Beamforming Techniques ForWireless Comm

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UNIVERSIT A DEGLI STUDI DI TRIESTE

DIPARTIMENTO DI ELETTROTECNICA, ELETTRONICA ED INFORMATICA

XX Ciclo delDottorato di Ricerca in

Ingegneria dellInformazione(Settore scientico-disciplinare: ING-INF/03)

TESI DI DOTTORATO

Beamforming Techniques for WirelessCommunications in Low-Rank Channels:

Analytical Models and Synthesis Algorithms

Dottorando CoordinatoreMASSIMILIANO COMISSO Chiar.mo Prof. Alberto Bartoli

(Universit degli Studi di Trieste)

TutoreChiar.mo Prof. Fulvio Babich(Universit degli Studi di Trieste)

RelatoreChiar.mo Prof. Lucio Mani a(Universit degli Studi di Trieste)

CorrelatoreChiar.mo Prof. Roberto Vescovo

(Universit degli Studi di Trieste)


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Summary

The objective of this thesis is discussing the application of multiple antenna tech-

nology in some selected areas of wireless networks and fourth-generation telecom-munication systems. The original contributions of this study involve, mainly, tworesearch elds in the context of the emerging solutions for high-speed digital com-munications: the mathematical modeling of distributed wireless networks adopt-ing advanced antenna techniques and the development of iterative algorithms forantenna array pattern synthesis. The material presented in this dissertation is theresult of three-year studies performed within the Telecommunication Group of the Department of Electronic Engineering at the University of Trieste during thecourse of Doctorate in Information Engineering.

In recent years, an enormous increase in trafc has been experienced by wire-less communication systems, due to a signicant growth in the number of usersas well as to the development of new high bit rate applications. It is foreseenthat in the near future this trend will be conrmed. This challenging scenario in-volves not only the well established market of cellular systems, but also the eldof emerging wireless technologies, such as WiMAX (Worldwide interoperabil-ity for Microwave Access) for wireless metropolitan area networks, and Wi-Fi(Wireless Fidelity) for wireless local area networks, mobile ad-hoc networks andwireless mesh networks. The rapid diffusion of architectures adopting an ad-hocparadigm, in which the network infrastructure is partially or totally absent and thatcan be deployed using low-cost self-conguring devices, has further enlarged thenumber of systems that have to coexist within a limited frequency spectrum. Insuch evolving environment, the development of interference mitigation methodsto guarantee the communication reliability, the implementation of proper radio re-source allocation schemes for managing the user mobility as well as for support-ing multimedia and high speed applications, represent the most relevant topics.Classic approaches are focused on the use of the time-frequency resources of thepropagation channel. However, to satisfy the increasing demand of network ca-pacity, while guaranteeing at the same time the necessary levels in the quality of the offered services, operators and manufacturers must explore new solutions.

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iv Summary

In this scenario, the exploitation of the spatial domain of the communication chan-nel by means of multiple antenna systems can be a key improvement for enhancingthe spectral efciency of the wireless systems. In a rich scattering environment,the use of multiple antennas enables the adoption of diversity and spatial multi-plexing techniques for mitigating and, respectively, exploiting multipath fadingeffects. In propagation environments characterized by small angular spreads, thecombination of antenna arrays and beamforming algorithms provides the possi-bility to suppress the undesired sources and to receive the signals incoming fromthe desired ones. This leads to an increase of the signal to interference plus noiseratio at the receiver that can be exploited to produce relevant benets in terms of

communication reliability and/or capacity. A proper design of the medium ac-cess control layer of the wireless network can enable the simultaneous exchangeof packets between different node pairs as well as the simultaneous reception of packets from multiple transmitters at a single node. Switched-beam antennas,adaptive antennas (also referred to as smart antennas), and phased-antenna arraysrepresent some of the available beamforming techniques that can be applied toincrease the overall system capacity and to mitigate the interference, in a scenariowhere several different technologies must share the same frequency spectrum.

In the context of distributed wireless networks using multiple antenna systems,

the core of this thesis is the development of a mathematical model to analyzethe performance of the network in presence of multipath fading, with particularreference to a scenario in which the signal replicas incoming at the receiver areconned within a small angle and are characterized by small relative delays. Thispropagation environment, referred to as low-rank , is the typical operating scenarioof smart antennas, which necessitate high spatial correlation channels to work properly. The novel aspects of this study are represented by the theoretical andnumerical modeling of the sophisticated adaptive antennas in conjunction with adetailed description of the channel statistics and of the IEEE 802.11 medium ac-cess control scheme. A theoretical model providing a more realistic perspectivemay be desirable, considering that, at present, not only cost and competition is-sues, but also too optimistic expectations, as compared to the rst measurementson the eld, have induced the wireless operators to delay the adoption of smartantenna technology.The presented analysis includes the most relevant elements that can inuence thenetwork behavior: the spatial channel model, the fading statistic, the network topology, the access scheme, the beamforming algorithm and the antenna arraygeometry. This last aspect is numerically investigated considering that the sizeof the user terminal represents a strict constraint on the number of antennas thatcan be deployed on the device, and so the maximization of the performance be-


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Summary v

comes related to the geometrical distribution of the radiators. In ad-hoc and meshnetworks, the typical communication devices, such as laptops, palmtops and per-sonal digital assistants require compact and cheap antenna structures as well asbeamforming algorithms easy to implement. In particular, the low-cost character-istics have guaranteed a wide popularity to wireless mesh technology, which haveencouraged the birth of a new social phenomenon, known as wireless communitynetworks , whose objective is the reduction of the Internet access cost.The adoption of multi-antenna systems is the purpose of the IEEE 802.11n amend-ment, which, however, not considering modications of the medium access con-trol layer, provides higher bit rates for the single link, but does not allow simulta-neous communications between different couples of nodes. This aspect must be

taken into account together with the fact that, nowadays, IEEE 802.11x representsthe leading family of standards for wireless local communications, and enhance-ment proposals have to pay careful attention to the backward compatibility issues.The mathematical model presented in this thesis discusses the suitable parametersettings to exploit advanced antenna techniques in 802.11-based networks whenthe access scheme supports multiple communications at the same time, maintain-ing a realistic description for the antenna patterns and the channel behavior.

The presentation of two new iterative algorithms for antenna array pattern syn-thesis represents the core of the last part of this dissertation. The proposed solu-

tions are characterized by implementation simplicity, low computational burdenand do not require the modication of the excitation amplitudes of the array ele-ments. These advantages make the presented algorithms suitable for a wide rangeof communication systems, while matching also the inexpensiveness of mesh andad-hoc devices. In particular, phase-only synthesis techniques allow the adoptionof a cheaper hardware, including only phase shifters, which are available at a rea-sonable price, while avoiding the use of the more expensive power dividers.The rst presented algorithm employs the spatial statistic of the channel for prop-erly placing the pattern nulls, in order to suppress the undesired power incomingfrom a given angular interval. This solution exploits the improved knowledge of the spatial properties of the propagation environment for enhancing the interfer-ence suppression capabilities at the transmitter and receiver sides. The secondalgorithm is a phase-only technique that is able to generate multiple nulls towardsthe undesired directions and multiple main lobes towards the desired ones. Thismethod provides the possibility to perform spatial multiplexing adopting low-costelectronic components.

The thesis is organized in three parts. The rst one provides the background ma-terial and represents the basics of the following arguments, while the other twoparts are dedicated to the original results developed during the research activity.


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vi Summary

With reference to the rst part, the fundamentals of antenna array theory arebriey summarized in the rst chapter. The most relevant aspects of the wire-less propagation environment are described in the second chapter, focusing onthe characteristics of the spatial domain in a low-rank scenario. The third chap-ter presents a classication of the different multiple antenna techniques accordingto the channel properties and provides an overview of the most common beam-forming algorithms. The fourth chapter introduces the most signicant aspects of the distributed wireless networks, presenting the main open issues and the currentproposals for the exploitation of the potential offered by antenna array systems.The second part describes the original results obtained in the mathematical mod-eling of ad-hoc and mesh networks adopting smart antennas in realistic propa-

gation scenarios. In particular, the fth chapter presents the theoretical analysisto evaluate the number of simultaneous communications that can be sustained bya distributed wireless network using adaptive antennas in presence of multipath.The sixth chapter extends this model to switched-beam antennas, while address-ing the mobility aspects and discussing the cost-benet tradeoff that is related tothe use of multiple antenna techniques in todays wireless networks. A detailedthroughput-delay analysis is performed in the seventh chapter, where the impactof advanced antenna systems on 802.11-based networks is investigated using aMarkov chain model. The inuence of the antenna array geometry is examined inthe eighth chapter adopting a numerical approach based on a discrete-time simula-

tor, which is able to take into account the details of the channel and of the antennasystem behavior.The third part describes the original results obtained in the eld of antenna arraypattern synthesis. The ninth chapter presents the technique developed to modifythe excitation phases of an antenna array in order to reject interferers spread overan angular region according to a given spatial statistic. The tenth chapter describesthe iterative algorithm for phased arrays, which is able to produce low side-lobelevel patterns with multiple prescribed main lobes and nulls. Finally, the eleventhchapter summarizes the thesis contributions and remarks the most important con-clusions.

The intent of the work presented hereafter is to examine the benets that derivefrom the employment of smart antenna techniques from a realistic perspective, aswell as to provide some useful solutions to improve the reliability of the commu-nications and to increase the network capacity.


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List of acronyms

AA Adaptive Antenna.

ADC Analog-to-Digital Converter.ACK ACKnowledgement.AP Access Point.BER Bit Error Rate.BPSK Binary Phase Shift Keying.BSS Basic Service Set.CDMA Code Division Multiple Access.CFP Contention Free Period.CLA Cantor Linear Array.CMA Constant Modulus Algorithm.

CP Contention Period.CPU Central Processing Unit.CRA Concentric Ring Array.CS Carrier Sensing.CSE Cumulative Square Error.CSMA Carrier Sensing Multiple Access.CTS Clear To Send.CW Contention Window.DA Directional Antenna.DC DownConversion.DCTS Directional CTS.DCF Distributed Coordination Function.DD Directional DATA.DFT Discrete Fourier Transform.DIFS Distributed InterFrame Space.DNAV Directional NAV.DOA Direction Of Arrival.DS Distribution System.DSP Digital Signal Processor.DSSS Direct Sequence Spread Spectrum.

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viii List of acronyms

DWN Distributed Wireless Network.ECB Efcient Coding Bound.E-SPC Extended-SPC.ESPRIT Estimation of Signal Parameters via Rotational Invariance Techniques.ESS Extended Service Set.FDMA Frequency Division Multiple Access.FHSS Frequency Hopping Spread Spectrum.FIR Finite Impulse Response.FNBW First Null BeamWidth.FPGA Field Programmable Gate Array.GBSBM Geometrically Based Single Bounce Macrocell.

HPBW Half Power BeamWidth.IBSS Independent Basic Service Set.ICI InterCarrier Interference.IF Intermediate Frequency.IR InfraRed.ISI InterSymbol Interference.ISM Industrial, Scientic and Medical.LMS Least Mean Square.LOS Line Of Sight.MAC Medium Access Control.

MANET Mobile Ad-hoc NETwork.MIMO Multiple Input Multiple Output.MRC Maximal Ratio Combining.MSE Mean Square Error.MUSIC MUltiple SIgnal Classication.MVDR Minimum Variance Distortionless Response.NAV Network Allocation Vector.OCTS Omnidirectional CTS.OFDM Orthogonal Frequency Division Multiplexing.PAS Power Azimuth Spectrum.PC Point Coordinator.PCF Point Coordination Function.PCMCIA Personal Computer Memory Card International Association.PDA Personal Digital Assistant.PDP Power Delay Prole.PER Packet Error Rate.pdf probability density function.PHY PHYsical (layer).QAM Quadrature Amplitude Modulation.QPSK Quadrature Phase Shift Keying.


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List of acronyms ix

RCB Random Coding Bound.RF Radio Frequency.RTS Request To Send.SBA Switched-Beam Antenna.SCM Single Coordinate Method.SCSMA/CN Selective CSMA with Cooperative Nulling.SD Smart DATA.SDMA Space Division Multiple Access.SIFS Short InterFrame Space.SINR Signal to Interference plus Noise Ratio.SLL Side-Lobe Level.

SNR Signal to Noise Ratio.SPC Single Parity Check.SQP Sequential Quadratic Programming.STC Space-Time Coding.TDMA Time Division Multiple Access.TEM Transverse ElectroMagnetic.UCA Uniform Circular Array.ULA Uniform Linear Array.URA Uniform Rectangular Array.Wi-Fi Wireless Fidelity.

WiMAX Worldwide interoperability for Microwave Access.WLAN Wireless Local Area Network.WMN Wireless Mesh Network.


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Contents

Summary iii

List of acronyms vii

List of symbols 1

I Background 7

1 Fundamentals of Antenna Arrays 91.1 Maxwells equations . . . . . . . . . . . . . . . . . . . . . . . . 91.2 Antenna fundamentals . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.1 Poynting vector . . . . . . . . . . . . . . . . . . . . . . . 101.2.2 Antenna regions . . . . . . . . . . . . . . . . . . . . . . 111.2.3 Radiation properties . . . . . . . . . . . . . . . . . . . . 12

1.3 Antenna arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3.1 Linear arrays . . . . . . . . . . . . . . . . . . . . . . . . 161.3.2 Rectangular arrays . . . . . . . . . . . . . . . . . . . . . 181.3.3 Circular arrays . . . . . . . . . . . . . . . . . . . . . . . 191.3.4 Conformal arrays . . . . . . . . . . . . . . . . . . . . . . 20

2 Propagation Channel Modeling 212.1 The wireless channel . . . . . . . . . . . . . . . . . . . . . . . . 21

2.1.1 Path-loss attenuation . . . . . . . . . . . . . . . . . . . . 212.1.2 Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.1.2.1 Rayleigh fading . . . . . . . . . . . . . . . . . 232.1.2.2 Rician fading . . . . . . . . . . . . . . . . . . 252.1.2.3 Nakagami fading . . . . . . . . . . . . . . . . 26

2.1.3 Shadowing . . . . . . . . . . . . . . . . . . . . . . . . . 272.2 Spatial channel models . . . . . . . . . . . . . . . . . . . . . . . 27

2.2.1 Low-rank environment . . . . . . . . . . . . . . . . . . . 29

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xii Contents

2.2.1.1 Uniform distribution . . . . . . . . . . . . . . . 302.2.1.2 Truncated cosine . . . . . . . . . . . . . . . . . 312.2.1.3 Truncated Gaussian . . . . . . . . . . . . . . . 322.2.1.4 Ring of scatterers . . . . . . . . . . . . . . . . 332.2.1.5 Disk of scatterers . . . . . . . . . . . . . . . . 352.2.1.6 Truncated Laplacian . . . . . . . . . . . . . . . 36

3 Multiple Antenna Systems 373.1 Benets of multi-antenna systems . . . . . . . . . . . . . . . . . 373.2 Classication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3 MIMO-spatial multiplexing . . . . . . . . . . . . . . . . . . . . . 39

3.4 Spatial diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.5 Beamforming in low-rank environment . . . . . . . . . . . . . . . 423.6 Fixed beamforming . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.6.1 Switched-beam antennas . . . . . . . . . . . . . . . . . . 443.6.2 Delay and sum beamforming . . . . . . . . . . . . . . . . 453.6.3 Beam-space beamforming . . . . . . . . . . . . . . . . . 45

3.7 Adaptive beamforming . . . . . . . . . . . . . . . . . . . . . . . 463.7.1 Spatial reference techniques . . . . . . . . . . . . . . . . 48

3.7.1.1 DOA estimation algorithms . . . . . . . . . . . 493.7.2 Temporal reference techniques . . . . . . . . . . . . . . . 51

3.7.2.1 Unconstrained LMS algorithm . . . . . . . . . 523.7.2.2 RLS algorithm . . . . . . . . . . . . . . . . . . 533.7.3 Blind techniques . . . . . . . . . . . . . . . . . . . . . . 54

4 Distributed Wireless Networks 574.1 General concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 574.2 IEEE 802.11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2.1 Transmission rates . . . . . . . . . . . . . . . . . . . . . 604.2.2 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . 604.2.3 The 802.11 DCF . . . . . . . . . . . . . . . . . . . . . . 61

4.2.3.1 Basic access . . . . . . . . . . . . . . . . . . . 614.2.3.2 RTS/CTS access . . . . . . . . . . . . . . . . . 62

4.3 DWNs and advanced antenna techniques . . . . . . . . . . . . . . 634.3.1 MAC layer problems . . . . . . . . . . . . . . . . . . . . 64

4.3.1.1 Hidden terminal due to unheard RTS/CTS . . . 654.3.1.2 Hidden terminal due to asymmetry of gain . . . 664.3.1.3 Exposed terminal . . . . . . . . . . . . . . . . 674.3.1.4 Deafness . . . . . . . . . . . . . . . . . . . . . 674.3.1.5 Muteness . . . . . . . . . . . . . . . . . . . . . 684.3.1.6 Suicide ACK . . . . . . . . . . . . . . . . . . . 69


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4.3.2 MAC layer proposals . . . . . . . . . . . . . . . . . . . . 704.3.2.1 Directional NAV . . . . . . . . . . . . . . . . . 714.3.2.2 Synchronous communications . . . . . . . . . . 714.3.2.3 Tones . . . . . . . . . . . . . . . . . . . . . . . 724.3.2.4 Multiple RTS packets . . . . . . . . . . . . . . 734.3.2.5 Longer handshake . . . . . . . . . . . . . . . . 74

4.3.3 Theoretical approaches . . . . . . . . . . . . . . . . . . . 74

Original Results 79

II Advanced Antenna Systems for Distributed Wireless Net-works in Low-Rank Environment 79

5 Simultaneous Communications in DWNs Using Adaptive Antenna Ar-rays 815.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.2 Denitions and assumptions . . . . . . . . . . . . . . . . . . . . 82

5.2.1 MAC layer assumptions . . . . . . . . . . . . . . . . . . 83

5.2.2 PHY layer assumptions . . . . . . . . . . . . . . . . . . . 835.3 Multipath model and equivalent gains . . . . . . . . . . . . . . . 845.4 Interference model . . . . . . . . . . . . . . . . . . . . . . . . . 875.5 Sustainable links . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.5.1 High number of sustainable links . . . . . . . . . . . . . 895.5.2 Low number of sustainable links . . . . . . . . . . . . . . 92

5.6 Topology and access scheme . . . . . . . . . . . . . . . . . . . . 925.6.1 Uniform distribution . . . . . . . . . . . . . . . . . . . . 92

5.6.1.1 Omnidirectional CTS (OCTS) . . . . . . . . . . 935.6.1.2 Directional CTS (DCTS) . . . . . . . . . . . . 94

5.6.2 Random distribution . . . . . . . . . . . . . . . . . . . . 955.6.3 Renement for Smart DATA transmission . . . . . . . . . 96

5.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.7.1 Packet transmission policy . . . . . . . . . . . . . . . . . 985.7.2 Angular spread and topology . . . . . . . . . . . . . . . . 1005.7.3 Path loss and spatial channel model . . . . . . . . . . . . 102

5.8 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106


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6 Multi-Antenna and Channel Coding Techniques for Wireless MeshRouters 1096.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.2 Sustainable links of SBAs in WMNs . . . . . . . . . . . . . . . . 1106.3 Mobility effects . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.3.1 Modication of the topology . . . . . . . . . . . . . . . . 1136.3.2 Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.4 Results in not mobile environment . . . . . . . . . . . . . . . . . 1156.5 Model application: multiple antennas and channel coding . . . . . 118

6.5.1 Coding techniques . . . . . . . . . . . . . . . . . . . . . 1186.5.1.1 Convolutional codes . . . . . . . . . . . . . . . 118

6.5.1.2 Efcient codes . . . . . . . . . . . . . . . . . . 1186.5.1.3 Extended-Single Parity-Check codes . . . . . . 119

6.5.2 Performance gure and design parameters . . . . . . . . . 1196.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.5.3.1 Not mobile environment . . . . . . . . . . . . . 1216.5.3.2 Mobile environment . . . . . . . . . . . . . . . 127

6.6 Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7 Throughput-Delay Analysis of 802.11 DWNs Using Beamforming Tech-niques 133

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.2 Markov chain model . . . . . . . . . . . . . . . . . . . . . . . . 1347.3 Throughput-delay analysis . . . . . . . . . . . . . . . . . . . . . 1387.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.4.1 Parameter settings . . . . . . . . . . . . . . . . . . . . . 1427.4.2 Optimum contention window . . . . . . . . . . . . . . . 1437.4.3 Non saturated behavior . . . . . . . . . . . . . . . . . . . 1467.4.4 Number of nodes . . . . . . . . . . . . . . . . . . . . . . 148

7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

8 On the Inuence of Array Geometry in DWNs Employing Smart An-tennas 1518.1 Introduction and array geometry description . . . . . . . . . . . . 1518.2 Signal and channel model . . . . . . . . . . . . . . . . . . . . . . 1548.3 Adopted MAC protocol . . . . . . . . . . . . . . . . . . . . . . . 1568.4 Simulation platform . . . . . . . . . . . . . . . . . . . . . . . . . 157

8.4.1 Adopted parameters . . . . . . . . . . . . . . . . . . . . 1598.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

8.5.1 Access scheme . . . . . . . . . . . . . . . . . . . . . . . 1608.5.2 Array geometry . . . . . . . . . . . . . . . . . . . . . . . 162


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8.5.3 Training sequence . . . . . . . . . . . . . . . . . . . . . 1648.5.4 Multipath fading . . . . . . . . . . . . . . . . . . . . . . 165

8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

III Antenna Array Synthesis Techniques 169

9 Exploitation of Spatial Channel Model for Antenna Array Synthesis 1719.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1719.2 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . 1729.3 Projection operators . . . . . . . . . . . . . . . . . . . . . . . . . 173

9.4 Exploitation of the spatial channel model . . . . . . . . . . . . . 1749.5 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . 1779.6 Considerations and summary . . . . . . . . . . . . . . . . . . . . 179

10 Multi-Beam and Null Synthesis of Antenna Arrays by Phase-OnlyControl 18110.1 Introduction and problem formulation . . . . . . . . . . . . . . . 18110.2 Synthesis technique . . . . . . . . . . . . . . . . . . . . . . . . . 18210.3 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . 18510.4 Setting of the weights . . . . . . . . . . . . . . . . . . . . . . . . 190

11 Conclusions 191

Appendix. Smart DATA transmission cases 193

Bibliography 197

List of publications 215


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List of symbols 1

a () Antenna array steering vector in the azimuth plane.AF (,) Antenna array factor.

Brx Receiver lter bandwidth.bpl Number of bits of the payload.bts Number of bits of the training sequence.C r Coding rate.CW i Contention window at i -th transmission attempt.CW min Minimum contention window.CW opt Optimum contention window.D Destination node.det( ) Matrix determinant.E{} Expectation.E (w ,) Antenna system eld pattern in the azimuth plane.

E k () Field pattern of the k-th antenna element in the azimuth plane.E s(r ) Electric complex eld.F D () Equivalent power gain pattern in the azimuth plane.F T (r, ) Topology function.f d Doppler spread.G() Antenna system power gain pattern in the azimuth plane.Gd Average equivalent power gain in the desired direction.Gm Average equivalent power gain in [0, 2 ].Gm Average equivalent power gain outside the FNBW.Gm Average equivalent power gain outside the HPBW.Gn Average equivalent power gain in a null.G tx 1 Transmitting equivalent power gain of the interferers in the region R 1.G tx 2 Transmitting equivalent power gain of the interferers in the region R 2.g Weight vector for the terms of the cost function (w ).gl Weight for the l-th term of the cost function (w ).H s(r ) Magnetic complex eld.I Generic interferer.

1This list contains the symbols that recur along the thesis and whose explanation is not re-peated in each section where they are mentioned. Mathematical quantities without direct physicalmeaning and dened only for calculation purposes are not reported.

1


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2 List of symbols

I N Identity matrix with rank N . j Imaginary unit.

Lc Area covered by the communication range of a node.Lt Area covered by the entire network.Lmax Number of sustainable links.

M lNumber of array pattern nulls that are necessary to suppress the l-thspread interferer.

m Retry Limit of the 802.11 DCF.m Maximum backoff stage of the 802.11 DCF.m N Nakagami parameter.N Number of antennas.N CRA Number of antennas of a CRA.

N hop Average number of hops between source and destination.N rx Number of receiving antennas of a MIMO system.N tx Number of transmitting antennas of a MIMO system.N UCA Number of antennas of a UCA.N ULA Number of antennas of a ULA.N URA Number of antennas of a URA.n Number of nodes in the entire network.n 2 Number of nodes in the region R 2.n des Number of desired sources.n int Number of interferers.n tx Number of transmitting sources.P des Received desired signal power.P int Received interference power.P int 1 Interference power received from region R 1.P int 2 Interference power received from region R 2.P int 3 Interference power received from region R 3.P rx Total received power.P rx Average power at the input of the receiving antenna system.P tx Transmitted power.P () Power Azimuth Spectrum. pc Conditional collision probability. poutage Outage probability. ptx Transmission probability of a single node.Q Number of multipath components corresponding to a generic source.

R Bit rate for the DATA packet.R 1 Region of insuppressible interference.R 2 Region of suppressible interference.R 3 Region of no interference.R c Communication range of a node.

Rc Bit rate for the control packets.R H() Radius bounding regions R 1 and R 2.


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List of symbols 3

R L() Radius bounding regions R 2 and R 3.R sd Average source-destination distance.R ss Correlation matrix corresponding to the desired part of x (t).R t Radius of the area occupied by the entire network.R uu Correlation matrix corresponding to the undesired part of x (t).R xx Array correlation matrix.r Position vector.r k Radial coordinate of the k-th array element.rank( ) Matrix rank.S Source node.S ag Normalized aggregate throughput.S input Net offered trafc load.S max Sustainable throughput.SINR th SINR threshold in not mobile environment.SINR out SINR at the antenna system output.sgn() Sign function.T Successful packet delay.T ACK Time required to transmit an ACK packet.T CTS Time required to transmit a CTS packet.T DATA Time required to transmit a DATA packet.T RTS Time required to transmit an RTS packet.T col Time wasted because of collision.T s Transmitted symbol duration.T succ Time required by a successful transmission.t Time variable.tr( ) Matrix trace.

v Vector speed of a mobile node.vc Speed of light in the free space.W Noise power.w Vector of antenna array excitations.w (i) Vector of antenna array excitations at time instant i .wk Current excitation of the k-th array element.wk (i) Current excitation of the k-th array element at time instant i .x (i) Antenna input signal vector at time instant i .x (t) Antenna input signal vector at time t .xk (t) Input signal at the k-th antenna array element at time t .x s(i) Desired part of x (i) at time instant i .x u (i) Undesired part of x (i) at time instant i . Path-loss exponent. G Normalization constant for the truncated Gaussian pdf. L Normalization constant for the truncated Laplacian pdf. LMS Step size for the LMS algorithm. m1 Maximum angular spread for the ring of scatterers pdf.


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4 List of symbols

m2 Maximum angular spread for the disk of scatterers pdf. Term accounting for the antenna height in the path-loss model.Ki m Kronecker delta. Permittivity of the medium. Zenith angle. Mean value of a Poisson packet arrival process.1 Probability of packet arrival during the processing of a previous packet.2 Probability of packet arrival in the idle state. Wavelength. Permeability of the medium.

num _slotsAverage number of slots required for processing a packet in the 802.11DCF.

slotAverage time between two consecutive backoff time counter decrementsin the 802.11 DCF.

succ _slotsAverage number of slots required for a successful packet transmissionin the 802.11 DCF.

k Angular position of the k-th element of a UCA.c Radius of a UCA.l Interelement spacing of a ULA.act (r, ) Active node density.

DOA () Pdf of the DOAs.lDOA () Pdf of the DOAs corresponding to the l-th interferer.FAD (z) Pdf of the envelope of the received signal.

FAD (z) Pdf of the squared envelope of the received signal.SOU (r, ) Pdf of the sources around the destination.TOP (r, ) Pdf of the interferers around the destination.() r (r ) Marginal of the pdf ()(r, ) with respect to r .() () Marginal of the pdf ()(r, ) with respect to .

slot Slot time. Azimuth spread of the channel.

lAzimuth spread of the channel between the l-th source and the destina-tion.

Delay spread of the channel. Angle between source-destination LOS and relative vector speed v.

Vector of array excitation phases.k Excitation phase of the k-th array element. Azimuth angle.0 Mean DOA.

3dB HPBW in the azimuth plane.

FN FNBW in the azimuth plane.

d Desired azimuth direction.

dl Desired azimuth direction corresponding to the l-th source.k Azimuth coordinate of the k-th array element.


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List of symbols 5

lq DOA of the q-th signal replica corresponding to l-th source.n Undesired azimuth direction.

nl Undesired azimuth direction corresponding to the l-th source.

col Collision probability.drop Drop probability.i ,i Stationary probability of being in the state (i , i ).succ Probability of successful transmission.

s(t)Stochastic process representing the backoff stage of the 802.11 DCF attime t .

tx Transmission probability.

t (t)Stochastic process representing the backoff timer of the 802.11 DCF attime t .

(w ) Cost function. (w ) Mean square norm.

Floor function. Ceiling function.

() Complex conjugate.() Matrix pseudoinverse.()H Complex conjugate transpose of a vector or matrix.()T Transpose of a vector or matrix.


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Part I

Background


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Chapter 1

Fundamentals of Antenna Arrays

This chapter briey summarizes the basic principles of antennas, explaining themechanism of wireless electromagnetic propagation. Some fundamental deni-tions of antenna theory are recalled from the literature and an introduction toantenna arrays is provided together with a description of the most common arraygeometries.

1.1 Maxwells equations

Wireless communications are based upon the transmission and reception of elec-tromagnetic signals from antennas. The physics laws that describe the propagationof an electromagnetic wave are summarized by the Maxwells equations, whichcan be expressed for an isotropic and homogeneous medium as [1]:

E (r , t ) =vol(r , t )

, (1.1a)

H (r , t ) = 0 , (1.1b)

E (r , t ) =

H (r , t )

t, (1.1c)

H (r , t ) = E (r , t )

t+ J (r , t ), (1.1d)

where r denotes the spatial position vector, t is the time variable, E (r , t ) is theelectric eld intensity vector, is the permeability of the medium, H (r , t ) is themagnetic eld intensity vector, is the permittivity of the medium, J (r , t ) is thecurrent density vector and vol(r , t ) is the volume charge density.According to the mathematical meaning of the divergence operator, which mea-sures the magnitude of a vector elds source or sink and can be viewed as a ux

9


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10 Chapter 1. Fundamentals of Antenna Arrays

density, and to the meaning of the curl operator, which shows the vector eldsrate of rotation (the direction of the axis of rotation and the magnitude of therotation), the four Maxwells equations describe the principles of electrodynam-ics. The rst equation (Gausss law) states that the presence of static or dynamiccharges in a given volume determines a diverging electric eld, while the secondone (Gausss law for magnetism) means that there is nothing available in naturewhich makes a magnetic eld diverge. The third equation (Faradays law) statesthat a non-stationary magnetic eld causes a curl in the electric eld and, nally,the last equation (Amperes law) means that a non-stationary electric eld and/ora current through a medium capable of carrying a ow of electric charges deter-mines a curl in the magnetic eld.

The Faradays and the Amperes laws are fundamental to obtain a wave propagat-ing in a wireless environment, where no charge and current densities are present.In this case, a stationary current density J (r ) is useless, being unable to generate aspace-time varying electromagnetic eld. Instead, a time-varying current densityJ (r , t ) generates a space-time varying magnetic eld H (r , t ), which, in turn, gen-erates a space-time varying electric eld E (r , t ). At this point, the electric eldcan produce a space-time varying magnetic eld even in the absence of a currentdensity, and so the magnetic and the electric elds are able to sustain each other.

1.2 Antenna fundamentals

An antenna is a device capable of carrying the time-varying current density that isnecessary to generate the electromagnetic wave. The IEEE Standard Denitionsof Terms for Antennas , [2], denes an antenna as that part of a transmitting orreceiving system that is designed to radiate or to receive electromagnetic waves.The antenna represents a transitional structure between free-space and a guidingdevice, where the guiding device is a transmission line that transports the elec-tromagnetic energy from the transmitter to the antenna or from the antenna to thereceiver [3].

1.2.1 Poynting vector

Assuming harmonic variations, the instantaneous radiated elds E (r , t ) and H (r , t )can be expressed in terms of the complex elds E s(r ) and H s(r ) as:

E (r , t ) = Re {E s(r )e jt }, (1.2a)H (r , t ) = Re {H s(r )e jt }, (1.2b)

where j = 1 is the imaginary unit and is the angular frequency. The com-ponents of the complex elds produced by an antenna are directly related to the


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1.2. Antenna fundamentals 11

Figure 1.1: Antenna eld regions.

physical properties of the antenna itself and can be derived solving the Maxwellsequations by proper mathematical and numerical techniques. The quantity used todescribe the power associated to an electromagnetic eld is the Poynting vector,which is dened in the sinusoidal case as:

W (r )12E s(r ) Hs (r ), (1.3)

where ()denotes the complex conjugate. The real part of W (r ) represents theactive power density of the eld generated by the antenna, while the imaginarypart of W (r ) represents the reactive power density associated to this eld. There-fore, the average power radiated over a closed surface Msurrounding the antennacan be evaluated as:

P rad = M

W (r ) ds = M

12

Re{E s(r ) Hs (r )} ds. (1.4)

1.2.2 Antenna regions

The generated electromagnetic eld and the radiation properties of an antennaare related to its physical size and to the operating wavelength. The space sur-rounding an antenna is usually subdivided into three regions, which are denedby proper boundaries (Fig. 1.1). The rst region, called the reactive near-eld region, is bounded by the antenna surface and by the spherical surface having ra-dius 0.62

D 3max / , where Dmax is the largest dimension of the antenna and


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is the wavelength. This region contains the reactive energy stored in the vicinityof the antenna, while the active radiated power is negligible. The second region,called the radiating near-eld or Fresnel region, is dened by the intersection of the spheres having radii 0.62 D 3max / and 2D 2max / . In this region the radi-ation of active power prevails, but the angular eld distribution depends on thedistance from the antenna. The far-eld or Fraunhofer region lies outside thesphere having radius 2D 2max / and represents the principal region of operationfor many antennas. In the Fraunhofer region the imaginary part of the Poyntingvector approaches zero much faster than its real part and so the reactive power isnegligible. Besides, the electric and magnetic eld components are perpendicularto each other and transverse to the radial direction of propagation r . Therefore,

in the Fraunhofer region, E s(r ) and H s(r ) form a Transverse ElectroMagnetic(TEM) wave:

E s(r ) = 0H s(r ) r , (1.5a)H s(r ) =

10

r E s(r ), (1.5b)

where 0 = / = 377 is the intrinsic impedance of the free space.1.2.3 Radiation properties

The radiation intensity W u (,) is a far-eld parameter that represents the radi-ated power per unit solid angle in a given direction dened by the zenith angle and the azimuth angle . This parameter can be evaluated multiplying the com-ponent of the Poynting vector in the direction of propagation by r 2:

W u(,) = r 2Re{W (r ) r}, (1.6)and is used to dene the antenna power gain , which represents the ratio betweenthe radiation intensity and the power at the input of the antenna, P input , divided by4 :

G(,) 4W u (,)

P input. (1.7)

The antenna power gain is also given by the product between the antenna radiationefciency ecd and the directivity D(,). In particular, the radiation efciencyaccounts for the conduction and the dielectric losses, and is dened as the ratio of the radiated power to the input power:

ecdP rad

P input=

P radP rad + P loss

, (1.8)


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1.2. Antenna fundamentals 13

Figure 1.2: Example of radiation pattern.

where P loss is the antenna power loss. Besides, the directivity is the ratio betweenthe radiation intensity and the radiated power divided by 4 :

D(,)4W u(,)

P rad. (1.9)

The radiation properties of an antenna as a function of the space coordinates aredescribed by mathematical functions called radiation patterns . These functionscan be adopted to represent several antenna parameters, such as radiation intensity,eld strength, directivity and power gain. With reference to the example shownin Fig. 1.2, the following characterizing elements can be dened in a radiation

pattern.

Null : direction in which the pattern assumes very small values, ideally zero. Lobe : any angular region bounded by two nulls. Main lobe : lobe that contains the direction of maximum radiation. Minor lobe : any lobe except the main one. If the pattern assumes the max-

imum radiation value in unwanted directions external to the main lobe, thelobes containing these directions are called grating lobes .


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Side lobe : a minor lobe that is usually adjacent to the main lobe and occu-pies the same hemisphere in the direction of maximum gain.

Half Power BeamWidth (HPBW) or 3 dB BeamWidth : angular region con-taining the direction of maximum radiation that lies between the two direc-tions in which the radiation is one-half of this maximum. In the gure 3dB

denotes the HPBW in the azimuth plane.

First Null BeamWidth (FNBW) : entire angle spanned by the main lobe. TheFNBW can be associated to the ability of an antenna to reject interference.In the gure FN represents the FNBW in the azimuth plane.

Side-Lobe Level (SLL) : maximum relative radiation of the highest side lobewith respect to the maximum radiation of the main lobe.

1.3 Antenna arrays

Usually the beamwidth of a single antenna element pattern is too wide for manywireless terrestrial and space applications, which, in many cases, require highgains towards certain directions [4]. Besides, a narrower HPBW (or FNBW) canbe necessary for spatial ltering operations and to increase the gain in the desireddirections as well as to reduce it in the undesired ones. Directional patterns can beobtained by increasing the single antenna element size or by using more radiatingelements in order to form an array. In this second case the individual antennasare arranged according to a proper geometrical conguration and the current ex-citations of each element are synthesized to provide the desired radiation pattern.For practical purposes all radiators belonging to an array are usually chosen asidentical, even if, for specic applications, antenna arrays consisting of differentelements can be built. By adopting multi-antenna structures, it is possible to gen-erate radiation patterns with multiple main beams, each with a desired beamwidth,while satisfying side-lobe level and null constraints. The synthesis process can beperformed by properly selecting the number of array elements, their geometricalconguration and the interelement spacing. Besides, the radiation pattern can beelectronically controlled by modifying the phase and/or the amplitude of the cur-rent excitations.The total eld radiated by an antenna array is determined by the vector additionof the individual elements. The far-eld radiation properties of an antenna arraycan be mathematically summarized by the array steering vector:

a (,) [E 1(,)e j2v c

1 (,) ,..., E N (,)e j2v c

N (,)]T , (1.10)


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1.3. Antenna arrays 15

where (

)T denotes the transpose of a vector or matrix,

E k(,) =

Gk(,) is

the k-th single element eld (or amplitude) pattern, vc is the speed of light in freespace and k(,) represents the delay of a plane wave arriving from direction(,) and measured from the k-th element of the array with respect to the origin.The array steering vector includes both the radiation properties of each elementand the geometrical characteristics of the antenna array. These characteristicsdetermine the delay, which can be evaluated as:

k(,) =r k r i

vc, (1.11)

where r k = ( r k sin k cosk , r k sin k sink , r k cosk)T is the position of thek-th array element in spherical coordinates, and:

r i = (sin cos, sin sin, cos)T , (1.12)

is the unit vector of the incoming wave. According to the principle of patternmultiplication, if the individual elements are identical, the pattern produced by anarray can be expressed as the product between the pattern of the single elementwith respect to a given reference point and the array factor:

AF (,)N

k=1

wke j2v c

k (,) , (1.13)

where wk is the complex excitation of the k-th array element. The characteristicsof AF (,) can be controlled by varying the excitations, the number of elements,the interelement spacing and the geometrical conguration of the array.When two antenna array elements are sufciently close, the electromagnetic eldradiated by one element couples into the other and vice versa. This phenomenonis called mutual coupling and depends on the interelement spacing, the radiationcharacteristics and the orientation of the single element. This interchange of en-ergy complicates the array design, because mutual coupling is difcult to predictby analytical methods, but, in many scenarios, it must be taken into account be-cause of its signicant contribution [3]. In fact, mutual coupling leads to a distor-tion of the single element radiation pattern, which inuences the resulting patternof the entire antenna array and may lead to unprecise steering of the main lobeand the nulls. An interelement distance larger than or equal to half the wavelengthis commonly considered sufcient to neglect mutual coupling effects, while, forlower distances, the distorted element patterns can be evaluated with numericaltechniques.


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Figure 1.3: Uniform linear array.

1.3.1 Linear arrays

Usually, in the design of an antenna array, some constraints, such as the SLL,the FNBW, the HPBW and the directivity, are specied, while others, such as thephase/amplitude of the elements, the number of radiators and the geometry of thearray, must be properly derived to satisfy the design requirements.The most common and most analyzed geometry is the linear antenna array, whichconsists of N antenna elements displaced on a straight line. If the adjacent ele-ments are equally spaced (Fig. 1.3), the array is referred to as a Uniform LinearArray (ULA). If, in addition, all excitations have identical amplitudes ( |w1| =|w1| = ... = |wN |) and the phase of the k-th element is increased by a constantprogressive phase with respect to the (k 1)-th element, the array is referredto as a uniform array. In this particular case, the normalized array factor in the

azimuth plane can be expressed as:

AF norm =2

, =1N

sinN 2

2 l

cos +

sin12

2 l

cos +

, (1.14)

where l is the interelement spacing. The main lobe can be steered towards thedesired direction by properly modifying the progressive phase shift, while a nar-


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0 45 90 135 18080

70

60

50

40

30

20

10

0

d B

(o)

Figure 1.4: Array gain of a ULA for N = 5 and l = 0 .5 .Uniform array Binomial array Dolph-Tschebyscheff array

row HPBW can be obtained by increasing N .A limitation of uniform arrays is due to the fact that, independently of the numberof elements, the ratio between the maximum of the main lobe and the maximumof the rst side lobe is approximately equal to 13.5 dB. This level may be not suit-able for certain applications, where more stringent constraints must be imposed onthe level of the secondary lobes. In fact, to reduce the transmitted/received poweroutside the main lobe, the minor lobes should be as low as possible. In general,the problem of low SLL array design is substantially equivalent to the problem of designing Finite Impulse Response (FIR) digital lters in a Digital Signal Proces-sor (DSP). Therefore, a large number of techniques have been taken from digitalsignal processing to produce patterns with low side lobes. These techniques per-form the weighting of the array elements by adopting proper functions, such asGaussian, Kaiser-Bessel and Blackman windows [5].Widely adopted synthesis techniques for ULAs are the Dolph-Tschebyscheff andthe binomial methods, which consider a nonuniform distribution of the excita-tion amplitudes. Comparing the characteristics of uniform, Tschebyscheff andbinomial arrays, it can be observed that the uniform arrays provide the smallestHPBW and the highest SLL, while the binomial arrays yield the largest HPBWand the lowest SLL (Fig. 1.4). In particular, a binomial array with interelement


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Figure 1.5: Uniform rectangular array.

spacing lower than or equal to / 2 has no side lobes. The HPBW and the SLL of a Tschebyscheff array lie between those of binomial and uniform arrays. Besides,for a given SLL, the Dolph-Tschebyscheff arrays provide the smallest FNBW and,reciprocally, for a given FNBW, the Dolph-Tschebyscheff arrays provide the low-est possible SLL [3].Even if ULAs are widely applied, there are scenarios in which the linear geometryis not appropriate. Other congurations must be adopted to satisfy some partic-ular encumbrance requirements on buildings or vehicles and to provide higherperformance in terms of beam scanning.

1.3.2 Rectangular arrays

Rectangular arrays are more versatile with respect to linear arrays and can be em-ployed to obtain patterns with a lower SLL. Similarly to ULAs, proper weightingmethods can be considered to further reduce the side-lobe level and the beamwidth.Besides, a rectangular conguration has the capability to perform the beam scan-ning in both the azimuth and the elevation planes.As shown in Fig. 1.5, a rectangular array is obtained when the individual radi-ating elements are positioned along a rectangular grid. If the adjacent elementsare equally spaced the array is called a Uniform Rectangular Array (URA). Thisconguration nds application in a wide range of systems, such as remote sens-


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ing, tracking and search radar. An N x

N y URA can also be viewed as N y linear

arrays placed at distance yr , where each array is formed by N x elements withinterelement spacing xr . Therefore, for a progressive phase URA with uniformamplitudes, the normalized array factor can be expressed as:

AF norm (,) =1

N x

sinN x2

2xr

sin cos + x

sin12

2xr

sin cos + x

1

N ysin

N y2

2yr sin sin + y

sin12

2yr

sin sin + y

,

(1.15)

where x and y are the progressive phase shifts along the x and the y axis, re-spectively. When the interelement spacing is larger than or equal to half the wave-length, grating lobes can appear in the radiation pattern because of the in-phaseaddition of the radiated elds towards directions different from that scanned bythe main lobe.

1.3.3 Circular arrays

Another commonly employed conguration is the Uniform Circular Array (UCA),in which the elements are regularly arranged on a circular ring (Fig. 1.6). TheUCA is of very practical interest and is often adopted in radar and sonar systemsas well as in cellular base stations. Considering a UCA of radius c, the normal-ized array factor can be expressed as:

AF (,) =N

k=1

wke j2 c sin cos(k ) , (1.16)

where k is the angular position of the k-th element. Thanks to its high degreeof symmetry the UCA is able to provide an identical HPBW towards all azimuthdirections. Besides, a direct comparison between a UCA and a ULA shows that,adopting the same number of elements and the same spacing between adjacentradiators, the circular array produces narrower main beams with respect to thecorresponding linear array. The performance of the circular congurations canbe improved by using multiple rings in order to obtain a Concentric Ring Array(CRA). This planar geometry enables the scanning in both azimuth and elevationplanes [67].


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Figure 1.6: Uniform circular array.

1.3.4 Conformal arrays

ULAs, URAs and UCAs are widely adopted geometries, based upon a regular andsymmetrical design. These congurations are suitable for applications in whichthe mounting support is able to sustain the structure and particular size or shapeconstraints are not present. However, in many practical scenarios, such as space-craft, aircraft or missile applications, the mounting surface is irregular and/or theavailable space is limited. In these situations the array geometry must be designedto match the particular requirements of the support and so a conformal array isneeded. The antenna elements can be disposed on an ellipse, on an arc, or canbe placed according to more complex three-dimensional topologies, usually cir-cularly symmetric surfaces, such as cylinders, cones or spheres [8]. In general,the patterns of the elements can be oriented towards different directions, becauseof the irregularity of the geometry, and so the single element pattern cannot befactored out from the total array pattern. [9].Proper antenna elements may be required for conformal arrays, because the genericradiator may have to adhere to aerodynamic proles. Besides, particular single el-ement radiation patterns may be necessary to satisfy the design specications fordedicated array topologies [10].


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Chapter 2

Propagation Channel Modeling

This paper introduces the main characteristics of the wireless propagation envi-ronment and provides some basic denitions. To provide realistic models for eval-uating the performance of advanced antenna array systems, particular attentionis dedicated to the spatial properties of the wireless communication channel. Themost important statistical distributions for the Power Azimuth Spectrum (PAS) are presented together with the classical fading models.

2.1 The wireless channelFree-space propagation occurs when a unique direct signal path exists between atransmitter and a receiver. However, this model oversimplies the real behavior of the wireless channel, in which obstacles and scatterers characterize the surround-ing environment of two communicating nodes. Reections, refractions, diffrac-tions and scattering determine the presence of many signal replicas at the receiver,leading to a phenomenon referred to as multipath. Besides, the complexity of thescenario is increased by the effects due to mobility, which cause short-term uc-tuations (fading) and long-term uctuations (shadowing) of the received signal

envelope. Therefore, taking into account these characteristics, the signal attenua-tion in a wireless propagation channel is usually schematized as the combinationof three main factors: path-loss, fading and shadowing.

2.1.1 Path-loss attenuation

Path-loss attenuation is the power density reduction of an electromagnetic wavepropagating through space and is mainly due to the distance between the transmit-ter and the receiver. However, additional environmental elements, due to location

21


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22 Chapter 2. Propagation Channel Modeling

of antennas, terrain contours, vegetation, foliage and dry, may increase the losses.The path-loss attenuation can be described by a parameterized ground model, inwhich the power received by a node at distance r from a transmitter is evaluatedas [11]:

P rx =P tx Gtx Grx

r , (2.1)

where P tx is the transmission power, (> 2) is the path-loss exponent, ac-counts for the height of the transmitting and the receiving antennas with respect tothe oor, Gtx and Grx are, respectively, the transmitting and the receiving antennasystem gains. The value assumed by the parameter is chosen according to theparticular attenuation characteristics of the wireless channel. A value equal to 2

models the behavior of the free space, while = 4 is considered adequate for arelatively lossy scenario, such as a two ray ground propagation environment. Thetypical value for the path-loss exponent in a dense urban environment, in presenceof several buildings, ranges from 4 to 6.

2.1.2 Fading

In a multipath scenario each signal component is characterized by its amplitude,phase shift, delay and Direction Of Arrival (DOA). A fundamental metric for de-scribing the behavior of the multipath channel is the Power Delay Prole (PDP),

which provides the signal power as a function of the delay of the multipath com-ponents. Usually, in a wireless environment, the PDP has one or more peaks,whose presence indicates an inherent clustering of the delays. The informationobtained from the PDP can be used to evaluate the delay spread, which is denedas:

= Qq=1 P rx q 2qQq=1 P rx q

Qq=1 P rx q q

Qq=1 P rx q

2

, (2.2)

where Q is the number of multipath components, P rx q and q are, respectively, thepower level and the delay corresponding to the q-th path. The delay spread is thestandard deviation of the PDP and represents a measure of the time dispersion of the channel. The widening of the channel impulse response in the time domaincan lead to InterSymbol Interference (ISI), an unwanted phenomenon in which thepreviously transmitted symbols have inuence on the currently received receivedone.Another relevant feature of the wireless channel is caused by the Doppler effect,which is due to the relative motion between transmitter, receiver and obstacles.Doppler effect determines a frequency broadening of the received signal that isproportional to the relative motion speed and to the carrier frequency. By con-sequence, adjacent frequency channels may experience InterCarrier Interference


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2.1. The wireless channel 23

(ICI). Besides, the combination of multipath and mobility leads to uctuations of the received signal envelope (multipath fading), caused by the constructive anddestructive addition of the signal replicas due to the different phase shifts.Multipath fading is dened as at fading when the delay spread is much lowerthan the inverse of the receiver lter bandwidth Brx , while it is dened as fre-quency selective fading when 1/ Brx , namely when the delay spread is largeror close to 1/ Brx . In the rst case the multipath characteristics of the channel donot degrade the received signal quality, while in the second case amplitude andphase distortions are experienced at the receiver.The temporal rate of change of the wireless channel is measured by the Dopplerpower spectrum, which provides statistical information regarding the variation of

the frequency of a signal received by a mobile node traveling at a given speed.The classical approach, known as the Clarke model, assumes that the receivedsignal comes from directions uniformly distributed in the azimuth domain. As-suming the use of a single / 2 vertical dipole antenna, having power gain G( =/ 2,) = 3 / 2 in the entire azimuth plane, the Doppler power spectrum for a atfading channel is given by [12]:

S D(f ) =

3P rx

2f d 1 f f 0f d2 |f f 0| < f d

0 elsewhere

, (2.3)

where P rx is the average received power from all multipath components, f 0 isthe carrier frequency and the Doppler spread can be expressed as f d = f 0| v|/v c,with v representing the relative vector speed. Multipath fading can also be dis-tinguished between fast fading when the Doppler spread is larger or close to theinverse of the symbol duration T s, and in slow fading when f d 1 it is classied as overspread [13].The small-scale uctuations of the received power, leading to fast fading, can beobserved over distances in the order of half wavelength. These variations are an-alytically described by proper statistic distributions that characterize the envelopeand the squared envelope of the received signal.

2.1.2.1 Rayleigh fading

When there is no direct path between the transmitter and the receiver, the entirereceived electric eld is due to multipath. The in-phase component, xI(t), and the


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0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

z

FAD z

Figure 2.1: Statistics of the received signal envelope for P rx = 1 .Rice ( K R = 2 ) RayleighNakagami ( mN = 4 ) Nakagami ( mN = 1 / 2).

quadrature component, xQ(t), of the incoming signal can be modeled as complexGaussian random processes. These two processes have zero mean because of theabsence of Line Of Sight (LOS) between transmitter and receiver. Therefore, ap-plying a bivariate transformation, it can be proved that the statistic of the envelope

x2I (t) + x2Q (t) follows a Rayleigh distribution:FAD (z) =

2zP rx

ez 2

P rx z 0

0 elsewhere

, (2.4)

while the statistic of the squared envelope x2I (t) + x2Q (t) is exponential:

FAD (z) =

1P rx

ez

P rx z 0

0 elsewhere

. (2.5)

Experimental studies have shown that Rayleigh fading is a proper model for heav-ily built-up urban environments, characterized by the presence of rich scattering


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2.1. The wireless channel 25

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

z

(z)FAD

Figure 2.2: Statistics of the square of the received signal envelope for P rx = 1 .Rice ( K R = 2 ) RayleighNakagami ( mN = 4 ) Nakagami ( mN = 1 / 2).

and absence of LOS between the communicating nodes [14].

2.1.2.2 Rician fading

The Rician distribution, instead, is suitable when, in addition to the multipathcomponents, there exists a direct path between the transmitter and the receiver.The received signal envelope is characterized by the probability density function(pdf):

FAD (z)=2z(K R +1)

P rxeK R (

KR +1)

z 2

P rx I 0 2z K R (K R +1)

P rxz 0

0 elsewhere

(2.6)

where I 0(z) = 12 20 ez cos d is the modied Bessel function of the rstkind and zero-order, and K R is the Rice factor, representing the ratio betweenthe power of the direct signal and the power of the scattered components. WhenK R = 0 the Rician distribution coincides with the Rayleigh distribution, while


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for K R

+

the channel does not exhibit fading. In presence of Rician fading

the squared envelope has a non-central chi-square distribution with two degreesof freedom:

FAD (z)=

K R +1P rx

eK R ( K R +1) z

P rx I 0 2 K R (K R +1) zP rx z 00 elsewhere

(2.7)

In both cases (Rayleigh and Rice) the phase of the received signal is assumeduniformly distributed in [0, 2].

2.1.2.3 Nakagami fading

Another commonly adopted fading statistic, derived from empirical studies, hasbeen introduced by Nakagami [12]. This distribution describes the envelope of thereceived signal by a central chi-square distribution with mN degrees of freedom:

FAD (z) =2

mNP rx

m Nz2m N 1(mN)

em N z

2

P rx z 0, mN 1/ 2

0 elsewhere

, (2.8)

and the squared envelope by a Gamma density:

FAD (z) =

mNP rx

m Nzm N 1(mN)

em N zP rx z 0, mN 1/ 2

0 elsewhere

, (2.9)

where mN is also called the Nakagami parameter and (mN) =

+

0zm N 1ez dz

is the Euler gamma function. The Nakagami parameter mN can be used to obtainmore or less severe fading conditions with respect to the Rayleigh pdf. In partic-ular, for mN = 1 the Nakagami distribution coincides with the Rayleigh distrib-ution, while for mN + fading is absent. In essence, as mN gets larger thefading conditions become less severe. The Rice distribution can be closely ap-proximated by choosing the Nakagami parameter as a function of the Rice factorK R according to mN = ( K R + 1) 2/ (2K R + 1) . Besides, with respect to the Ricedistribution, the Nakagami distribution has the advantage to provide in many casesclosed form analytical expressions, thanks to the absence of Bessel functions.


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2.2. Spatial channel models 27

2.1.3 Shadowing

Slow fading is due to long-term variations of the mean value of the received signalenvelope. This phenomenon is also known as large-scale fading or shadowing,because the uctuations in the mean signal level are usually caused by the nodemovement in the proximity of objects, such as buildings and hills, which producea shadow effect. Empirical studies have shown that shadowing can be describedby a log-normal distribution:

SHA (z) =

1zS2 e

(log z z S )2

2 2S z 0

0 elsewhere

, (2.10)

where 2S and zS are the mean and the variance of log z, respectively. The usualvalue for the standard deviation S, which is inuenced by the density of thescatterers, ranges from 5 to 12 dB and have a slight dependence on frequency, butis nearly independent of the path length.

2.2 Spatial channel modelsClassical models involve time and frequency domains, however, when advancedantenna array techniques are adopted, the spatial characteristics of the scatteringenvironment have an enormous impact on the system performance. In the pastyears, researchers assumed that the DOAs of the received signal replicas wereuniformly distributed in the entire azimuth plane. However, this hypothesis canbe not realistic when referred to the uplink channel between a mobile node anda cellular base station, or considering the communication between the backbonenodes of a wireless mesh network in outdoor environment.With reference to the spatial domain, some parameters have been dened to takeinto account the antenna characteristics with respect to the spatial distributionof the different signal components [15]. In a multipath environment, the signalreplicas arrive at the receiver with angles that, in general, are different from themean DOA corresponding to the direct path. The Power Azimuth Spectrum (PAS)P () and the angular spread are used to characterize the spatial properties of the channel in the azimuth domain. The PAS represents the power distributionalong all the possible DOAs, while, from a theoretical point of view, the angularspread can be viewed as the square root of the variance of the PAS. In general, theangular spread (or azimuth spread) provides a measure of the angular dispersion


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Figure 2.3: The wireless channel.

of the channel and is dened as:

= Qq=1 P rx q2qQq=1 P rx q

20, (2.11)

where q is the DOA of the q-th signal replica (having power P rx q ), and

0 =Qq=1 P rx qq

Qq=1 P rx q

, (2.12)

is the mean DOA. Recalling the denition given in [15], a channel is called low-rank if


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2.2.1 Low-rank environment

A low-rank channel model basically consists of a local scattering model aroundthe transmitting node and is associated with the LOS component. The contri-butions from scatterers around the receiving node and from distant scatterers areconsidered negligible. Therefore, the distance and the height of the receiving nodewith respect to the transmitting ones play a fundamental role in determining theangular spread [1617].The study of the azimuthal dispersion in a low-rank scenario, where the angulardistribution cannot be resolved by the main lobe of the antenna radiation pattern,gets a considerable interest in the eld of multiple antenna techniques. This inter-est is due to three main motivations.

When the antenna array is adopted for interference suppression purposes,the main objective is to place pattern nulls towards the undesired sources.The nulls are much sharper than the main lobe and so the amount of residualinterference incoming from directions different than the mean DOA have aconsiderable impact on the communication system performance. The sta-tistic of the angular distribution of each undesired source provides usefulinformation for modeling in a realistic manner the interference mitigationcapabilities of the antenna system.

Even if in a low-rank channel the main lobe of the radiation pattern is ableto receive all multipath components relative to a desired source, the signalreplicas are received with a lower gain as they become more distant fromthe mean DOA. Therefore, the PAS becomes helpful to take into account thedegradation of the antenna power gain towards the directions correspondingto the desired source.

The knowledge of the PAS in a high spatial correlation environment im-proves the level of accuracy of the DOA estimation algorithms, which canbe much higher than the HPBW. In fact, the actual resolution accuracy ismainly limited not only by the Signal to Noise Ratio (SNR), but also by the

angular spread around the mean DOA.Several models have been developed in the literature to describe the PAS in dif-ferent low-rank propagation environments [1823]. Some of these statistics havebeen analytically derived adopting a geometrical approach that takes into accountthe displacement of the scatterers in the proximity of the transmitting node. Otherstatistics have been derived by curve tting techniques applied on empirical datacollected during environmental measurements. In this second case a closed formexpression that describes the position of the scatterers around the transmitter isdifcult to obtain and usually numerical approaches are adopted to simulate the


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60 40 20 0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

P ()

(o)

Figure 2.4: Uniform PAS for P rx = 1 and 0 = 0 . = 5 o ( = 8.7

o) = 10 o ( = 17.3

o) = 20 o ( = 34.6

o)

channels that obey to these statistics. A brief overview of the most common dis-tributions for the PAS is provided in the following of this subsection.

2.2.1.1 Uniform distribution

This statistic for the PAS has been proposed in [18], where it is assumed that theDOAs are uniformly distributed in the angular interval [0 ,0 + ], denedby the mean DOA and by the width 2 . The PAS, shown in Fig. 2.4 for three

values of the angular spread, is described by:

P () =

P rx2 |0| 0 elsewhere

, (2.13)

where P rx denotes the power received from all directions and the angular spreadis equal to / 3.In practice, distributions of scatterers that lead to a uniform distribution of the


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60 40 20 0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

P ()

(o)

Figure 2.5: Truncated cosine PAS for P rx = 1 and 0 = 0 . = 5 o ( = 130) = 10 o ( = 32) = 20 o ( = 7)

DOAs are difcult to justify from a physical point of view. However, in somecases, this statistic is employed because it simplies the calculations and enablesthe derivation of closed form analytical expressions.

2.2.1.2 Truncated cosine

The truncated cosine distribution has been derived analyzing the results obtainedfrom channel measurements in urban areas in the early 1970s [19]. In particular,

this statistic has been adopted to evaluate the correlation between two base stationantennas. Analytically, the truncated cosine PAS can be described by:

P () =

P rx c

cos (0) |0| / 20 elsewhere

, (2.14)

where c is a proper constant that can be obtained imposing the normalizationcondition

0 + / 20/ 2 P () = P rx , while the exponent determines (Fig. 2.5).


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60 40 20 0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

P ()

(o)

Figure 2.6: Truncated Gaussian PAS for P rx = 1 and 0 = 0 . = 5 o = 10 o = 20 o

To evaluate the desired value for a given angular spread, numerical techniquesare usually adopted, even if, theoretically, a closed form computation is possible.

2.2.1.3 Truncated Gaussian

The use of a truncated Gaussian has been proposed in [20] in order to provide aPAS model directly related to the angular spread. This PAS is described by:

P () =

P rx G2 e

( 0 ) 2

2 2 |0| / 2

0 elsewhere

, (2.15)

where G is the normalization constant. For small values of the angular spread thetruncated cosine and the Gaussian distributions are very close to each other, as itcan be noticed by comparing Fig. 2.5 and Fig. 2.6. The truncated cosine provides arealistic behavior for the uplink channel between a mobile node and a cellular basestation, but the values that are required to model a low-rank environment, beingin the order of 100, are not practical. The Gaussian distribution, instead, allows aclosed form computation as a function of the angular spread, while representing aproper model for the PAS.


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Figure 2.7: Ring of scatterers model.

2.2.1.4 Ring of scatterers

The PAS can also be derived geometrically, taking into account the displacementof the scatterers inside a region close to the transmitter.Considering a uniform distribution of the scatterers on a circumference of radiusd surrounding the transmitting node, it can be assumed that the transmitted poweris uniformly distributed in the angle (Fig. 2.7). In particular, the power scatteredby the differential element of , d, can be evaluated as:

dP =P rx2

d. (2.16)

The angle can be calculated by geometrical considerations from:

dsin[ (0)]

=d

sin(0), (2.17)

where d is the distance between the transmitter and the receiver. Dening m1 =arcsin( d/d ), (2.17) can be written as:

= arcsin sin(0)sin m1 (0), (2.18)to obtain as a function of the generic azimuth DOA. The power received at thedifferential element of , d, can be evaluated as 2dP because, for any givenazimuth, the power contribution is due to the portion of the ring facing the arrayand the portion on the opposite side. Therefore, the PAS can be obtained from:

P () = 2P rx2

dd

, (2.19)


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60 40 20 0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

P ()

(o)

Figure 2.8: PAS corresponding to the ring of scatterers geometry for P rx = 1 and0 = 0 .

= 5 o ( m1 = 7.3o)

= 10 o ( m1 = 15.1o)

= 20o

( m1= 28.3

o

)

which provides the following expression:

P ()=

P rx

cos(0) sin2 m1 sin2(0) sin2 m1 sin2(0) |0| < m1

0 elsewhere

(2.20)

The PAS corresponding to the ring of scatterers presented here has been calculatedadopting the process proposed in [21] for the case d


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60 40 20 0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

P ()

(o)

Figure 2.9: PAS corresponding to the disk of scatterers geometry for P rx = 1 and0 = 0 .

= 5 o ( m2 = 10.1o)

= 10 o ( m2 = 20.0o)

= 20o

( m2= 40.0

o

)

is associated to the minimum power and the major contribution is given by thefarther components.

2.2.1.5 Disk of scatterers

The spatial propagation model deriving from a disk of scatterers has been pre-sented in [22] and is also known as the Geometrically Based Single BounceMacrocell (GBSBM) channel model. The PAS is determined by the diameterof the disk surrounding the transmitter. This diameter denes a circle, called cir-cle of inuence, in which the scatterers are considered uniformly distributed. ThePAS, plotted in Fig. 2.9, is described by:

P ()=

2P rx

cos(0) sin2 m2 sin2(0)sin2 m2 |0| m20 elsewhere

(2.22)

where m2 denotes the maximum angular shift from mean DOA.


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60 40 20 0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

P ()

(o)

Figure 2.10: Truncated Laplacian PAS for P rx = 1 and 0 = 0 . = 5 o = 10 o = 20 o

2.2.1.6 Truncated Laplacian

Recent eld measurements reveal a PAS having a Laplacian distribution aroundthe mean DOA. The empirical data have been obtained in areas characterized bybuildings ranging from four to six oors and irregular street grids, correspondingto a typical urban environment. The statistic is described by [23]:

P () =

P rx L2e

2 | 0 | |0| m1

0 elsewhere

, (2.23)

where L is the normalization constant. The truncated Laplacian PAS suggeststhat the distribution of scatterers is not uniform in area, but more energy is re-ected from the regions closer to the transmitter (Fig. 2.10). As described in [21],this phenomenon may be due to a shielding effect of the scatterers that are closerto the transmitter with respect to the farther scatterers. Besides, additional prop-agation loss may occur due to the larger distance of these scatterers from thetransmitter.


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Chapter 3

Multiple Antenna Systems

This chapter introduces the main advantages of multi-antenna techniques and provides a classication, based on the wireless channel characteristics, of thedifferent multiple antenna approaches. The fundamental concepts regarding Mul-tiple Input Multiple Output (MIMO) systems, spatial diversity, xed and adaptivebeamforming, are presented, and some common theoretical denitions are illus-trated. Besides, with particular reference to a low-rank environment, some of the most frequently adopted signal processing algorithms are recalled from theliterature.

3.1 Benets of multi-antenna systems

The recent development of high bit rate applications, such as multimedia stream-ing and video conferencing, together with the raised number of users, have in-creased the bandwidth demand in both cellular and Wireless Local Area Network (WLAN) environments. Traditionally, user communications are separated by fre-quency, as in Frequency Division Multiple Access (FDMA), by time, as in TimeDivision Multiple Access (TDMA), or by code, as in Code Division Multiple Ac-cess (CDMA) [24]. Recently, the possibility of separating the different users byspace has led to the development of a new multiplexing technique, called SpaceDivision Multiple Access (SDMA) [25]. The fundamental element of SDMA isthe antenna array, whose elements are dynamically controlled to produce multiplebeams towards the desired directions and nulls towards the undesired ones. Theuse of multi-antenna techniques, only recommended for Beyond Third Generation(B3G) cellular systems, represents a key concept in Fourth Generation (4G) sys-tems and in WLAN scenarios for supporting higher bit rates [26]. The increasedinterest of researchers, operators and manufacturers in multi-antenna technologies

37


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38 Chapter 3. Multiple Antenna Systems

is due to some fundamental benets that can be achieved in terms of quality, ca-pacity and communication reliability [2728].Antenna arrays can be employed to improve the link quality by combating theeffects due to multipath propagation. Alternatively, adopting multiple antennas,the different signal paths can be exploited to combat fading by spatial diversitytechniques or can be used to increase the link capacity by allowing transmissionof different data streams from different antennas. Therefore, the amount of trafcthat can be sustained by a communication system for a given frequency bandwidthcan be increased, leading to considerable spectral efciency improvements.Antenna arrays can also be employed to focus the energy towards certain direc-tions and to mitigate or, adopting more sophisticated adaptive solutions, to sup-

press the transmission/reception towards other directions. This leads to a reduc-tion of the transmitted/received interference and enables the spatial ltering of theincoming signals.Wireless networks in which the topology is subdivided by cells, such as the wire-less mesh networks or the classical cellular systems, may obtain large benetsfrom the adoption of multiple antennas. In particular, the increased coveragerange, which decreases the power requirements, and the possibility to track themobile nodes using proper non-overlapping beams, reduce the number of requiredhandovers together with the need to deploy new base stations or mesh routers.Therefore, multi-antenna technology may have a considerable impact not only in

terms of performance improvement, but also in terms of cost reduction for wire-less operators.

3.2 Classication

As described in Section 2.2, the wireless propagation environment can be classi-ed as high-rank or low-rank, depending on the angular spread of the channel, theseparation between the antenna elements, the delay spread and the signal band-width. This interaction between the characteristics of the multipath channel andthe physical properties of the antenna system determines the received signal statis-tics. In particular, the different multi-antenna approaches can be classied takinginto account the spatial fading correlation between the signals received by the dif-ferent elements of the array (Fig. 3.1). In a low correlation environment (high-rank channel) it is expected that the different multipath components provide a statisti-cally independent behavior, which can be exploited by spatial multiplexing, toincrease the bit rate, or by diversity, to improve the reliability of the communi-cations. In particular, the objective of MIMO-spatial multiplexing is the increaseof the system capacity, while spatial diversity is adopted to reduce the Bit ErrorRate (BER). In a high correlation environment (low-rank channel), instead, xed


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3.3. MIMO-spatial multiplexing 39

Figure 3.1: Classication of multiple antenna systems.

and adaptive beamforming techniques are adopted for maximizing the Signal toInterference plus Noise Ratio (SINR) at the antenna system output. This goal isobtained focusing the energy towards certain desired directions and

Beamforming Techniques ForWireless Comm

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