Wireless Communications Over Rapidly Time-Varying Channels

Description

Wireless Communications Over Rapidly Time-Varying Channels Contributing Authors About the Editors Preface Notations and Symbols Basic Notations Basic Symbols Transceiver and Channel Parameters Channel and Signal Representations Special Functions and Signals Vectors, Matrices, and Operators Probability, Random Variables, and Random Processes Abbreviations Fundamentals of Time-Varying Communication Channels Introduction The Physics of Time-Varying Channels Wave Propagation Multipath Propagation and Time Dispersion Doppler Effect and Frequency Dispersion Path Loss and Fading Spatial Characteristics Deterministic Description Delay-Doppler Domain – Spreading Function Delay-Scale Domain – Delay-Scale Spreading Function Time-Frequency Domain – Time-Varying Transfer Function Time-Delay Domain – Time-Varying Impulse Response Extension to Multiantenna Systems Stochastic Description WSSUS Channels The WSS, US, and WSSUS Properties Scattering Function and TF Correlation Function Statistical Input–Output Relations Delay and Doppler Profiles, Time and Frequency Correlation Functions Global Channel Parameters Extension to Multiantenna Systems Scattering Function Matrix and Space-Time-Frequency Correlation Function Matrix Canonical Decomposition Non-WSSUS Channels Local Scattering Function and Channel Correlation Function Reduced-Detail Channel Descriptions Global Channel Parameters Underspread Channels Dispersion-Underspread Property Correlation-Underspread Property Approximate Eigenrelation Approximate Eigenfunctions Approximate Eigenvalues Time-Frequency Sampling Approximate Karhunen–Loève Expansion Parsimonious Channel Models Basis Expansion Models Complex Exponential (Fourier) Basis Polynomial Basis Slepian Basis Parsimonious WSSUS Models AR, MA, and ARMA Models Other Parametric WSSUS Models Parsimonious Non-WSSUS Models Non-WSSUS ARMA Models BEM Statistics Measurement Spread-Spectrum-Like Channel Sounding Idealized Impulse-Train Sounder Generic Correlative Channel Sounder Model Sounder Types Measurement Errors Multicarrier Channel Sounding Multicarrier Basics Measurement Principle Measurement Errors Extension to Multiantenna Systems Measurement of Second-Order Statistics Nonparametric Estimation Parametric Estimation Non-WSSUS Case Conclusion Acknowledgment References Information Theory of Underspread WSSUS Channels The Role of a System Model A Realistic Model A Brief Literature Survey Capacity Bounds Answering Engineering-Relevant Questions A Discretized System Model The Channel Model Continuous-Time Input–Output Relation The Underspread Assumption Continuous-Time Channel Model and Capacity Discretization of the Continuous-Time Input–Output Relation Sampling and Basis Expansion Discretization through Channel Eigendecomposition Discretization through Transmission and Reception on a Weyl-Heisenberg Set Construction of WH Sets Diagonalization and Loss of Degrees of Freedom Large-Bandwidth and High-SNR Regimes The Large-Bandwidth Regime: Diagonalized I/O Relation Power Constraints Definition of Noncoherent Capacity A Coherent-Capacity Upper Bound An Upper Bound on Capacity that Is Explicit In CH(τ, v) Bounding Idea The Actual Bound Some Simplifications Impact of Channel Characteristics Channel spread Shape of the scattering function A Lower Bound on Capacity Bounding Idea The Actual Bound Some Approximations A Numerical Example Extension to the Multiantenna Setting Modeling Multiantenna Channels – A Formal Extension Capacity Bounds for MIMO Channels in the Large-Bandwidth Regime The Upper Bound The Lower Bound Numerical Examples The Large-Bandwidth Regime: I/O Relation with Interference A Lower Bound on Capacity The Bounding Idea A lower bound on the first term An upper bound on the second term Completing the bound The Actual Bound Large-Bandwidth Approximation Reduction to a Square Setting Maximization of the Lower Bound Numerical Examples The High-SNR Regime A Lower Bound on Capacity Some Remarks on the Lower Bound Numerical Examples Conclusions References Algebraic Coding for Fast Fading Channels Introduction Fading Channel Model System Model Product Distance Based Code Design Signal Space Diversity and Product Distance Lattice Constellations Lattices First Definitions Sublattices and Equivalent Lattices Algebraic Number Theory Algebraic Number Fields Integral Basis and Canonical Embeddings Algebraic Lattices Ideal Lattices Algebraic Rotations with High Product Distance Zn Ideal Lattices Rotated Zn–Lattice Codes A Simple Two-Dimensional Rotation Based on the Golden Number The Cyclotomic Construction Sphere Decoding The Sphere Decoder Algorithm The Sphere Decoder with Fading Performance of Rotated Constellations Conclusions References Estimation of Time-Varying Channels – A Block Approach Introduction System and Channel Model System Model OFDM System with CP Single-Carrier System with CP BEM Channel Model Channel Estimation Based on a Single Block Introduction Channel Estimation Data Model Single-Carrier System with CP OFDM System with CP Channel Estimators The LMMSE Estimator The Least-Squares Estimator An Iterative BLUE Optimization of l Channel Identifiability Channel Identifiability for Single-Carrier System Channel Identifiability for OFDM System Simulation Results Results for the OFDM System Results for the Single-Carrier System Channel Estimation Based on Multiple Blocks Introduction Data Model and BEM for Multiple OFDM Symbols Channel Identifiability Based on Multiple Blocks Simulation Results Extension to MIMO Systems Introduction Single-Carrier System OFDM System Adaptive Channel Estimation Conclusions References Pilot Design and Optimization for Transmission over Time-Varying Channels Introduction Pilot Design: A Framework Modeling of Pilot-Assisted Transmission The Multidimensional PAT Model Power Constraints Transceiver Architectures Performance Criteria Information-Theoretic Metrics Channel Estimation: Mean Square Error and Cramér-Rao Bound Source Estimation: BER, Error-Exponent Function, and MSE Optimal TDM Pilot Insertion Pattern in Single Carrier Systems Channel Model Periodic TDM Pilot Placement Receiver Structure Optimization Criteria Optimal TDM Pilot Placement Bibliographical Notes Training Design for Block Fading Channels Training Design for Fast Fading Channels Training Design for Doubly Selective Channels Alternative Pilot Insertion Strategy – Superimposed Training Kalman Tracking with Superimposed Training Superimposed versus TDM Schemes: Performance Comparison Bibliographical Notes Resource Allocation: Amount of Training and Power Optimization Cutoff Rate Analysis Energy Allocation Amount of Training Bibliographical Notes Pilot Design for MIMO Channels Pilot Design for Wideband Systems OFDMA Systems CDMA Systems Ultra Wideband Conclusion Acknowledgment Appendix The Kalman Filter for TDM Training Proof of Proposition 5.1 Proof of Lemma 5.1 Proof of Theorem 5.1 References Equalization of Time-Varying Channels Introduction System Model Basic Assumptions The Structure of the Effective Channel Matrix Q Single-Carrier Modulation/Demodulation Time-Frequency Concentrated Modulation/Demodulation Other Modulation/Demodulation Schemes Coherent Equalization Coherent Equalization Criteria Hard Symbol or Bit Estimates Complex-Field Symbol Estimates Soft Bit Estimates Coherent Equalization Tools Trellis-Based Equalization Linear Equalization Decision Feedback Equalization Equalization Based on Tree Search Iterative Soft Equalization Remarks on Complexity Coherent Equalization for Time-Frequency Concentrated Modulation/Demodulation Fast Serial Equalization Fast Joint Equalization Other Approaches to Equalization for Time-Frequency Concentrated Schemes Coherent Equalization for Single-Carrier Modulation/Demodulation Frequency-Domain Equalization Other Approaches to Equalization for Single-Carrier Schemes Noncoherent Equalization Noncoherent System Model Noncoherent Equalization Criteria Hard Symbol Estimates Complex-Field Symbol Estimates Soft Bit Estimates Noncoherent Equalization Tools Suboptimality of Trellis-Based Noncoherent Equalization Noncoherent Equalization through Per-Survivor Processing Iterative Noncoherent Equalization through the EM Algorithm Other Noncoherent Equalization Schemes Noncoherent Equalization for Single-Carrier Modulation/Demodulation Near-Optimal Trellis-PSP Equalization for Single-Carrier Schemes Reduced-Complexity Trellis-PSP Equalization for Single-Carrier Schemes Near-Optimal Tree-PSP Equalization for Single-Carrier Schemes Iterative Noncoherent Equalization for Single-Carrier Schemes Noncoherent Equalization for Time-Frequency Concentrated Modulation/Demodulation Conclusion Appendices Derivation of Posterior LLR Expression (6.36) Derivation of the Noncoherent MLSD Expression (6.73) Explanation of EM Recursion (6.91) Info EM(B) Algorithms for Noncoherent Equalization References OFDM Communications over Time-Varying Channels OFDM Systems System Model LTI Channels and One-Tap Equalizers OFDM Standards Effects of Rapidly Time-Varying Channels ICI and SINR Analysis BER Performance with One-Tap Equalizers MIMO-OFDM ICI Mitigation Techniques Linear Equalization Serial Equalizers Block Equalizers Receiver Windowing Performance-Complexity Trade-Off Nonlinear Equalization Decision-Feedback Equalizers ICI Cancellers Near-ML Equalizers Iterative and Turbo Approaches Performance-Complexity Trade-Off Transmitter Preprocessing Data Precoding Pulse Shaping and Transmitter Windowing Extension to MIMO-OFDM OFDM with Spatial Multiplexing OFDM with Space-Time-Frequency Coding Time-Varying Channel Estimation Basis Expansion Model of LTV Channels Training-Based Channel Estimation Estimation with Optimal Frequency-Domain Training Estimation with Suboptimal Training Data-Aided Channel Estimation and Tracking Iterative Channel Estimation and Turbo Equalization Impact of Channel Estimation on BER Performance Channel Estimation in MIMO-OFDM Concluding Remarks System and Application Aspects Open Issues References Multiuser MIMO Receiver Processing for Time-Varying Channels Introduction Multiuser MIMO Systems Tools for Complexity Reduction Iterative Approximation of the MAP Detector Reduced-Rank Model for the Time-Varying Channel The Krylov Subspace Method Basic Idea The Algorithm Sphere Decoding Dimensionality Reduction Sphere Decoding Iterative Multiuser MIMO Time-Varying Channel Estimation Signal Model Reduced-Rank LMMSE Channel Estimator Comparison of the Slepian and Fourier Bases Krylov Approximation of the Reduced-Rank LMMSE Channel Estimator Linear Joint Antenna Multiuser Detection Multiuser Detection in Chip Space Multiuser Detection in User Space Nonlinear Detection Exploiting the Reduced-Rank Channel Model Soft Sphere Decoding Definition of Log-Likelihood Ratios Explicit Computation of Extrinsic Probabilities Computational Complexity Hard Sphere Decoder Soft Sphere Decoder Simulation Results Bit Error Rate Comparison Computational Complexity Comparison Conclusions Acknowledgments Appendix Computation of the Log-Likelihood Ratio (8.44) References Time-Scale and Dispersive Processing for Wideband Time-Varying Channels Introduction Need for Wideband Channel Characterizations Examples of Wideband Dispersive Channel Characteristics Chapter Organization Narrowband Channel Characterization Narrowband Spreading Function Discrete Channel Characterization and Finite Approximations Wideband Delay-Scale Channel Characterization Narrowband and Wideband Conditions Wideband Spreading Function Discrete Delay-Scale Channel Characterization Finite Approximations Multipath-Scale Diversity Time-Scale Rake Receiver Wideband Dispersive Channel Characterization Dispersive Time-Frequency Structures Dispersive Spreading Function and Unitary Warping Relations Discrete Dispersive Channel with Physical Limitations Generalized Time-Frequency Rake Receiver Underwater Wireless Communication Channels Shallow Water Environment Model Time-Frequency Characteristics of Shallow Water Environments Mode Separation in Time-Frequency Dispersion Diversity Receiver Design Numerical Simulations for Shallow Water Communications Application Example Conclusions References Index A B C D E F G H I J K L M N O P Q R S T U V W Y Z