RF Imperfections in High-rate Wireless Systems

The Netherlands

by

RF Imperfections in High-rateWireless Systems

Impact and Digital Compensation

Tim SchenkPhilips Research, Eindhoven

ABC

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Contents

Foreword xiPreface xiii

1. INTRODUCTION 1

1.1 Wireless communications 1

1.2 OFDM 3

1.3 MIMO 4

1.4 RF transceiver impairments 6

1.5 Outline of the book 9

2. MULTIPLE-ANTENNA OFDM SYSTEMS 11

2.1 Introduction 11

2.2 Channel modelling 112.2.1 Multipath propagation 122.2.2 Stochastic channel model 16

2.3 System modelling 182.3.1 MIMO 192.3.2 OFDM 222.3.3 MIMO OFDM 26

2.4 Conclusions 29

3. DESIGN AND IMPLEMENTATION OF A MIMO OFDMSYSTEM 31

3.1 Introduction 31

3.2 Transmission format and preamble design 323.2.1 IEEE 802.11a 323.2.2 MIMO OFDM 34

vi Contents

3.3 Frequency synchronisation 393.3.1 Influence of CFO 403.3.2 Algorithm description 423.3.3 Performance analysis 443.3.4 Numerical results 473.3.5 Summary 51

3.4 Channel estimation 523.4.1 Algorithm and performance analysis 523.4.2 Numerical results 583.4.3 Summary 62

3.5 Timing synchronisation 623.5.1 System description 633.5.2 Algorithm description 663.5.3 Numerical results 683.5.4 Summary and discussion 72

3.6 Multiple-antenna OFDM system implementation 733.6.1 Test system description 733.6.2 Baseband design 743.6.3 Measurement results 763.6.4 Comparison with simulation results 79

3.7 Conclusions 81

4. PHASE NOISE 83

4.1 Introduction 83

4.2 System and phase noise modelling 844.2.1 Oscillator modelling 854.2.2 Influence on signal model 88

4.3 Impact and distribution of the ICI term 914.3.1 System model 914.3.2 Bit-error probabilities 944.3.3 Properties of the ICI term 954.3.4 Simulation results 1044.3.5 Summary 107

4.4 ICI-caused error term in MIMO OFDM 1084.4.1 Transmitter phase noise 1094.4.2 Receiver phase noise 110

Contents vii

4.4.3 Phase noise process 1124.4.4 Numerical results 1134.4.5 Summary and discussion 116

4.5 Compensation of the CPE 1174.5.1 Maximum-likelihood estimator 1174.5.2 MLE optimisation algorithm 1194.5.3 Sub-optimal estimator 1214.5.4 Cramer-Rao lower bound 1224.5.5 Numerical results 1244.5.6 Summary 130

4.6 Compensation of the ICI 1304.6.1 Suppression algorithm 1314.6.2 Numerical results 1344.6.3 Summary 136

4.7 Conclusions 137

5. IQ IMBALANCE 1395.1 Introduction 1395.2 System and IQ imbalance modelling 140

5.2.1 TX/RX front-end architecture 1415.2.2 IQ mismatch 1435.2.3 Influence on MIMO signal model 1455.2.4 RX filter imbalance 148

5.3 Impact of IQ imbalance on system performance 1505.3.1 Error in symbol detection 1505.3.2 Probability of erroneous detection

for M -QAM 1525.3.3 Numerical results 1595.3.4 Summary and discussion 163

5.4 Preamble based estimation and mitigation 1635.4.1 Preamble design 1645.4.2 TX IQ imbalance estimation 1665.4.3 RX IQ imbalance estimation 1675.4.4 TX and RX IQ imbalance estimation 1685.4.5 Iterative TX and RX IQ imbalance estimation 1705.4.6 Numerical results 1725.4.7 Summary 177

viii Contents

5.5 Decision-directed mitigation 1785.5.1 Adaptive filter based algorithm 1785.5.2 Numerical results 180

5.6 Conclusions 182

6. NONLINEARITIES 1856.1 Introduction 1856.2 System and nonlinearities modelling 187

6.2.1 Nonlinearity modelling 1876.2.2 Influence on signal model 192

6.3 Impact of nonlinearities on system performance 1956.3.1 TX nonlinearities 1966.3.2 RX nonlinearities 2016.3.3 Numerical results 2036.3.4 Summary and discussion 207

6.4 PAPR reduction by spatial shifting 2086.4.1 Signal modelling 2096.4.2 Spatial shifting 2106.4.3 Combining SS and PS 2116.4.4 Subcarrier grouping schemes 2136.4.5 Side information/Transparency 2136.4.6 Numerical results 2156.4.7 Summary and discussion 217

6.5 RX-based correction of nonlinearities 2196.5.1 Baseband amplitude clipping 2206.5.2 Estimation of linear and nonlinear channel 2216.5.3 Postdistortion 2306.5.4 Iterative distortion removal 2316.5.5 Simulation results 2336.5.6 Summary 242

6.6 Conclusions 242

7. A GENERALISED ERROR MODEL 2457.1 Introduction 2457.2 Error model 246

7.2.1 TX and RX impairment model 2477.2.2 Mapping of RF impairments 2487.2.3 Nonstationarity of the impairments 2507.2.4 Transmission structure 252

Contents ix

7.3 Performance evaluation 2527.3.1 Preamble phase 2537.3.2 Data phase 2537.3.3 Probability of error 254

7.4 Numerical results 2577.5 Conclusions 261

8. DISCUSSION AND CONCLUSIONS 2638.1 Summary and conclusions 263

8.1.1 Synchronisation for MIMO OFDM systems 2648.1.2 Multiple-antenna OFDM proof of concept 2658.1.3 Behavioural RF impairment modelling 2658.1.4 Performance impact of front-end imperfections 2668.1.5 Mitigation approaches for RF impairments 2678.1.6 A generalised error model 269

8.2 Scope of future research 2708.2.1 Influence of RF impairments 2708.2.2 Mitigation approaches 2718.2.3 Towards mm-wave systems 272

Glossary 275

Appendices 281A MSE in CFO estimation 281B MSE in channel estimation 283

B.1 MSE in linear channel interpolation 283B.2 MSE in linear channel extrapolation 284

C Measurement setup 287C.1 Baseband 287C.2 IF stages 289C.3 Antennas 290

D Proof of Theorem 4.1 291E Orthonormal polynomial basis 299

References 301

Index 315

Foreword

This book takes a modern, multidisciplinary view on radio system de-sign: the advantages of digital signal processing are exploited to satisfythe ever increasing demands on better performing, flexible radio fre-quency (RF) circuits. By accepting that analog circuits are inherentlyimperfect, but by searching for methods to mitigate and compensate forthis, significant steps can be made to improve the overall system solu-tion. This is in contrast to the more traditional approach of designingRF circuits themselves to satisfy the demanding specifications set bycurrent standards.

Wireless communication has progressed dramatically in past years.Yet, the main research challenges changed focus to sustain this growthover many decades. In the early days, the main challenge of radio com-munications was to cover large distances. When in late 1980s, digitalmobile communication emerged as a precursor to today’s mass-marketcell phones, the priority shifted to achieving reliable communicationover a difficult, i.e., time-varying and frequency-selective mobile chan-nel. About a decade or research in many institutes around the worldhas been devoted to this challenge, exploiting the opportunities givenby increasing computational power in digital circuits. Today we face adifferent paradigm: the technology for analog front-ends progress signif-icantly slower than that of digital processors. So the imperfections ofthe RF have increasingly become the major bottleneck in our drive to-wards faster, yet more power-efficient radio circuits. Since digital signalprocessing can mitigate the design constraints for analog RF circuits,it allows more cost-effective and lower power consuming designs for theanalog part.

At the time of writing this book, algorithms for digital compensation,or digitally controlled calibration of the RF circuits start to be usedin chipsets in the market. But the concepts addressed in this book

xii Foreword

may not be limited to only offering a proprietary advantage to smartimplementers. It is not unlikely that future standards will increasinglybe designed to anticipate for digital RF compensation, for instance bydefining new preambles or pilots that also allow receivers to track phasedrifts, or to estimate I-Q imbalance.

An important step made in this book is to bring together models de-scribing analog circuits with insights of digital signal processing. Tracta-ble but realistic models to evaluate the effect of compensation measuresare essential to support the design of effective practical solutions. Rightfrom the start the book follows a timely approach that coincides withclear direction taken in many modern systems, namely the use of mul-tiple antennas to accommodate more radio traffic, to offer better linkthroughput, and to reduce interference.

Prof. Dr. Ir. Jean-Paul M.G. LinnartzSenior Director, Connectivity Systems and Networks, Philips ResearchProfessor, Eindhoven University of Technology

Preface

Wireless connectivity has truly become ubiquitous over the last fewyears, as can be concluded from the increasing number of electronic de-vices that are being equipped with wireless communication capabilities.While several years ago the application of wireless was largely limitedto mobile and portable telephones, the application range has currentlybeen extended to a wide variety of consumer lifestyle areas. Examplesof new products currently being equipped with wireless connectivity so-lutions are music players, game consoles, streaming audio and videosolutions, computer peripherals and cameras. This causes wireless sys-tems to move towards the commodity markets, where price pressure ishigh. This creates a drive for low-cost solutions.

In parallel, there is a persistent demand for increasing performance ofwireless solutions, since the same throughput and quality of service aredemanded as that of the wired solutions they are replacing. To meetthese requirements, wireless communication systems are continuouslyapplying wider bandwidths, larger signal dynamics and higher carrierfrequencies. This results in an ever increasing demand on the perfor-mance of radio frequency (RF) front-ends, which at the same time haveto be low-cost and power-efficient. Since the RF technology is, conse-quently, pushed to its operation boundaries, the intrinsic imperfectionsof the RF IC technology are more and more governing the system per-formance of wireless modems.

ScopeThis book, therefore, presents a new vision on the design of wirelesscommunication systems. It is motivated by the continuous functionalscaling of digital IC technology, which allows for more and more func-tionality on a limited chip area. The presented approach is based ondigital compensation algorithms for the RF impairments, which relieve

xiv Preface

the specifications of the analogue front-end ICs, at the cost of only alimited increase in area of the digital baseband IC.

To illustrate this approach, the book focuses on multiple-antenna or-thogonal frequency division multiplexing (MIMO OFDM), which will beapplied as the basis for the majority of near-future high-rate wireless sys-tems. First the book introduces the basics of MIMO OFDM and presentsthe typically applied signal processing in implementations of such sys-tems. Subsequently, several RF front-end impairments are treated, in-cluding phase noise, IQ imbalance and nonlinearities. The book presentsbaseband equivalent models for these RF impairments and, to provide anin-depth understanding of their impact, derives analytical performanceresults. These results are then used to design different compensationapproaches based on digital baseband processing.

The book was written for wireless system designers, focussing on base-band and/or analogue front-end design, who want to familiarise with thedigital compensation of RF imperfections. Another goal was to provideresearchers in the field of wireless communications or signal processingan overview of this emerging research topic.

AcknowledgementsMy interest in the topic of RF impairments was initiated in the pe-riod 2001-2002, when I was performing the research for my M.Sc. thesiswithin Agere Systems in Nieuwegein, The Netherlands. There I ob-served several challenges in the development activities of Agere’s wirelesslocal-area-network solutions, which could be attributed to the inherentimperfections of RF front-ends. Many valuable discussions with my col-leagues at Agere and prof. Gert Brusaard resulted in the definition ofa Ph.D. project focussing on digital compensation of RF front-end im-pairments in 2002. This project was carried out within the wirelesssystems research department of Agere Systems and the radio communi-cations chair of the Eindhoven University of Technology (TU/e). I wantto thank prof. Gert Brussaard, Jan Kruys and Bruce Tuch for arrangingfunding and providing the possibility to perform my research in an in-teresting environment. The publications and Ph.D. thesis resulting fromthis project are the basis for this book.

I also thank my supervisors at Agere, dr. Allert van Zelst and dr.Xiao-Jiao Tao, and my supervisors at TU/e, dr. Peter Smulders andprof. Erik Fledderus, for the inspiring cooperation and their feedbackon previous versions of the texts incorporated in this book. Parts of thework presented in this book resulted from valuable cooperations withBas Driesen, Isabella Modonesi, Paul Mattheijssen, dr. Guido Dolmans,

Preface xv

prof. Remco van der Hofstad, Cedric Dehos and dr. Dominique Morche.Their contributions are highly appreciated.

Furthermore, I would like to acknowledge prof. Heidi Steendam, prof.Jaap Haartsen, prof. Remco van der Hofstad, prof. Leo Ligthart andHaibing Yang for their thorough reviews of my Ph.D. thesis, which wasused as the basis for this book. I thank prof. Jean-Paul Linnartz forstimulating me to consider publishing this work as a book and for writingthe foreword.

The contributions, support and feedback of many colleagues at Agereand TU/e were greatly appreciated. Also, I acknowledge the support ofmy colleagues at Philips Research, which helped me to finish this book.

Tim Schenk

Chapter 1

INTRODUCTION

1.1 Wireless communicationsThe unguided transmission of information using electromagnetic waves

at radio frequency (RF) is often referred to as wireless communications,the first demonstration of which took place at the end of the 19th cen-tury and is attributed to Hertz. The technology was, shortly thereafter,commercialised by, amongst others, Marconi in one of the first wire-less communication systems, i.e., wireless telegraphy. In the first half ofthe 20th century the technology was developed further to enable morethan the mere transmission of Morse code. This first resulted in uni-directional radio broadcasting and several years later also in televisionbroadcasting.

The research into, and development of, bi-directional wireless commu-nication systems was during, and shortly after, the Second World Warmainly fuelled by police and military applications. In the 1940s and1950s the first commercial two-way communications products were in-troduced, including the popular Citizens’ Band radio. It took, however,until the 1970s for mobile cellular communications to be commerciallydeployed. While first deployed as car-phone networks, due to the sizeof terminals, they were in ten years converted into networks with realportable handhelds. The popularity of these analogue systems, oftenreferred to as first generation (1G), was quickly surpassed with the in-troduction of digital communication systems, like GSM (global standardfor mobile communications), in the 1990s [1].

The success of second generation (2G) systems like GSM stirred upresearch and development efforts in the field of digital wireless com-munications. The results of these activities over the last 20 years can

2 1 Introduction

10 kb/s 100 kb/s 1 Mb/s 10 Mb/s 100 Mb/s 1 Gb/s

ZigBee BluetoothUWB

MB-OFDM

IEEE 802.11b 11a/g 11n

GSM GPRS EDGE UMTSHSDPA

HSUPA 3G-LTE

DAB DVB-T -T2DVB-H

WiMAX

OFDMMIMO OFDM

802.16d/e

WAN

MAN

LAN

PAN

Broad-

casting

data rate

applicati

on

are

a

Figure 1.1. The wireless communications landscape of today and the near future.

be observed from today’s diverse wireless communications landscape asschematically depicted in Fig. 1.1. This figure sketches, without theintention to be complete, the major wireless communication standardscurrently deployed or to be deployed in the near future. They are orderedby means of their data rate versus the application area. Standards stillunder development are given in dashed lines. The shading is used to indi-cate whether the systems are based on the multicarrier technique orthog-onal frequency division multiplexing (OFDM) or OFDM combined withthe multiple-antenna technique multiple-input multiple-output (MIMO),i.e., MIMO OFDM.

Figure 1.1 shows that the digital broadcasting standards, i.e., digitalaudio broadcasting (DAB) and digital video broadcasting (DVB), areall based on OFDM technology. Currently, standardisation is ongoingfor the next-generation terrestrial DVB (DVB-T2), which should enablethe transmission of multichannel high-definition television (HDTV). Theapplication of MIMO OFDM is considered a likely solution to fulfill thisrequirement [2]. For the mobile wide-area-network (WAN) communica-tions standards, the long-term-evolution of 3G (3G-LTE), which is cur-rently under development, is very likely to be based on MIMO OFDM[3]. For metropolitan-area-networks (MANs) the IEEE 802.16 standardprovides an OFDM-based solution, which is often referred to as WiMAX.The evolution of this standard as IEEE 802.16d/e provides higher data

1.2 OFDM 3

rates, is based on MIMO and OFDM and enables a higher degree ofmobility, so that the application area is shifted towards WAN.

Wireless local-area-networks (LANs), as mainly deployed in office andhome environments, are predominantly based on the OFDM standardIEEE 802.11a/g. This kind of systems is often referred to as Wi-Fi andachieves peak data rates up to 54 Mb/s. A high data rate extension ofWi-Fi is currently being standardised as IEEE 802.11n, which will alsobe based on MIMO OFDM. Also for personal-area-networks (PANs)OFDM is chosen as basis. An ultra wideband (UWB) design based onmulti-band OFDM (MB-OFDM) was recently standardised as ECMA-368 [4] and adopted as the basis for wireless USB systems. MB-OFDM isable to achieve maximum data rates of 480 Mb/s, while future extensionwill be able to achieve at least the double rate [5], for which MIMOOFDM is also considered a natural technology candidate.

Overall, it can be concluded that throughout the application areasOFDM and MIMO are, and will be, forming the basis for high datarate systems. This justifies a careful investigation of systems based onthese techniques, the results of which are presented in this book. First,however, a short introduction of these two communication techniques isgiven in Sections 1.2 and 1.3.

1.2 OFDMOFDM is a special case of frequency-division multiplexing (FDM). In

FDM multiple baseband signals are multiplexed onto multiple carriers tocreate a composite transmission signal. The frequency spectrum of theresulting signal can schematically be depicted as in Fig. 1.2(a). At thereceiver filtering is applied to separate the parallel signals. When a singledata signal is demultiplexed onto the different carriers, these systemsare also referred as multicarrier systems [6, 7]. It can be concludedfrom Fig. 1.2 that the conventional multicarrier technique is not verybandwidth efficient since it has to apply appropriate separation betweenthe signal bands to allow for receiver filtering. Another disadvantage isthat multiple RF carriers are required for up-conversion and multiplecarriers and filters are needed for down-conversion.

Both major drawbacks are solved in OFDM, which generates thedifferent subcarrier signals in an orthogonal way, as a result of whichthe total signal bandwidth is much smaller than for conventional FDM.Hence, the total bandwidth is reduced from B1 to B2, see Fig. 1.2(b),which means more data can be transmitted in the same bandwidth us-ing OFDM. Furthermore, the multicarrier signal can be generated inthe baseband part of the transmitter and the signals are separatedin the baseband part of receiver using the (inverse) discrete Fourier

4 1 Introduction

B1

frequency

(a) Conventional FDM

B2

frequency

(b) OFDM

Figure 1.2. Concept of OFDM.

transformation ((I)DFT) [8]. In that way only one RF carrier is neces-sary for up-conversion and only one RF carrier and one filter for down-conversion.

The technical basics of OFDM are further worked out in Section 2.3.2of this book, which will show the ability of OFDM to deal with multi-path channels. For the definition of the main objectives of this book,it is useful, however, to already mention two major drawbacks of theapplication of OFDM here:

Accurate time/frequency synchronisation is required in OFDM sys-tems to maintain the subcarrier orthogonality; synchronisation errorssignificantly reduce system performance.

The time-domain OFDM signal exhibits a high peak-to-average powerratio (PAPR), which results into a high sensitivity to nonlinearitiesin the transmission chain.

1.3 MIMOMIMO systems are systems that apply multiple antennas at both TX-

and RX-side of the transmission link. The term multiple-input multiple-output refers to the wireless channel which possesses multiple inputs,i.e., the TX antennas, and multiple outputs, i.e., the RX antennas.Basically MIMO applies the spatial dimension to improve performanceand/or data rate of a single-user link, as is schematically depicted inFig. 1.3. The conventional exploitation of the spatial dimension is shownin Fig. 1.3(a), where the different TXs apply the same carrier frequency.Now due to path-loss effects the coverage of one TX is limited to the

1.3 MIMO 5

TX1TX2

TX3

RX1

RX2

RX3

(a) Conventional spatial reuse

TX

RX

(b) MIMO spatial use

Figure 1.3. Concept of MIMO.

sketched cell, in which the corresponding RX is located. By applyingappropriate spatial separation between the different TXs, the differentcommunications links can exist in parallel without interfering each other.This spatial reuse increases the total throughput of the network; in thedepicted case it will be three times higher than the average single-linkrate.

In a MIMO link, as depicted in Fig. 1.3(b), the different TX andRX antennas are all placed in a joint TX and RX terminal, respec-tively. In this case no simultaneous parallel transmissions exist as inFig. 1.3(a), but the different transmissions will interfere with each other(remember that they are applying the same carrier frequency for trans-mission). Consequently, the different RX branches of the RX-terminalwill receive linear combinations of the signals transmitted on the differ-ent TX antennas. When the received signals are independent enough,the transmitted signals can be separated by applying processing to thereceived signals [9]. This independence of the received signals clearly de-pends on the MIMO channel, which can achieve this requirement whenthere exist different propagation paths between the different TX-RX an-tenna pairs. In this way, the combination of the MIMO channel and thesignal processing effectively creates spatially parallel transmissions andincreases, next to the network throughput as for conventional spatialreuse, also the link data rate.

Information theoretical research at the end of the 1990s showed thatMIMO can improve the data rate by a factor equal to the minimum ofthe number of TX and RX antennas [10, 11]. With limited bandwidth

6 1 Introduction

allocated to specific wireless applications by regulations, MIMO tech-niques provide the potential to achieve high data rate extensions of pre-viously deployed systems, without allocating new spectrum. Therefore,MIMO has since then grown to be one of the major research areas inwireless communications. The developed MIMO approaches can be ba-sically split into two main groups: space time coding (STC) and spacedivision multiplexing (SDM).

The first is used to increase the coverage area of the wireless net-work or to decrease power consumption of the terminals and was origi-nally proposed in [12, 13]. In STC the codewords are in the transmitterspread over the different TX branches. These systems can work in con-figurations where the TX has more antennas than the RX side. A goodoverview of STC techniques can be found in [14–16].

The second approach, SDM or layered space time, was originallyproposed in [17, 18]. Here increase in link data rate is achieved bytransmitting independent data streams on the different TX branches,which obviously linearly increases the data rate with the number of TXbranches, provided that the rank of the MIMO channel is high enough. Atthe receiver the streams are recovered by appropriate signal processing,a subject to which immense research effort was/is focussed. For thesetechniques to work properly, generally, the number of RX branches hasto be greater than or equal to the number of TX branches. A goodoverview of the different SDM techniques can be found in [14, 16, 19].

The technical basics of MIMO are further worked out in Section 2.3.1of this book. For the definition of the main objectives of this book,it is useful, however, to already mention two major drawbacks of theapplication of MIMO here:

MIMO requires multiple TX/RX branches at both sides of the trans-mission link, which increases the cost of the solution.

Since MIMO is an immature technique, the impact of synchronisationerrors and system imperfections on system performance is largelyunknown.

1.4 RF transceiver impairmentsThe implementation of a wireless communication transceiver based

on the presented MIMO-concept, as depicted schematically in Fig. 1.4,is considered here. The figure depicts the physical layer (PHY) of thesystem, as under investigation in this work, which consist of a basebandsection and multiple RF front-ends and multiple antennas connected tothat. Since the baseband processing is generally digital and the RF front-end processing analogue, they are connected through an analogue-to-

1.4 RF transceiver impairments 7

RF

Front-end 1

RF

Front-end N

Baseband

Section

......

AD

/D

AA

D/D

A

Digital Analogue

Figure 1.4. RF and baseband structure of the PHY of a general MIMO transceiver.

digital/digital-to-analogue (AD/DA) convertor, respectively. The base-band section of the PHY is also connected (in the left of the figure) tothe higher layers, e.g., the medium-access-controller layer (MAC).

The baseband part of the TX creates the modulated signals for trans-mission, which are up-converted to RF and amplified in the analoguefront-end. The RX front-end amplifies and down-converts the signalsto baseband and the digital baseband part performs detection to thereceived signals to retrieve the transmitted signals. Although the signalprocessing in the digital baseband section of the PHY is several ordersmore complex compared to that of the RF front-end, most of the designeffort in system design is required for the RF part. This is explainedby the fact that the front-ends have to operate at frequencies and withdynamic ranges that are several orders higher than that of the base-band part. The difficulty of meeting these boundary conditions makestradeoffs between different performance parameters like power consump-tion, linearity, gain, cost and noise level unavoidable [20]. Furthermore,process/implementation spread in RF integrated circuits (ICs) can belarge, yielding a spread of the performance in the different realisations ofthe same front-end. It is noted that in a MIMO system this can createspread between the different front-ends used in one transceiver.

While currently most wireless consumer products operate at carrierfrequencies of up to 6 GHz, there is an increasing interest in the ap-plication of the mm-wave band for high-speed wireless communicationpurposes [21–23], since several GHz of bandwidth is available around60 GHz for license-free use. Since current low-cost CMOS-based IC tech-nology is enabling operation at these high frequencies, it is likely thatnext generation high speed wireless systems will exploit this frequency

8 1 Introduction

band. The process spread and impairments at these high frequencies,however, are much larger. As such, RF impairments will form a keydesign challenge for this kind of mm-wave systems.

Although the RF front-end can thus greatly influence the system per-formance, it is generally modelled as almost ideal when evaluating theperformance of a communication system. One of the reasons is that theexact modelling and simulation of the RF front-end is extremely involvedand time-consuming. Therefore the influence of the front-ends is mostlymodelled as an additive white Gaussian noise (AWGN) source in the RX.Depending on the design choices, design tradeoffs and process spread,however, other imperfections of the implementation can dominate theperformance of the total system.

It is therefore useful to apply baseband equivalent impairment models,which, instead of modelling the actual RF front-end, characterise the in-fluence of its specific imperfections on the baseband signal. These mod-els are then easily implemented in the baseband system simulation setup,but can also be applied in analytical studies. As such, the models canbe used to derive the performance impact of a specific impairment andto calculate tolerable levels of the imperfections. Furthermore, they canbe used as a basis for the design of digital baseband algorithms, whichcan be applied to compensate for the influence of the RF imperfections.For these behavioural baseband models to be of use for these two pur-poses, it is crucial that they both accurately model the non-idealities andexhibit a minimal number of parameters. A major advantage of thesebehavioural models is that they do not depend on the specific front-enddesign, but do have a direct link with the resulting performance mea-sures of these designs. As such, a wide range of implementations can beevaluated using the same models.

The impact of a certain imperfection depends on the applied transmis-sion technology, i.e., MIMO OFDM in this work. Since several studieswere performed previously focussing on impaired conventional single-input single-output OFDM, conclusions from these studies can be usedto make an informed decision on the key imperfections to be studied fora MIMO OFDM system. The first two major impairments follow fromthe two drawbacks of OFDM mentioned in Section 1.2. First, loss of or-thogonality due to phase noise, which was identified by several authors[24–26] as a major performance degradation factor. Secondly, the highPAPR of the OFDM time-domain signal creates a high performance sen-sitivity to nonlinearities, as identified by several authors [27–29]. Finally,the imbalance between the I and Q path (the real and imaginary signalpath) in the RF front-end, creating limited matching, was identified asa major performance limiting imperfection in several papers [30–32]. In

1.5 Outline of the book 9

MIMO systems, additionally, the parameters of these impairments canvary per TX/RX branch.

Since these RF imperfections exhibit a distinct behaviour, i.e., theydo not merely induce additive white Gaussian RX noise, there is thepossibility to compensate for their influence by means of digital sig-nal processing, as was mentioned above. For that purpose, however,knowledge about the parameters of the impairments has to be gathered,which might require complex algorithms. Although the computationalcomplexity of such algorithms might have been prohibitive before, thecontinuous functional scaling of digital IC technology allows for moreand more functionality on a limited chip area. The digital compensa-tion can be applied to relieve the specifications of the analogue front-endICs, at the cost of only a limited increase in area of the digital basebandIC. Such approaches might especially be promising for system applyinghigh system bandwidths and high carrier frequencies, where the designtradeoffs for the analogue part are more strenuous.

1.5 Outline of the bookSections 1.1 to 1.4 show that MIMO OFDM will be the basis of the

majority of (near) future high data rate wireless communication sys-tems. It is, however, also shown that there are some drawbacks to theuse of these techniques, which need careful investigation, i.e., synchroni-sation and RF front-end imperfections. That is why the content of thisbook is focussed on these two subjects. To reduce the influence of theRF impairments, mitigation approaches based on digital signal process-ing were shown to be promising [33–36]. The work is focussed on themajor imperfections as identified above: phase noise, IQ imbalance andnonlinearities.

Hence, the main subjects of this book are:� synchronisation for MIMO OFDM-based wireless systems,� the verification of the MIMO OFDM concept by means of a test

system,� baseband equivalent RF impairment models, applicable in the MIMO

OFDM context,� the performance impact of RF imperfections in multiple antenna

OFDM,� mitigation algorithms/approaches for the influence of front-end im-

pairments,� a generalised error model mapping the impact of the key performance

limiting non-idealities.The structure of this work is schematically depicted in Fig. 1.5. First

the foundation of the book is laid down in Chapters 2 and 3. Chapter 2

10 1 Introduction

Chapter 2:

Multiple-antenna OFDM systems

Chapter 3:

Design and implementation of a MIMO OFDM system

Chapter 4:

Phase Noise

Chapter 5:

IQ imbalance

Chapter 6:

Nonlinearities

Chapter 7:

A generalised error model

Figure 1.5. Structure of this book.

introduces a model for the MIMO multipath channel, which is usedthroughout this book. Subsequently, the basics of MIMO, OFDM andtheir combination, i.e., MIMO OFDM, are presented. Chapter 3 in-troduces algorithms for symbol timing, frequency synchronisation andchannel estimation for these MIMO OFDM systems. It also presentsan implementation of a test system applying the proposed algorithms,together with results from performance measurements. In the followingchapters this basis is assumed and the focus is on RF front-end impair-ments. Chapters 4 to 6 treat the three identified major imperfectionsfor MIMO OFDM, i.e., phase noise, IQ imbalance and nonlinearities,respectively. The organisation of these chapters comprises three parts:modelling of the imperfections and system, derivation of the impact ofthe impairments on system performance and the design of compensationapproaches for the influence of the non-idealities. The different impair-ments are brought together in Chapter 7, which proposes a generalisederror model for their aggregate impact.

Chapter 2

MULTIPLE-ANTENNA OFDM SYSTEMS

2.1 IntroductionIt was highlighted in the general introduction of this book that the

application of multiple antennas in transmitter (TX) as well as receiver(RX) of wireless systems provides the possibility to exploit the degrees offreedom provided by the spatial multiple-input multiple-output (MIMO)wireless channel. These systems are generally named after the chan-nel used for the transmission, i.e., MIMO systems. To overcome thefrequency selectivity and time dispersion introduced by the widebandmultipath propagation channel, the combination of MIMO with the mul-ticarrier technique orthogonal frequency division multiplexing (OFDM)is considered in this book. It was shown in Chapter 1 that this com-bination, i.e., MIMO OFDM, is also considered as the basis for severalnext-generation high data rate wireless systems.

In the next chapters different aspects of such multiple-antenna OFDMsystems are considered. Since the properties of the wireless channel,and the understanding hereof, are crucial for the design of this kindof systems, this chapter introduces a model for the wideband MIMOwireless channel. This is followed by a review of the basics of MIMO,OFDM and MIMO OFDM. This chapter derives system models for thesesystems, which will be used throughout this book.

2.2 Channel modellingTo design and evaluate wireless systems, it is important to have an

accurate model of the channel experienced in the transmission from TXto RX. To that end, this section introduces a channel model for theMIMO wireless channel. First, in Section 2.2.1, the multipath channel

12 2 Multiple-antenna OFDM systems

is introduced, from which, subsequently, a time-discrete equivalent isderived. In Section 2.2.2, this model is used as the basis for a stochasticchannel model, which is applied for design and evaluation purposes inthe remainder of the book.

2.2.1 Multipath propagationConsider the wireless transmission between the ntth TX and nrth

RX of a MIMO system. When this system is deployed in a reflectiveenvironment, e.g., an indoor or microcellular environment, the trans-mitted signal will experience multipath propagation, as schematicallydepicted in Fig. 2.1. This implies that the RX receives signals via indi-rect paths, next to the signal component propagating through the directpath. These indirect paths can experience different propagation effects,e.g., reflections and diffractions.

The signals propagating via these indirect paths will be delayed, at-tenuated and phase shifted relatively to the signal received via the directpath. To reveal the effect of this multipath propagation on the receivedsignals, it is useful to have an expression for the baseband equivalent ofthe transfer of the multipath channel at radio frequency fc. It can beshown that the impulse response of the channel between the ntth TXand nrth RX at time instant t and propagation delay τ is well modelledby [37, 38]:

cnrnt(t, τ) =Nm(t)∑

n=1

αn(t)e−jφn(t)δ(τ − τn(t)), (2.1)

TX nt RX nr

......

Figure 2.1. Multipath propagation between the ntth TX and nrth RX in a multipathenvironment.

2.2 Channel modelling 13

where the attenuation, phase shift and delay corresponding to the nthpath are given by αn, φn and τn, respectively. The number of multi-path components is given by Nm and j denotes the imaginary unit, i.e.,j2 = −1. Furthermore, δ(·) denotes the Dirac delta function. The phaseshift φn(t) consists of a component due to free space propagation plus acomponent θn(t, τ) due to other phase shifts experienced in the channel,e.g., by reflections. It can, thus, be expressed by

φn(t) = 2πfcτn(t) + θn(t). (2.2)

We note that all parameters in the channel model, αn(t), φn(t), τn(t),θn(t, τ) and Nm(t), are expressed as a function of time, since the chan-nel varies over time. This is caused by movement of either the TX, RXor the objects in their propagation environments. Although this time-dependence is generally valid, we will, in the remainder of this work,assume a quasi-static channel. This means that we assume that for atransmission centred around time instant t0, the channel impulse re-sponse cnrnt does not vary. It is noted that this is only valid when thetransmission length is short as compared to the coherence time of thechannel [37]. The quasi-static channel can at time instant t0 thus beexpressed as

cnrnt(t0, τ) = cnrnt(τ) =Nm∑

n=1

αne−jφnδ(τ − τn). (2.3)

The expression for the channel impulse response in (2.3) allows us todefine some relevant channel parameters, which will be used later on tocharacterise the channel. When we first consider the power delay profile(PDP), which defines the power of the channel impulse response as afunction of the propagation delay, we find that it is given by

Pnrnt(τ) =Nm∑

n=1

|αn|2δ(τ − τn) =Nm∑

n=1

α2nδ(τ − τn). (2.4)

When we, subsequently, regard the first moment of the PDP, i.e., themean propagation delay, we find that it is given by

τ =

∞∫−∞

Pnrnt(τ)τdτ

∞∫−∞

Pnrnt(τ)dτ

=

Nm∑n=1

α2nτn

Nm∑n=1

α2n

. (2.5)

The root-mean-square (rms) delay spread στ is often used as a measurefor the time-dispersiveness of the channel and is given by the square root

14 2 Multiple-antenna OFDM systems

of the second moment of the PDP, which is given by

σ2τ =

∞∫−∞

Pnrnt(τ)[τ − τ ]2dτ

∞∫−∞

Pnrnt(τ)dτ

=

Nm∑n=1

α2n[τn − τ ]2

Nm∑n=1

α2n

. (2.6)

It is furthermore useful to derive the frequency-domain response of thechannel, which is given by the Fourier transform of the impulse responsein (2.3) and expressed as a function of frequency f by

Hnrnt(f) =

∞∫

−∞

cnrnt(τ)e−j2πfτdτ. (2.7)

The multipath channel as expressed in (2.3) and (2.7) will only beobserved by a system with unlimited bandwidth. Any practical system,however, will experience a time-discrete and bandlimited version of thischannel model. Due to filtering in both TX and RX and sampling in thereceiver, the taps of the experienced channel will be equispaced weightedsums of the actual multipath components, as will be shown below.

Let us, therefore, consider the relevant system parameters of the ban-dlimited link between the ntth TX and nrth RX, as illustrated in Fig. 2.2[39]. When we define unt(nTs) to be the discrete TX signal at sample in-stant n, we can observe in Fig. 2.2 that it is filtered by the bandlimitingfilter FTX and then transmitted through the multipath channel cnrnt(τ).At the receiver, the signal experiences additive RX noise wnr(t) and isfiltered by the RX filter FRX. Subsequently, the signal is sampled at ratefs = 1/Ts yielding the sampled RX signal ynr(nTs).

This transmission chain allows us to express the RX signal as a func-tion of the transmitted signal. It is given by

ynr(nTs) =Lmax∑

l=Lmin

gnrnt(lTs)unt([n − l]Ts) + vnr(nTs), (2.8)

Figure 2.2. Block-diagram of a bandlimited communication link between the ntthTX and nrth RX.

2.2 Channel modelling 15

where vnr(nTs) is the equivalent of the additive RX noise wnr(t) afterRX filtering and sampling. The sample index of the first and last tapare given by Lmin = �τ1fs� and Lmax = �τNmfs�, respectively. The flooroperator �·� and ceil operator �·� round their argument to the closestlower and higher integer, respectively. The elements of the equispacedbandlimited channel, containing the TX and RX filtering, are given by

gnrnt(lTs) = FRX(lTs) � cnrnt(lTs) � FTX(lTs)

=Nm∑

n=1

αne−jφnF(lTs − τn), (2.9)

where F(τ) denotes the combined response of the TX and RX filter, i.e.,F = FTX � FRX, and � denotes convolution. The convolution between aand b is defined as

a � b =∫ t

0a(τ ′)b(t − τ ′)dτ ′. (2.10)

Here we assume the TX and RX filters FTX and FRX to be ideal bandpassfilters, i.e., their combined frequency response is given by

√Tsrect(f/fs),

where rect(·) is the rect function, which equals 1 for |x| < 1/2 and 0,otherwise. Since the inverse Fourier transform of

√Tsrect(f/fs) is given

by sinc(πtfs) = sin(πtfs)πtfs

, we can rewrite the bandlimited discrete-timeimpulse response as

gnrnt(lTs) =Nm∑

n=1

αne−jφnsinc (π[l − τnfs]) . (2.11)

It is clear from (2.11) that the taps of this impulse response are weightedsums of the original multipath components.

Above we regarded the link between one TX/RX pair, but in a MIMOsystem an RX simultaneously receives signals originating from all Nt

TXs. For the nrth RX branch the noiseless received signal can be ex-pressed as

ynr(nTs) =Nt∑

nt=1

Lmax∑

l=Lmin

gnrnt(lTs)unt([n − l]Ts)

=Nt∑

nt=1

L−1∑

l=0

gnrnt(lTs)unt([n − l]Ts), (2.12)

where in the last step it was assumed that the delay of the first arrivingpath is zero, i.e., Lmin = 0, and where L = Lmax − Lmin + 1. We willkeep using this assumption throughout this book.

16 2 Multiple-antenna OFDM systems

z−1 z−1 z−1

· · ·

· · ·u(n)

y(n)

G(0) G(1) G(L − 1)

u(n − L + 1)

Figure 2.3. Tapped delay line channel model.

When we want to simultaneously express (2.12) for all Nr branches,(2.12) can be written in matrix notation as a function of the sampleindex as

y(n) =L−1∑

l=0

G(l)u(n − l), (2.13)

where

y(n) = [y1(n) y2(n) . . . yNr(n)]T , (2.14)u(n) = [u1(n) u2(n) . . . uNt(n)]T , (2.15)

G(l) =

⎡

⎢⎢⎢⎣

g11(l) g12(l) . . . g1Nt(l)g21(l) g22(l) . . . g2Nt(l)

......

. . ....

gNr1(l) gNr2(l) . . . gNrNt(l)

⎤

⎥⎥⎥⎦ , (2.16)

and where T denotes the matrix transpose.It is clear from (2.13) that the transmission through the time-discrete

equivalent channel model can, without loss of information, be modelledas a tapped delay line. This is schematically illustrated in Fig. 2.3, wherez−1 denotes a delay of one sample period.

2.2.2 Stochastic channel modelFor the time-discrete channel model, as presented in (2.13), to be use-

ful for system design and evaluation, a wide range of realisations has tobe generated, on which a model of the possible channels for the regardedenvironment can be based. For that purpose channel measurements [40]or ray tracing simulations [41] can be applied. Although these techniquescan provide reliable results, they are cumbersome and time-consumingto perform. Especially since for every environment separate measure-ments/simulations have to be performed.

2.2 Channel modelling 17

Therefore, the use of a stochastic channel model was chosen for theresearch presented in this work. This approach enables the generation ofrepresentative channel realisations on the basis of only a few parameterscharacterising a certain environment. Here we will regard the PDP,path loss, rms delay spread, fading distribution and spatial correlationas sufficient parameters to accurately model the channel.

If we regard (2.13) as the basis of the channel model, then the (nr,nt)thelement of G(l) is given by

gnrnt(l) =√

PrPd(l)βnrnt(l), (2.17)

where Pr models the average path loss of the MIMO channel, Pd(l) is thenormalised PDP and βnrnt(l) models the fading of the channel taps. Notethat Pr and Pd(l) are here defined to be equal for all channel elements,since the path loss is a function of the distance, which is almost equalfor all TX/RX pairs, and since the PDP is environment dependent.

When we first consider the normalised PDP, we can use the factthat signals that arrive with higher delays in general will have trav-elled longer paths and that their attenuation will, therefore, on averagealso be higher. Hence, it is reasonable, for both indoor and outdoorchannels, to model the PDP as exponentially decaying as a function ofthe excess delay [42]. The time-discrete version of the normalised PDPcan then be expressed as

Pd(l) =

{e−lTs/στ

∑L−1l=0 e−lTs/στ

for στ > 0,

1 for στ = 0,(2.18)

where στ is the rms delay spread, which (like the PDP) is equal for allbranches.

The fading term βnrnt(l) is here modelled to have a standard complexnormal distribution, i.e., CN (0, 1). For this fading model it is easilyverified that the resulting phase and amplitude of βnrnt(l) are distributedaccording to a uniform and Rayleigh distribution, respectively. Thismodel for the fast fading is commonly used for indoor and non-line-of-sight (NLOS) outdoor environments [37].

Another important parameter in MIMO channels is the correlationbetween the elements of the channel matrix G(l). It has been shownin several publications over the last few years that the spatial channelcorrelation can be split into correlation at the TX and correlation atthe RX [43–45]. The main assumption here is that the correlation isdominated by propagation effects that occur in the vicinity of the TXand RX. The channel matrix can then be expressed as

G(l) =√

RRX(l)Gi(l)√

RTX(l)T, (2.19)