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Space-Time Wireless Channels

Space-Time Wireless Channels

by Gregory D. Durgin
Publisher: Prentice Hall
Release Date: October 2002
ISBN: 013065647X
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Book Description

A practical, "first-principles" approach to space-time wireless channel design.

  • A practical approach to space-time wireless channel design

  • Integrates essential principles from communications, electromagnetics, and random process theory

  • Includes detailed coverage of diversity, multipath applications, and antenna array design

  • Contains extensive examples, illustrations, and problem sets

Next-generation broadband radio systems must deliver unprecedented performance and higher data rates, while coping with increased spectral congestion. To achieve these goals, engineers need an in-depth understanding of radio channels that fade in time, frequency, and space. In Space-Time Wireless Channels, leading researcher Gregory D. Durgin presents a pragmatic, first-principles approach that integrates crucial concepts and techniques from communications, electromagnetics, and random process theory.

Durgin focuses on comprehension and practicality, offering extensive examples, illustrations, and problem sets, while avoiding gratuitious mathematics and moving most derivations to end-of-chapter appendices. Coverage includes:

  • Fundamentals of space, time, and frequency transmission and random process theory

  • Electromagnetic description of space-time channels and the physics of small-scale fading

  • First- and second-order statistics of fading channels

  • Angle spectrum concepts and applications, including vector/scalar space and multipath shape factors

  • Antenna diversity, temporal diversity, and bit error rates

  • Multipath channels: separation, signaling, block coding, and antenna array design

Appendices list special functions, Fourier transform examples, and random process theory concepts, as well as all relevant mathematical symbols, conventions, and acronyms.

Table of Contents

  1. Copyright
    1. Dedication
  2. Prentice Hall Communications Engineering and Emerging Technologies Series
  3. Preface
  4. 1. Introduction
    1. 1.1. Perspectives in Propagation
      1. 1.1.1. Early Years of Radio
      2. 1.1.2. Cellular on the Scene
      3. 1.1.3. Origins of Channel Modeling
      4. 1.1.4. Rayleigh Pessimism
        1. Fade Margin
        2. Update Rate
        3. Changing Paradigm
      5. 1.1.5. Channels with Multiple Dependencies
    2. 1.2. The Case for Space
      1. 1.2.1. Complexities of Wireless Channels
      2. 1.2.2. Channel Primacy in Communications
      3. 1.2.3. Wasted Space
    3. 1.3. Trends in Wireless Communications
      1. 1.3.1. Higher and Higher Data Rates
      2. 1.3.2. Ubiquity of Wireless Devices
      3. 1.3.3. Smart Antennas
      4. 1.3.4. Faster, Smaller, Cheaper Hardware
      5. 1.3.5. Frequency Congestion
      6. 1.3.6. Multiple-Input, Multiple-Output Systems
    4. 1.4. About This Book
      1. 1.4.1. The Basic Disciplines
      2. 1.4.2. Contents
      3. 1.4.3. Features of This Book
  5. 2. Signal Transmission
    1. 2.1. Baseband Representation
      1. 2.1.1. Signal Spectrum
      2. 2.1.2. Signal Modulation
      3. 2.1.3. Inverse Modulation
      4. 2.1.4. The Baseband Channel
      5. 2.1.5. Time-Invariant Versus Time-Varying Channels
      6. 2.1.6. Detection Terminology
    2. 2.2. Channel Coherence
      1. 2.2.1. Coherence Versus Selectivity
      2. 2.2.2. Temporal Coherence
      3. 2.2.3. Frequency Coherence
      4. 2.2.4. Spatial Coherence
        1. Large-Scale Versus Small-Scale Fading
        2. Mobile Fading
    3. 2.3. Using the Complete Baseband Channel
      1. 2.3.1. Spectral Domain Representations
      2. 2.3.2. General Signal Transmission
      3. 2.3.3. Time-Invariant Channel Transmission
      4. 2.3.4. Mobile Receiver Transmission
    4. 2.4. Chapter Summary
    5. Problems
  6. 3. Random Fading Channels
    1. 3.1. Channel Correlation
      1. 3.1.1. The Meaning of Correlation
      2. 3.1.2. Autocorrelation Relationships
      3. 3.1.3. Autocovariance
      4. 3.1.4. Unit Autocovariance
    2. 3.2. Power Spectral Density (PSD)
      1. 3.2.1. Correlation in Spectral Domains
      2. 3.2.2. The Wiener-Khintchine Theorem
      3. 3.2.3. Statistics with Three-Dimensional Space
      4. 3.2.4. Summary of Single-Dependency PSDs
    3. 3.3. Joint Statistics
      1. 3.3.1. Joint Autocorrelation and Spectrum
      2. 3.3.2. Time–Frequency Transform Map
      3. 3.3.3. Space–Frequency Transform Map
      4. 3.3.4. Complete Transform Map
    4. 3.4. Width of the PSD
      1. 3.4.1. RMS Delay Spread
      2. 3.4.2. RMS Doppler Spread
      3. 3.4.3. RMS Wavenumber Spread
      4. 3.4.4. Channel Duality Principle
      5. 3.4.5. Definition of a Rate Variance
      6. 3.4.6. Fundamental Spectral Spread Theorem
    5. 3.5. Chapter Summary
    6. Problems
  7. 4. Physics Of Small-Scale Fading
    1. 4.1. Plane Wave Representation
      1. 4.1.1. Electromagnetic Fields and Received Signals
        1. The Physical Channel Convention
        2. The Normalized Channel Convention
      2. 4.1.2. The Maxwellian Basis
      3. 4.1.3. Homogeneous Plane Waves
      4. 4.1.4. Inhomogeneous Plane Waves
      5. 4.1.5. Homogeneous Versus Inhomogeneous Plane Waves
        1. An Analogy From Circuit Theory
        2. Analogy to Free-Space Plane Waves
    2. 4.2. The Local Area
      1. 4.2.1. Definition of a Local Area
      2. 4.2.2. Scatterer Proximity
      3. 4.2.3. A Wideband Plane Wave
        1. Adding Signal Bandwidth
        2. Adding More Bandwidth
      4. 4.2.4. The Bandwidth-Distance Threshold
    3. 4.3. Wave Groupings for Multipath Components
      1. 4.3.1. Specular Wave Component
      2. 4.3.2. Nonspecular Wave Component
      3. 4.3.3. Diffuse Wave Component
      4. 4.3.4. Reduced Wave Grouping
    4. 4.4. The SLAC Model
      1. 4.4.1. Stochastic Model
      2. 4.4.2. Random Phases
      3. 4.4.3. Other Random Quantities
      4. 4.4.4. Random Phase Models
        1. Uncorrelated Phases
        2. Independent Phases
      5. 4.4.5. Fourier Transforms
      6. 4.4.6. Autocorrelation Functions
      7. 4.4.7. Heterogeneous Scattering
      8. 4.4.8. SLAC Power Spectral Density
        1. Diffuse Components
        2. Specular Components
    5. 4.5. Chapter Summary
    6. Problems
  8. 5. First-Order Channel Statistics
    1. 5.1. Mean Received Power
      1. 5.1.1. Average Versus Received Power
      2. 5.1.2. Stationarity
      3. 5.1.3. Mean U-SLAC Power
      4. 5.1.4. Frequency and Spatial Averaging
      5. 5.1.5. Ergodicity
    2. 5.2. Envelope Probability Density Functions
      1. 5.2.1. Notes and Concepts
      2. 5.2.2. Characteristic Functions
      3. 5.2.3. Specular Characteristic Function
      4. 5.2.4. Diffuse, Nonspecular Characteristic Function
      5. 5.2.5. The I-SLAC PDF Generator
    3. 5.3. Closed-Form PDF Solutions
      1. 5.3.1. The One-Wave PDF
      2. 5.3.2. The Two-Wave PDF
      3. 5.3.3. The Three-Wave PDF
      4. 5.3.4. The Rayleigh PDF
      5. 5.3.5. The Rician PDF
    4. 5.4. Two-Wave with Diffuse Power PDF
      1. 5.4.1. Approximate Representation
      2. 5.4.2. Graphical Analysis
      3. 5.4.3. Rayleigh and Rician Approximations
      4. 5.4.4. TWDP PDF Applications
      5. 5.4.5. Closing Remarks on TWDP Fading
    5. 5.5. Chapter Summary
    6. Problems
    7. 5.A. Envelope Characteristic Functions
  9. 6. The Angle Spectrum
    1. 6.1. Vector and Scalar Space
      1. 6.1.1. Scalar Collapse of Position Vectors
      2. 6.1.2. Scalar Collapse of Wavevectors
    2. 6.2. Angle Spectrum Concepts
      1. 6.2.1. Definition of the Angle Spectrum
      2. 6.2.2. Mapping Angles to Wavenumbers
      3. 6.2.3. From-the-Horizon Propagation
      4. 6.2.4. Summary of Angle Spectrum Concepts
    3. 6.3. Multipath Shape Factors
      1. 6.3.1. Definition of Shape Factors
        1. Angular Spread
        2. Angular Constriction
        3. Azimuthal Direction of Maximum Fading
      2. 6.3.2. Basic Wavenumber Spread Relationship
      3. 6.3.3. Comparison to Omnidirectional Propagation
    4. 6.4. Illustrative Examples
      1. 6.4.1. Two-Wave Channel Model
      2. 6.4.2. Sector Channel Model
      3. 6.4.3. Double-Sector Channel Model
      4. 6.4.4. Rician Channel Model
    5. 6.5. Chapter Summary
    6. Problems
  10. 7. Second-Order Channel Statistics
    1. 7.1. The Level-Crossing Problem
      1. 7.1.1. Level-Crossing Rate
      2. 7.1.2. Average Fade Duration
      3. 7.1.3. Level Crossing in Frequency
      4. 7.1.4. Level Crossing in Space
    2. 7.2. Envelope Unit Autocovariance
      1. 7.2.1. Temporal Unit Autocovariance
      2. 7.2.2. Frequency Unit Autocovariance
      3. 7.2.3. Spatial Unit Autocovariance
      4. 7.2.4. Joint Unit Autocovariance
      5. 7.2.5. Second-Order Statistic Summary
    3. 7.3. Classical Spatial Channel Models
      1. 7.3.1. Classical Models
      2. 7.3.2. Channel Model Solutions
      3. 7.3.3. Additional Comments
    4. 7.4. Properties of Wideband Channels
      1. 7.4.1. Discrete Wideband Channels
      2. 7.4.2. Time-Varying Wideband Channels
      3. 7.4.3. Discrete Transmission
      4. 7.4.4. Notes on Temporal Modeling
      5. 7.4.5. Rician Fading in Time-Varying Channels
    5. 7.5. Chapter Summary
    6. Problems
    7. 7.A. Approximate Spatial Autocovariance
    8. 7.B. Classical Envelope Autocovariance
    9. 7.C. Rician Mean Approximation
  11. 8. Diversity
    1. 8.1. Diversity Concept
      1. 8.1.1. The Role of Diversity
      2. 8.1.2. Antenna Diversity
      3. 8.1.3. Temporal Diversity
      4. 8.1.4. Diversity Failure
    2. 8.2. Combining Techniques
      1. 8.2.1. Gain Combining
      2. 8.2.2. Signal Envelope for Gain Combining
      3. 8.2.3. Switch Combining
      4. 8.2.4. Two-Branch Example
    3. 8.3. BER and Capacity
      1. 8.3.1. BER for Nonfading Channels
      2. 8.3.2. BER for Fading Channels
      3. 8.3.3. Fading Channel Capacity
      4. 8.3.4. Empirical BER and Capacity
      5. 8.3.5. Diversity Gain for Multiple Branches
      6. 8.3.6. Illustration of Branch Correlation on Diversity
      7. 8.3.7. Illustration of Unequal Branch Power on Diversity
    4. 8.4. Chapter Summary
    5. Problems
  12. 9. MIMO Channels
    1. 9.1. Conventional Multiple Antenna Systems
      1. 9.1.1. Single-Input, Single-Output (SISO)
      2. 9.1.2. Single-Input, Multiple-Output (SIMO)
      3. 9.1.3. Multiple-Input, Single-Output (MISO)
      4. 9.1.4. Multiple-Input, Multiple-Output (MIMO)
    2. 9.2. Separating Channels in Multipath
      1. 9.2.1. MIMO Channel Matrix
      2. 9.2.2. Processing the MIMO Signal
        1. At the Transmitter
        2. At the Receiver
        3. Singular Value Decomposition
      3. 9.2.3. Separate Channels
      4. 9.2.4. Formal Capacity Expressions
      5. 9.2.5. MIMO Channels with Impaired Capacity
        1. Absence of Multipath
        2. Channel Correlation
        3. Unequal Average Branch Power
        4. Keyhole Channel
    3. 9.3. Practical MIMO Signaling
      1. 9.3.1. Practical Signal Extraction
      2. 9.3.2. Transmission Technique
      3. 9.3.3. Subtraction of Interference
      4. 9.3.4. Layered Reception Technique
    4. 9.4. Space–Time Block Coding
      1. 9.4.1. MISO Revisited
      2. 9.4.2. Space–Time Block Codes
      3. 9.4.3. Other Codes
    5. 9.5. Chapter Summary
    6. Problems
  13. 10. Array Design in Multipath
    1. 10.1. Rules of Spatial Decorrelation
      1. 10.1.1. Co-polar Versus Dissimilar Antenna Elements
      2. 10.1.2. Approximate Autocovariance
      3. 10.1.3. Forbidden Zones of Correlation
      4. 10.1.4. Coupling Considerations
      5. 10.1.5. Random Orientation
    2. 10.2. Modeling Double Spatial Dependencies
      1. 10.2.1. SLAC Modeling Technique for MIMO Channels
      2. 10.2.2. Double Spatial Channel Correlation
      3. 10.2.3. Example Model
    3. 10.3. Example System
      1. 10.3.1. Problem Statement
      2. 10.3.2. Angle-of-Arrival Models
      3. 10.3.3. Base-Station Design
      4. 10.3.4. User Terminal Design
    4. 10.4. Peer-to-Peer Space–Time Measurements
      1. 10.4.1. The Peer-to-Peer Channel
      2. 10.4.2. Description of Peer-to-Peer Measurement Technique
      3. 10.4.3. Delay Dispersion Results
      4. 10.4.4. Angle Dispersion Results
      5. 10.4.5. Joint Angle-Delay Statistics
    5. 10.5. Chapter Summary
    6. Problems
    7. 10.A. Description of Measured Parameters
      1. 10.A.1. Noncoherent Channel Measurements
      2. 10.A.2. Power Spectra
      3. 10.A.3. Time Delay Parameters
      4. 10.A.4. Angle-of-Arrival Parameters
  14. A. Special Functions
    1. A.1. Singularity Functions
    2. A.2. Sinc Function
    3. A.3. Gamma Function
    4. A.4. Bessel Functions
    5. A.5. Complete Elliptic Integral Functions
    6. A.6. Q-function
  15. B. Fourier Analysis
    1. B.1. Basic Fourier Transform Definitions
    2. B.2. Time–Doppler Transforms
    3. B.3. Frequency–Delay Transforms
    4. B.4. Space–Wavenumber Transforms
    5. B.5. Trigonometric Relationships
  16. C. Random Process Theory
    1. C.1. Definitions
      1. C.1.1. Random Variables
      2. C.1.2. Random Processes
    2. C.2. Probability Density Functions
      1. C.2.1. Definitions
      2. C.2.2. Joint Distributions
      3. C.2.3. Computing Statistics
    3. C.3. Functions of Random Variables
      1. C.3.1. Functions With Inverses
      2. C.3.2. Multiroot Functions
  17. D. Glossary
    1. D.1. Mathematical Symbols and Conventions
    2. D.2. Acronym List
  18. Bibliography