Wireless Communications Over Rapidly Time-Varying Channels

✍ Scribed by Franz Hlawatsch, Gerald Matz

• Publisher: sciencedirect
• Year: 2011
• Tongue: English
• Leaves: 435
• Edition: 1
• Category: Library

✦ Table of Contents

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
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