion problem in multi-cell tdd systems,” in Proc. IEEE Int. Symp. InformationTheory, Jun. 2009, pp. 2184–2188.

References 41

[47] S. Sesia, M. Baker, and I. Toufik, LTE-the UMTS long term evolution: fromtheory to practice. John Wiley & Sons, 2011.

[48] V. B. Yerrabommanahalli, P. H. Vashi, and A.-M. Al-Khudairi, “Methods andapparatus for radio link imbalance compensation,” Patent US20 140 051 449A1, 2016.

[49] O. E. Ayach, S. W. Peters, and R. W. Heath, “The practical challenges ofinterference alignment,” IEEE Wireless Commun., vol. 20, no. 1, pp. 35–42,Feb. 2013.

[50] K. Gomadam, V. R. Cadambe, and S. A. Jafar, “A distributed numericalapproach to interference alignment and applications to wireless interferencenetworks,” IEEE Trans. Inf. Theory, vol. 57, no. 6, pp. 3309–3322, Jun. 2011.

[51] R. Brandt, E. Bjornson, and M. Bengtsson, “Weighted sum rate optimizationfor multicell MIMO systems with hardware-impaired transceivers,” in Proc.Acoustics, Speech and Signal Processing (ICASSP) 2014 IEEE InternationalConference on, May 2014, pp. 479–483.

[52] H. Farhadi, C. Wang, and M. Skoglund, “Distributed interference alignmentand power control for wireless MIMO interference networks,” in Proc. IEEEWireless Communications and Networking Conf. (WCNC), Apr. 2013, pp.3077–3082.

[53] H. Farhadi, A. A. Zaidi, C. Fischione, C. Wang, and M. Skoglund, “Distributedinterference alignment and power control for wireless MIMO interference net-works with noisy channel state information,” in Proc. First Int. Black SeaConf. Communications and Networking (BlackSeaCom), Jul. 2013, pp. 23–27.

[54] V. R. Cadambe and S. A. Jafar, “Interference alignment and the degrees offreedom of wireless X networks,” IEEE Trans. Inf. Theory, vol. 55, no. 9, pp.3893–3908, Sep. 2009.

[55] B. Xie, Y. Li, H. Minn, and A. Nosratinia, “Adaptive interference alignmentwith CSI uncertainty,” IEEE Trans. Commun., vol. 61, no. 2, pp. 792–801,Feb. 2013.

[56] R. Tresch and M. Guillaud, “Cellular interference alignment with imperfectchannel knowledge,” in Proc. IEEE Int. Conf. Communications Workshops,Jun. 2009, pp. 1–5.

[57] R. K. Mungara, G. George, and A. Lozano, “Overhead and spectral efficiency ofpilot-assisted interference alignment in time-selective fading channels,” IEEETrans. Wireless Commun., vol. 13, no. 9, pp. 4884–4895, Sep. 2014.

42 References

[58] E. G. Larsson, O. Edfors, F. Tufvesson, and T. L. Marzetta, “Massive MIMOfor next generation wireless systems,” IEEE Commun. Mag., vol. 52, no. 2,pp. 186–195, Feb. 2014.

[59] E. Costa, M. Midrio, and S. Pupolin, “Impact of amplifier nonlinearities onOFDM transmission system performance,” IEEE Commun. Lett., vol. 3, no. 2,pp. 37–39, Feb. 1999.

[60] D. Dardari, V. Tralli, and A. Vaccari, “A theoretical characterization of non-linear distortion effects in OFDM systems,” IEEE Trans. Commun., vol. 48,no. 10, pp. 1755–1764, Oct. 2000.

[61] P. Banelli and S. Cacopardi, “Theoretical analysis and performance of OFDMsignals in nonlinear AWGN channels,” IEEE Trans. Commun., vol. 48, no. 3,pp. 430–441, Mar. 2000.

[62] C. Studer, M. Wenk, and A. Burg, “MIMO transmission with residualtransmit-RF impairments,” in Proc. Int. ITG Workshop Smart Antennas(WSA), Feb. 2010, pp. 189–196.

[63] ——, “System-level implications of residual transmit-RF impairments inMIMO systems,” in Proc. 5th European Conf. Antennas and Propagation (EU-CAP), Apr. 2011, pp. 2686–2689.

[64] E. Bjornson, P. Zetterberg, and M. Bengtsson, “Optimal coordinated beam-forming in the multicell downlink with transceiver impairments,” in Proc.IEEE Global Communications Conf. (GLOBECOM), Dec. 2012, pp. 4775–4780.

[65] E. Bjornson, P. Zetterberg, M. Bengtsson, and B. Ottersten, “Capacity lim-its and multiplexing gains of MIMO channels with transceiver impairments,”IEEE Commun. Lett., vol. 17, no. 1, pp. 91–94, Jan. 2013.

[66] E. Bjornson, J. Hoydis, M. Kountouris, and M. Debbah, “Massive MIMO sys-tems with non-ideal hardware: Energy efficiency, estimation, and capacity lim-its,” IEEE Trans. Inf. Theory, vol. 60, no. 11, pp. 7112–7139, Nov. 2014.

[67] J. Qi and S. Aissa, “Analysis and compensation of power amplifier nonlinearityin MIMO transmit diversity systems,” IEEE Trans. Veh. Technol., vol. 59,no. 6, pp. 2921–2931, July 2010.

[68] ——, “On the power amplifier nonlinearity in MIMO transmit beamformingsystems,” IEEE Trans. Commun., vol. 60, no. 3, pp. 876–887, March 2012.

[69] M. Fozooni, M. Matthaiou, E. Bjornson, and T. Q. Duong, “Performance limitsof MIMO systems with nonlinear power amplifiers,” in Proc. 2015 IEEE GlobalCommunications Conference (GLOBECOM), Dec 2015, pp. 1–7.

References 43

[70] M. Sabbaghian, A. I. Sulyman, and V. Tarokh, “Analysis of the impact ofnonlinearity on the capacity of communication channels,” IEEE Trans. Inf.Theory, vol. 59, no. 11, pp. 7671–7683, Nov 2013.

[71] M. Wu, D. Wuebben, A. Dekorsy, P. Baracca, V. Braun, and H. Halbauer,“Hardware impairments in millimeter wave communications using OFDM andSC-FDE,” in Proc. Smart Antennas (WSA), 2016 International ITG Workshopon, March 2016, pp. 1–8.

[72] A. Khansefid, H. Minn, Q. Zhan, N. Al-Dhahir, H. Huang, and X. Du, “Wave-form parameter design and comparisons for millimeter-wave massive MIMOsystems with RF distortions,” in Proc. IEEE Globecom Workshops (GC Wk-shps), Dec 2016, pp. 1–6.

[73] H. Yan and D. Cabric, “Digital predistortion for hybrid precoding architecturein millimeter-wave massive MIMO systems,” in Proc. 42nd IEEE Int. Conf.on Acoustics, Speech and Signal Process. (ICASSP), Mar. 2017.