Propagation Channel Characterization, Parameter Estimation, and Modeling for Wireless Communications Xuefeng Yin Xiang Cheng ③WILEY ④EEE IEEE PRESS
Xuefeng Yin Xiang Cheng Propagation Channel Characterization, Parameter Estimation, and Modeling for Wireless Communications
Contents 13131378 2 duration(3.4.2) 243 2.7.1 Classification of MIMO Channel Models 1244899035670 Classification of V2V Channel Models Bibli e 3 Model for time-division-multiplexn channel sounding 3.3.2 Transmitted signal 3.3.3 Receive 34 3.Movation for dispersive-path mode 343 model of sih y distribu ed sources 3.5 352 3.6 Power spectral density(D)mode 444650522333346678889666 3.6.2 Maximum-entrop 364 Model of the received signal The stochastic properties
Contents Acronyms and Symbols 7 Bibliography 12 1 Introduction 13 1.1 Book Objective 13 1.2 The Historical Context 13 1.3 Book Outline 17 Bibliography 18 2 Characterization of Propagation Channels 21 2.1 Three Phenomena in Wireless Channels 22 2.2 Path loss and shadowing 24 2.3 Multipath fading 24 2.4 Stochastic characterization of multipath fading 28 2.4.1 Received envelope and phase distribution 29 2.4.2 Envelope level cross rate and average fade duration (3.4.2) 29 2.4.3 Correlation functions 30 2.5 Duality of multipath fading 31 2.6 WSSUS assumption on multipath fading 35 2.7 A review of propagation channel modeling 36 2.7.1 Classification of MIMO Channel Models 37 2.7.2 Classification of V2V Channel Models 40 Bibliography 43 3 Generic channel models 45 3.1 Physical propagation mechanisms 45 3.2 Channel spread function 46 3.3 Specular-path model 50 3.3.1 Model for time-division-multiplexing channel sounding 51 3.3.2 Transmitted signal 52 3.3.3 Received signal 52 3.4 Dispersive-path model 53 3.4.1 Motivation for proposing dispersive-path model 53 3.4.2 Original model of slightly distributed sources 53 3.4.3 First-order Taylor expansion model I 54 3.4.4 First-order Taylor expansion model II 56 3.5 Time-evolution model 56 3.5.1 State-Space Model 57 3.5.2 Observation Model 58 3.6 Power spectral density (PSD) model 58 3.6.1 Estimation methods for PSD of individual dispersive components 58 3.6.2 Maximum-entropy-principle-based generic PSD models 59 3.6.3 Model of the received signal in MIMO systems 65 3.6.4 The stochastic properties of the channel 66
2 CONTENTS 3.7 374 ead function 3.7.5 379 elation matrix of a keyhole channel 88899000TRR aphy tic model (5.2) 42 RS-CBSM for V2V communication yems (52.2) n systems(5.2.1) 77888880090 Sum-o hicle channels(5.5.2) phy 5 Channel sounde 5.5.3 Mitigation of the impact on the high-resol tion parameter estimation 5.6 t of the pha 5.6.2 Signal model on 5.7 onses 57.3 009900001667192222222033 5.7.4 Simulation results mata validatio 5.8 de for Channel Sounding 58 Switching Mode Optimization Simulation Studie
2 CONTENTS 3.7 Model for relay in the amplify and forwards scenarios 68 3.7.1 Introduction 68 3.7.2 A generic model of keyhole channel responses 68 3.7.3 Delay spread function 69 3.7.4 Doppler frequency spread function 69 3.7.5 Bidirection spread function 70 3.7.6 DoD/DoA spread function 70 3.7.7 The transfer matrix and correlation matrix of a keyhole channel 70 3.7.8 Experimental evaluation 71 3.7.9 Conclusions 74 3.8 Models for the received signal 76 Bibliography 76 4 Geometry based stochastic channel modeling 79 4.1 General modeling procedure (5.1) 79 4.2 Regular-shaped geometry-based stochastic model (5.2) 81 4.2.1 RS-GBSM for conventional cellular communication systems (5.2.1) 81 4.2.2 RS-GBSM for V2V communication systems (5.2.2) 83 4.3 Irregular-shaped geometry-based stochastic model (5.3) 84 4.4 Filter simulation model (5.4) 87 4.5 Sum-of-sinusoids simulation model (5.5) 90 4.5.1 Sum-of-sinusoids simulation models for cellular channels (5.5.1) 90 4.5.2 Sum-of-sinusoids simulation models for vehicle-to-vehicle channels (5.5.2) 91 Bibliography 101 5 Channel measurements 103 5.1 Measurement methodologies 103 5.2 Channel sounder 104 5.3 Post-processing of the measurement data 104 5.4 Evaluation of the measurement efficiency 109 5.5 Impact of phase noise in a TDM channel sounding system 110 5.5.1 Introduction 110 5.5.2 Behavior of the short-term phase noise 110 5.5.3 Mitigation of the impact on the high-resolution parameter estimation 111 5.6 Impact of the phase noise in MIMO channel parallel sounding 116 5.6.1 Background information 116 5.6.2 Signal model 117 5.6.3 Analysis of the impact on angular parameter estimation 118 5.6.4 Cramer-Rao lower bound derivation 119 5.6.5 Proposed solution for mitigating the phase noise impact on estimation 120 5.6.6 Simulation results 120 5.6.7 Conclusions 123 5.7 Impact of array responses 126 5.7.1 Introduction 126 5.7.2 The impact of imperfect array responses 127 5.7.3 Determining DRAG 128 5.7.4 Simulation results 128 5.7.5 Measurements Data validation 130 5.7.6 Conclusions 131 5.8 Joint Estimation of Doppler Frequency and Directions 133 5.8.1 Switching Mode for Channel Sounding 133 5.8.2 Estimation of Doppler Frequency 134 5.8.3 Ambiguity in Parameter Estimation 136 5.8.4 Switching Mode Optimization 139 5.8.5 Simulation Studies 140
CONTENTS 3 14 Bibliography 6 th 6.2 Maximum-likelhood method 5555 6.3 555 6365Ema on when the hidden/complete data is known 6.5.2 elay Spread in a two-level EF SCage 69 6的iogpherbaseduacinggorithn 7 Statistical channel parameter esti 7.1 er estimators 7.12 Effective Signal Model erer (SS) 71.7 Simula 7704009 7.2 Po Revie of el 72.3 Derivation of 6-dimensional power spectral density 7.2.4 etraienofheaatbdieci -delay-D Bidirection-delay-Do frequen 加00 72.7 Channel Power Spectrum Estin ato tion of the PSD SAGE gorithm 720 7.2.10 Intrinsic resolution of the measurement system Measurement data evaluation 00000 Bblogap Summary an Mea nt based statistical channel modeling 8.1 General modeling procedures 812 Channel measureme 8.1.3 Stochastic modeling 2
CONTENTS 3 5.8.6 Experimental Investigations 144 5.8.7 Summary and Conclusions 147 Bibliography 147 6 Deterministic channel parameter estimation 151 6.1 Spectral-based method 151 6.1.1 Beamforming method 151 6.2 Maximum-likelihood method 154 6.3 The EM and SAGE algorithms 154 6.3.1 Signal model 155 6.3.2 Channel Sounding Technique 156 6.3.3 SAGE Algorithm 158 6.3.4 ML estimation when the hidden/complete data is known 162 6.3.5 Initialization 165 6.4 The RiMAX algorithm 168 6.5 Evidence framework based algorithms 168 6.5.1 The proposed multi-level evidence framework 168 6.5.2 Example I: Exponential decay used in three-level EF 169 6.5.3 Example II : Delay Spread in a two-level EF 171 6.6 Subspace-based algorithms 173 6.7 Extended Kalman filter based tracking algorithms for time-evolving channels 173 6.8 Particle filter based tracking algorithm 173 Bibliography 173 7 Statistical channel parameter estimation 175 7.1 Dispersive component estimation algorithms 175 7.1.1 A brief review of dispersive parameter estimators 175 7.1.2 Effective Signal Model 177 7.1.3 Specular-Scatterer (SS) Model Estimation 178 7.1.4 Parameter Estimation using the 1 st-order GAM Model 180 7.1.5 A New Definition of SDS and the Array Size Adaptation Technique 184 7.1.6 Simulation Studies 187 7.1.7 Array Size Adaptation 187 7.2 Power spectral density estimation 193 7.2.1 Review of PSD-based dispersive component estimation 194 7.2.2 Signal Model 194 7.2.3 Derivation of 6-dimensional power spectral density 197 7.2.4 Derivation of the MaxEnt bidirection-delay-Doppler-frequency PSD 200 7.2.5 Special case where the direction-delay-Doppler frequency PSD is highly-concentrated. 201 7.2.6 Bidirection-delay-Doppler frequency component PSD 203 7.2.7 Channel Power Spectrum Estimator 203 7.2.8 Implementation of the PSD-SAGE algorithm 205 7.2.9 Rank of the sample covariance matrix 207 7.2.10 Intrinsic resolution of the measurement system 208 7.2.11 Measurement data evaluation 208 7.2.12 Summary and conclusions 211 Bibliography 218 8 Measurement based statistical channel modeling 221 8.1 General modeling procedures 221 8.1.1 Channel measurement 221 8.1.2 Parameter estimation 222 8.1.3 Stochastic modeling 223 8.2 Methods for constructing stochastic channel models 224 8.3 Clustering algorithm based on specular path models 225
4 CONTENTS C&aneniganaaiasicdhstermodeimg 8.3.3 Experimental results for path clustering 8.4 84.2 Method I:Minimum-spread-variation-based approach 8.4.3 Method I:Kolgomorov-Smirnov hypothesis-testing-based approach 4.5 talevaluation 8.5 The non-station ity modeling for long-term evolving channels 8.6 elay and CoMP channel modeling 862 SSE CrO rrelation and modeling methodology 8.6.3 Experimental results 8.6. Conclusion ices:channel modein mmunication systems 9.1.1 Vehicle-to-vehicle communication scenarios ((10.1.1)) ications((10.1)) 9.1.2 9.2 Cooperative communication scenarios((10.1.2)) 92 ((10.2) (10.2113 9.2.2 channel chara eristics of coo erative communicat tion systems((10.2.2)) 5555 9.3 nel models for entional cellular MIMC .2 Generic Space rrelation Function 93 MIMO Simulation Models(10.3.3) 9.35 Numerical 10.3 nd Analysis ((10.3.4)) 9.Scattering theoretical channel models for vehicle-to-vehicle systems((10.)) 9.4.1 nd MIMO vehicle-to-vehicle channels:modeling and statistical properties investigation 9.4.2 Modeling and simulation of wideband MIMO vehicle-to-vehicle channels ((10.4.2)) 9.5 052 A IMO Channe .5.1 53 Multi-link Spatial Corr relation Functions (10..) 93 Summ Measurement-based channel models 325 9.8 models 0. DERIVATION OF(9.43)-(9.48) .0.6 COMPARISON BETWEEN THE DOPPLER PSDS WITH DIFFERENT CFS (9.49)AND(9.50) 328 DERIVATION OF (9.75B) 329 ITION MAX{RT,RR)<MIN(aI-a-1)THAT GUARANTEES THE TDL 3 0.9 THE REDUCED EXPRESSIONS OF SPATIAL CORRELATION Bibliography 34
4 CONTENTS 8.3.1 Conventional stochastic-cluster modeling 225 8.3.2 Clustering algorithms 226 8.3.3 Experimental results for path clustering 229 8.4 Data segment length selection 232 8.4.1 Problem statement 232 8.4.2 Method I: Minimum-spread-variation-based approach 234 8.4.3 Method II: Kolgomorov-Smirnov hypothesis-testing-based approach 239 8.4.4 Experimental evaluation 240 8.4.5 Conclusions 244 8.5 The non-stationarity modeling for long-term evolving channels 244 8.6 Relay and CoMP channel modeling 244 8.6.1 Introduction 244 8.6.2 SSF cross-correlation and modeling methodology 245 8.6.3 Experimental results 247 8.6.4 Conclusions 250 Bibliography 253 9 Practices: channel modeling for modern communication systems 255 9.1 Typical scenarios for vehicle-to-vehicle and cooperative communications ((10.1)) 255 9.1.1 Vehicle-to-vehicle communication scenarios ((10.1.1)) 255 9.1.2 Cooperative communication scenarios ((10.1.2)) 256 9.2 Channel characteristics ((10.2)) 257 9.2.1 Channel characteristics of V2V communication systems ((10.2.1)) 257 9.2.2 Channel characteristics of cooperative communication systems ((10.2.2)) 257 9.3 Scattering theoretical channel models for conventional cellular MIMO systems ((10.3)) 257 9.3.1 A Wideband Multiple-ring Based MIMO Channel Reference Model ((10.3.1)) 258 9.3.2 Generic Space-Time-Frequency Correlation Function ((10.3.2)) 261 9.3.3 MIMO Simulation Models (10.3.3) 263 9.3.4 Numerical Results and Analysis ((10.3.4)) 265 9.3.5 Summary ((10.3.5)) 268 9.4 Scattering theoretical channel models for vehicle-to-vehicle systems ((10.4)) 268 9.4.1 Narrowband MIMO vehicle-to-vehicle channels: modeling and statistical properties investigation ((10.4.1)) 268 9.4.2 Modeling and simulation of wideband MIMO vehicle-to-vehicle channels ((10.4.2)) 286 9.5 Scattering theoretical channel models for cooperative MIMO systems (10.5) 308 9.5.1 A Unified Cooperative MIMO Channel Model Framework (10.5.1) 308 9.5.2 A New MIMO GBSM for Cooperative Relay Systems (10.5.2) 310 9.5.3 Multi-link Spatial Correlation Functions (10.5.3) 315 9.5.4 Numerical Results and Analysis (10.5.4) 318 9.5.5 Summary (10.5.5) 321 9.6 Non-stationarity models 325 9.7 Measurement-based channel models 325 9.8 System level channel models 325 .0.1 DERIVATION OF DERIVATION OF (9.11) 325 .0.2 DERIVATION OF (9.16) 326 .0.3 DERIVATION OF (9.43)–(9.48) 326 .0.4 DERIVATION OF (9.53) 327 .0.5 DERIVATION OF (9.60) 328 .0.6 COMPARISON BETWEEN THE DOPPLER PSDS WITH DIFFERENT CFS (9.49) AND (9.50) 328 .0.7 DERIVATION OF (9.75B) 329 .0.8 DERIVATION OF THE CONDITION MAX{RT , RR}< MIN{al − al−1} THAT GUARANTEES THE TDL STRUCTURE OF OUR MODEL 331 .0.9 THE REDUCED EXPRESSIONS OF SPATIAL CORRELATION 331 Bibliography 334
CONTENTS 5 A ceof Neeoppler hhe A.2 Simplification of Noise Component in an Objective Function B Derivations of Identities(7.6),(7.8)and(7.7) 341 C Computation of the Gerschgorin Radii C.0.1 A Simulation Study of the Behavior of the As Estimator Bibli C.1 DERIVATION OF (4.20A)AND (4.20B)
CONTENTS 5 A Appendix 335 A.1 Influence of Neglecting Doppler Shift within the Sensing Periods 336 A.2 Simplification of Noise Component in an Objective Function 339 B Derivations of Identities (7.6), (7.8) and (7.7) 341 C Computation of the Gerschgorin Radii 345 C.0.1 A Simulation Study of the Behavior of the AS Estimator 347 Bibliography 347 C.1 DERIVATION OF (4.20A) AND (4.20B) 348 C.2 DERIVATION OF THE CF ρˆhˆhˆ (τ) 349 C.3 Probability density functions 351
Acronyms and Symbols List of Acronyms third ge ration parmership standards bodies Average Estimation Error AoA Azimuth of Arrival Am of Departure ASA Array Size Adaptation CCDF Complementary Cumulative Distribution Functions CMET-EXIP CRIR DFER Doppler Frequency Estimation Range DML Deterministic Maximum Likelihood Expectation-Maximization Elevation of Arrival vion of Departure ESPRIT Es ation of Signal Parameters Via Rotational Invariance Techniques Est. Estimated Multiple Access FHMA Joint Angle and Delay Estimation Line -Of-Sight MODE M-step Maximization step NFD NLOS Non-Line-Of-Sight
Acronyms and Symbols List of Acronyms 3GPP third generation partnership standards bodies AEE Average Estimation Error AoA Azimuth of Arrival AoD Azimuth of Departure AS Azimuth Spread ASA Array Size Adaptation CCDF Complementary Cumulative Distribution Functions CLEAN an iterative beam removing technique COMET-EXIP Covariance Matching Estimator-Extended Invariance Principle CRLB Cramér-Rao Lower Bound DFER Doppler Frequency Estimation Range DML Deterministic Maximum Likelihood DoA Direction of Arrival DoD Direction of Departure EM Expectation-Maximization EoA Elevation of Arrival EoD Elevation of Departure Emp. Empirical ESPRIT Estimation of Signal Parameters Via Rotational Invariance Techniques Est. Estimated E-step Expectation step FB Fisher-Bingham FFHMA Fast Frequency Hopping Multiple Access FHMA Frequency Hopping Multiple Access GAM Generalized Array Manifold GR Gerschgorin Radii ISI Improved Initialization and Search ISM Industrial, Scientific and Medical bands JADE Joint Angle and Delay Estimation LOS Line-Of-Sight MIMO Multiple-Input Multiple-Output ML Maximum Likelihood MODE Method of Direction Estimation M-step Maximization step MUSIC MUtiple SIgnal Classification NC-ML Non-Coherent-Maximum-Likelihood NFD Newton Forward Difference NLOS Non-Line-Of-Sight NSL Normalized Side-lobe Level OMUSIC Orthonormal-basis MUSIC PE Pseudo-Envelope
8 Acronyms and Symbols Pseudo.Noise right-hand side RF Radio Frequency Rx Receiver SAGE Subspace-Alternating Generalized Expectation-maximization SIOD Space-Invariance of Determinant Specular-Scatterer SVD singular-value decomposition SW Switch Time-Division Multiplexed Uniform Linear Array Vec-MUSIC Vector-MUSIC vMF von-Mises-Fisher List of Symbols real line omplex plane he mme rypart of the complex number absolute value of the given argument ix given as an argumen det() determinant of the matrix given as an argument Hermitian of the vector or matrix given as an argument transpose of the given an argument SCkKpodctofhegnemarguneat Dirac delra functior given as an index the projection operator onto the column space of the matrix %
8 Acronyms and Symbols pdf probability density function PSK Phase Shift Keying PN Pseudo-Noise r.h.s. right-hand side RF Radio Frequency RIMAX an iterative maximum likelihood method RMSEE Root Mean Square Estimation Error Rx Receiver SAGE Subspace-Alternating Generalized Expectation-maximization SIOD Space-Invariance of Determinant SML Stochastic Maximum Likelihood SNR Signal-to-Noise-Ratio SS Specular-Scatterer SVD singular-value decomposition SW Switch TDM Time-Division Multiplexed Tx Transmitter ULA Uniform Linear Array Vec-MUSIC Vector-MUSIC vMF von-Mises-Fisher w.r.t. with respect to WSS Wide-Sense-Stationary XPD Cross-Polarization Discrimination List of Symbols R real line C complex plane S p p-dimensional sphere D domains ⊗ Kronecker product ⊙ Hadamard, i.e. element-wise product R{·} real part of the complex number given as an argument I{·} imaginary part of the complex number k · kF Frobenius Form of the vector or matrix given as an argument | · | absolute value of the given argument det(·) determinant of the matrix given as an argument tr(·) trace of the matrix given as an argument (·) H Hermitian of the vector or matrix given as an argument (·) T transpose of the vector or matrix given an argument (·) ∗ complex conjugate of the scalar given as an argument (·) † pseudo inverse of the matrix given as an argument ( · ) scalar product of the given arguments δ(·) the Kronecker delta δ(·) Dirac delta function I(·) an identity matrix of dimension given as an index diag(·) diagonal matrix with diagonal elements listed as argument λd(·) the dth eigen-value of the matrix given as an argument Π(·) the projection operator onto the column space of the matrix given as an argument c(·) array response c ′ (·) the first derivative of the array response
Acronyms and Symbols 9 of kind and order standard deviation of random variable given as an argument parameters with indices specified in a set s in a subset of index tion of the SAGE algorithm output signal from an antenna array the region where the Tx array is confined the region where the path co hep ofthpo he日 a period separatio etween the beginnings of two consecutive measure. wave length the number of antennas in the transmitter site the ocation of the weight ot A(9 of the parameter() Dolkoegorfnominalaimuthofarmal azimuth spread the the radio channe power spectrum of the correlator output in theRxwith respect nel tra nster matrix Ro(r) autocorrelation function of the processiven as the argument in R)(r) ion parameter nominal azimuth ditectonaeae in the Nau ce formula step size in the Newton-Forward-Difference formula a forward shift operator in the Newton-Forward-Difference ovaparameter in the Fisher-Bingham5 distribution
Acronyms and Symbols 9 Γ( · ) the gamma function In ( · ) the modified Bessel function of the first kind and order n σ ( · ) standard deviation of random variable given as an argument θ parameter vector θS parameters with indices specified in a set S in a subset of { 1, . . . , p } θ S˜ parameters with indices listed in the complement of S intersected with { 1, . . . , p } X S hidden-data space for θ S S i index set in the ith iteration of the SAGE algorithm Y ( t ) output signal from an antenna array W ( t ) noise vector D total number of path components R1 the region where the Tx array is confined R2 the region where the Rx array is confined θℓ parameter vector associated with the ℓth path component Aℓ the polarization matrix of the ℓth propagation path fk,m,p(Ω) the field pattern of the mth element of Array k for polarization p u ( t ) the input signal vector Ω a unit direction vector Tt a sounding period Ts a sensing period of a Rx antenna Tr a period separating two consecutive sensing intervals Tcy separation between the beginnings of two consecutive measurement cycles Tg the guard interval σ2w noise variance λ wave length M1 the number of antennas in the transmitter site M2 the number of antennas in the receiver site rk,m the location of the mth element of Array k αℓ,p2,p1 weight of the polarization component with Tx polarization p1 and Rx polarization p 2 Λ( · ) loglikelihood function of the parameter(s) given as an argument ν Doppler frequency φˇ estimation error of nominal azimuth of arrival σφ˜ azimuth spread h(t; θ) the spread function of the radio channel Pd(θ) power spectrum of the dth path component with respect to θ P ( θ ) power spectrum of the correlator output in the Rx with respec t to θ H ( t ) channel transfer matrix H˜ ( t ) channel matrix distorted by noise R ( · ) ( τ ) autocorrelation function of the process given as the argument in the subscript R ( ·)( · ) ( τ ) cross-correlation function of the two processes given as arguments κ concentration parameter φ¯ nominal azimuth σΩ direction spread q differential order in the Newton-Forward-Difference formula h step size in the Newton-Forward-Difference formula ∆ a forward shift operator in the Newton-Forward-Difference formula β ovalness parameter in the Fisher-Bingham 5 distribution
Preface mprove 二 usoid approaches for mod ling the of channel tion of def generic chcaor representing the compos tion o a channel impulse respons Then the models are review of differe applica the dene Then,dborate th ese channel models are selected fo ns bas on the features ant of methods for headon e deombe the chame a dispersive- ruct the s channe used in eling are de sfor different Companng thth poin of book complete stories about channels by linking the methods applied in different stage of channe analysis.Furtherm ore,combining and t ssed in one o wo chapters do not describe ar used for cha s,such as and Mose 1997) (1997),where they are presem d for general We focus on the adaptationo During the book writing procedure,we got help from many of our colleagues and students.To be added
Preface The investigation of the propagation channel becomes more and more important in modern wireless communications. The high demanding of the spectral efficiency motivates exploiting more resources from channels that can be possibly used for communications. Nowadays, a typical trend for designing the physical layer algorithms is to adapt the transceiving strategy by either maximizing the diversity gains or utilizing the coherence of the channels to improve the signal to noise power ratio. Dr. Xiang Cheng and I have been working on the topics relevant with channel characterization for years. My major research has been focused on the measurement-based stochastic channel modeling by using the high-resolution estimates of the channel parameter from real measurement data. Xiang’s work more concentrates on the theoretical modeling of the channels, such as the sum-of-sinusoid approaches for modeling the correlation matrices of channels. This book is intended to cover both theoretical and experimental studies of channels by merging Xiang’s and my study results obtained in the last decade. Most of the contents has been published in journals and conference proceedings. New results that are still under review for publication are also addressed in order to keep the completeness of presentation of specific topics. In general, the book can be viewed as a collection of the latest results in the field of theoretical and experimental channel characterization. This book can be used as a textbook for the courses dedicated for propagation channel characterization, or for part of courses that focus on wireless communication systems and networks. We organize the book in such a way that the chapters are self-contained and can be selected individually for specific topics. We start with illustrating the generic channel models applicable for representing the composition of a channel impulse response. Then the definitions of different channel characteristics in both large-scale and small-scale are given. For exact behavior of the channels represented by these parameters, channel models are necessary. Thus, we give a review of different approaches for modeling the channels. These channel models are selected for applications based on the features of specific communication systems and the designing strategies. Then, we elaborate theoretical scattering-based channel modeling methods and the models obtained for certain scenarios. Another important category of methods for channel analysis is the measurement-based characterization. We describe the channel measurement methodologies, and explain the impacts of the measurement equipments on the observations. The parameters of the generic channel models are extracted by using high-resolution channel parameter estimation methods based on a specular-path model and a dispersive-path model. The estimates of the parameters are used to construct the stochastic channel models. Methods used in the modeling are described. In the end of the book, specific channel models for different communication systems are illustrated. There are already some books dedicated on channel investigations, such as Durgin (2003) Koivunen (Dec 2007) Parsons (2000) Saunders (1999) Pätzold (2002). Comparing with these works, our book includes more introduction of the methods used for the steps of channel characterization, instead of presenting only the final results. From this point of view, our book tells more complete stories about channels by linking the methods applied in different stages of channel analysis. Furthermore, combining the description of theoretical and the empirical methods in one book, helps reader conceive more clearly the merits of these methods. Another feature of the book is that we also cover the methods used for extracting the parameters of generic models. Normally books that channels are addressed in one or two chapters do not describe and comment on the methods used for characterizing channels, such as Correia (2001). However, since the readers usually want to know how realistic the models resulted are, it is important to give a clear view of the underlying methods. The methods described in our book have also been described in Stoica and Moses (1997) McLachlan and Krishnan (1997), where they are presented for general cases. We focus on the adaptation of the methods when being applied for analyzing the propagation channels. The book can be used for textbooks for both undergraduate and graduate students. To be added During the book writing procedure, we got help from many of our colleagues and students.To be added
