Eindhoven University of Technology TU/e technische Faculty of Electrical Engineering universiteit Division of Telecommunication eindhoven Technology and Telecommunications Radiocommunications group (ECR) SPACE AND MULTIPATH ANGULAR CHARACTERISTICS IN MIMO Fabiola Jimenez Cortes 26 January 2007 Master of Science Thesis Carried out from April 2006 until February 2007 Supervisors: ir. M.R.J.A.E. Kwakkernaat dr. ir. M.H.A.J. Herben Graduation professor: Prof. dr. ir. E.R. Fledderus The Faculty of Electrical Engineering of Eindhoven University of Technology dis claims all responsibility for the contents of traineeship and graduation reports. Contents Notation 5 Commonly Used Symbols 6 Abbreviations 8 1 Introduction 9 1.1 Background..... 9 1.2 Problem formulation 9 1.3 Objectives... 10 1.4 Thesis outline. . . . 11 2 Propagation Effects of the Wireless Communication Channel 12 2.1 Introduction........ 12 2.2 Fading........... 13 2.2.1 Large-scale fading 13 2.2.2 Small-scale fading 13 2.3 Scattering......... 17 2.3.1 Rayleigh criterion 19 2.3.2 Angular Spread . . 20 2.3.3 Scatterers around transceivers. 21 2.4 Conclusions............... 24 3 The MIMO Wireless Channel Matrix 26 3.1 Introduction............... 26 3.2 Modelling the MIMO channel matrix. 27 3.2.1 Line-of-Sight SIMO channel. . 27 3.2.2 Line-of-Sight MISO channel. . 29 3.2.3 MIMO Illultipath channel matrix 30 3.3 Conclusions............... 32 4 The Capacity of the MIMO Channel 33 4.1 Introduction...................... 33 4.2 Additive White Gaussian Noise (AWGN) Channel 33 3 CONTENTS 4 4.3 The Frequency flat MIMO Channel . 34 4.4 Entropy . . . . . . . . . . . . . . . . . . . . . . 35 4.4.1 Entropy of a real-value Gaussian vector 35 4.4.2 Entropy of a circular Gaussian vector 36 4.5 Capacity................... 36 4.5.1 Capacity ofthe Gaussian Channel 37 4.5.2 MIMO Channel Capacity 38 4.5.3 Rank and Singular Values 39 4.5.4 Correlation 40 4.6 Conclusions............ 40 5 Results: Models and Simulations 42 5.1 Introduction........ 42 5.2 Simulation model . 42 5.2.1 Election of factors . 43 5.3 Array Configuration Comparison 48 5.3.1 Simulations varying AOD and AOA mean location 49 5.3.2 Comparison of arrays, same length ..... 53 5.4 Capacity versus array size for a DCA. . . . . . . . 54 5.4.1 Capacity versus array diameter for a DCA. 56 5.5 Conclusions . 58 6 Comparison with Analytical Model 60 6.1 Introduction . 60 6.2 Channel Model . 60 6.3 Results comparison . . . . . . . 63 6.3.1 Correlation comparison 64 6.4 Conclusions . . . . . . . . . . 67 7 Conclusions and Future work 68 7.1 Conclusions. 68 7.2 Future work . 70 A Monte Carlo Simulations 71 References 62 Notation c 3 X 108 mls e 2.7183 J; erf(x) error function, defined as e-t2dt E:z:[.] statistical expectation over x multipaths counter q time counter J the imaginary unit (j = H) log2(x) the base-2 logarithm ofx T x transpose ofvector x t x complex conjugate-transpose x '" N (J-L, P) x is real-valued Gaussian with mean j1 and covariance matrix P (where the'" notation represents the phrase"is distributed as") x '" Nc (J-L, P) x is circularly symmetric-complex Gaussian with mean j1 and covariance matrix P Tr(.) the trace of a matrix 5 Commonly Used Symbols a attenuation of the path characteristic coefficient of2D scatterring environment O's t f3 wavenumber, defined as W Bandwidth of the bearing signal lVcoh Coherence bandwidth ofthe channel c speed of light C Capacity d distance between transmitter and receiver d nominal reference distance ref f frequency of the signal g('l/J) effective random complex gain fi height fic critical height H Channel matrix 1t Entropy 'l/J(1,(),'P) direction of the incoming or outcoming signal K normalization constant of Normal probability distribution L mean path loss .x wavelength of the signal .xc wavelength of the carrier signal Nt total number oftransmitter antennas in a MIMO system N total number ofreceiver antennas in a MIMO system r m path-loss exponent, with m ?: 2 'P azimuth angle () elevation angle {) angle between antenna array elements n unit sphere P('l/J) normalized average power received from direction 'l/J ¢ phase shift .xc D.t,r normalized to the unit of transmitter or receiver separation D.fi height change S seconds, order ofthe serie angular spread as a function of AOD or AOA (T<p 6 CONTENTS 7 T Coherence time coh Ts Symbol period relative delay of a multipath component compared to the first arriving component T Trms root mean square delay spread x eigenvalue ofthe channel matrix x vector with transmitted signals y vector with received signals xyz coordinates in a Cartesian system w white Gaussian noise incoming signal from direction 1/J noiseless received signal Abbreviations AWGN Additive white gaussian noise AOA Angle-of-Arrival AOD Angle-of-Departure i.i.d. independent and identically distributed lOs Interacting Objects MIMO Multiple-Input-Multiple-Output MISO Multiple-Input-Single-Output MC Monte Carlo iterations MPCs Multiple Path Components SIMO Single Input-Multiple-Output 8 Chapter 1 Introduction 1.1 Background Last year ended with more than two billion mobile subscribers worldwide and the forecasts said that the growth rate for the next 5 years would be around 250 to 300 million subscribers per year [GSM06]; it is not just that the number of new lines would increase but also that the demand for high data throughput will grow considerably as well. Thisincreasing demand for high datarates in wireless systems has driven a lot of interest in improving transmission techniques. Multiple-Input Multiple-Output (MIMO) techniques make use ofmulti-element antenna arrays at both the transmission and reception ends of a radio link, different data streams are transmitted simultaneously on different transmit antennas at the same carrier frequency; these data streams are recovered at the receiver, which also has multiple antennas. MIMO techniques have driven a lot of interest lately because of the promise of a considerable increase in capacity. The capacity represents intuitively the highest error-free transmission rate for a given channel under optimal space, time, coding and modulation scheme. This can be increased significantly because of the multipath scattering. The scattering in outdoor environments generally occurs with the surrounding vegetation and infrastructure i.e. buildings, houses, etc. In a rich scattering environment, the channel between any transmitter antennaand receiver antenna is independent from all other channels. The mixed up of parallel data streams can then be separated at the receiver using advanced signal processing techniques. 1.2 Problem formulation On its travel from transmitter to receiver, the transmitted signals will undergo any or a combination of the following process: absorbtion, reflection, refraction, diffractionand scatteringwith the obstacles and characteristicsofthe environment. The modified signals will arrive at the receiver antenna array with some properties caused by the experienced process, i.e. at a certain angle of arrival, with a given 9 1.3 Objectives 10 phase and magnitude. The impact ofthese signal properties on the MIMO system performance depends also on the transmitter and receiver antenna array geometry. In this project, the impact ofthese two factors on MIMO system performance will be studied. 1.3 Objectives Within this complete project, the main goal is to study the impact of the prop agation channel and antenna array geometry on the MIMO channel capacity. In order to achieve that, a physical model of the propagation channel followed by the capacity formula of the MIMO channel will be derived. Monte Carlo capacity simulations will be carried out, on these simulations, space and multipath angular characteristics will be varied. The specific objectives of the complete Project are as follows: 1. Study, within the frame of this project, the main propagation effects that impacts the MIMO channel. These are: (a) Fading (b) Scattering 2. Derive the physical model ofthe MIMO channel. It will be pursued to obtain a generalized model in terms of: (a) Multipath components. (b) Array geometry. 3. Derive the capacity of the MIMO channel: (a) The Foschini-Telatar MIMO capacity formula will be derived following the information theory approach. 4. Compute capacity. Monte Carlo capacity simulations as a function of: (a) Propagation channel characteristics such as: number ofmultipath com ponents, mean of angle-of-departure and angular spread at the trans mitter, angle-of-arrival and angular spread at the receiver. (b) Antenna array geometry characteristics such as: uniform linear and uni form circular array, number ofantenna elements and antenna array size. 1.4 Thesis outline 11 1.4 Thesis outline This thesis is organized as follows. Chapter 2 gives a briefdescription ofthe prop agation effects of the wireless channel, these effects are important in order to set up the conditions of the channel used in simulations later. Chapter 3 derives a compact model of MIMO wireless channel matrix. The channel matrix describes the wireless MIMO channel in terms of antenna array geometry and propagation channel characteristics. This model can be applied to any antenna array geometry in a tri-dimensional space. Chapter 4 shows the steps to derive the capacity for mula for MIMO channels, there the information theory approach is followed, also the spatial correlation is defined and its incidence in the capacity performance is addressed. Chapter 5 shows simulation results that give insight into the MIMO wireless channel performance capabilities. Chapter 6 compares the correlation re sults ofChapter 5 with an analytical model. Finally, chapter 7concludes the entire work.