Precoding and Signal Shaping for Digital Transmission

Transcription

1 Precoding and Signal Shaping for Digital Transmission Robert F. H. Fischer The Institute of Electrical and Electronics Engineers, Inc., New York WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION

2 Contents Preface xi 1 Introduction The Structure of the Book Notation and Definitions Signals and Systems Stochastic Processes Equivalent Complex Baseband Signals Miscellaneous 7 References 8 2 Digital Communications via Linear, Distorting Channels Fundamentals and Problem Description Linear Equalization Zero-Forcing Linear Equalization A General Property of the Receive Filter MMSE Filtering and the Orthogonality Principle MMSE Linear Equalization Joint Transmitter and Receiver Optimization 43

3 Vi CONTENTS 2.3 Noise Prediction and Decision-Feedback Equalization Noise Prediction Zero-Forcing Decision-Feedback Equalization Finite-Length MMSE Decision-Feedback Equalization Infinite-Length MMSE Decision-Feedback Equalization Summary of Equalization Strategies and Discrete- Time Models Summary of Equalization Strategies HR Channel Models Channels with Spectral Nulls Maximum-Likelihood Sequence Estimation Whitened-Matched-Filter Front-End Alternative Derivation 112 References Precoding Schemes Preliminaries Tomlinson-Harashima Precoding Precoder Statistical Characteristics of the Transmit Signal Tomlinson-Harashima Precoding for Complex Channels Precoding for Arbitrary Signal Constellations Multidimensional Generalization of Tomlinson-Harashima Precoding Signal-to-Noise Ratio Combination with Coded Modulation Tomlinson-Harashima Precoding and Feedback Trellis Encoding Combination with Signal Shaping Flexible Precoding Precoder and Inverse Precoder Transmit Power and Signal-to-Noise Ratio Combination with Signal Shaping Straightforward Combination with Coded Modulation Combined Coding and Precoding 161

4 CONTENTS Vii Spectral Zeros Summary and Comparison of Precoding Schemes Finite-Word-Length Implementation of Precoding Schemes Two's Complement Representation Fixed-Point Realization of Tomlinson- Harashima Precoding Nonrecursive Structure for Tomlinson-Harashima Precoding Precoding for IIR Channels Extension to DC-free Channels Information-Theoretical Aspects of Precoding Precoding Designed According to MMSE Criterion MMSE Precoding and Channel Capacity 203 References 211 Signal Shaping Introduction to Shaping Measures of Performance Optimal Distribution for Given Constellation Ultimate Shaping Gain Bounds on Shaping Lattices, Constellations, and Regions Performance of Shaping and Coding Shaping Properties of Hyperspheres Shaping Under a Peak Constraint Shaping on Regions AWGN Channel and Shaping Gain Shell Mapping Preliminaries Sorting and Iteration on Dimensions Shell Mapping Encoder and Decoder Arbitrary Frame Sizes General Cost Functions Shell Frequency Distribution Trellis Shaping Motivation Trellis Shaping on Regions 289

5 WW CONTENTS Practical Considerations and Performance Shaping, Channel Coding, and Source Coding Spectral Shaping Further Shaping Properties Approaching Capacity by Equiprobable Signaling AWGN Channel and Equiprobable Signaling Nonuniform Constellations Warping Modulus Conversion 328 References Combined Precoding and Signal Shaping Trellis Precoding Operation of Trellis Precoding Branch Metrics Calculation Shaping Without Scrambling Basic Principle Decoding and Branch Metrics Calculation Performance of Shaping Without Scrambling Precoding and Shaping under Additional Constraints Preliminaries on Receiver-Side Dynamics Restriction Dynamics Limited Precoding Dynamics Shaping Reduction of the Peak-to-Average Power Ratio Geometrical Interpretation of Precoding and Shaping Combined Precoding and Signal Shaping Limitation of the Dynamic Range Connection to Quantization and Prediction 397 References 400 Appendix A Wirtinger Calculus 405 A. 1 Real and Complex Derivatives 406 A.2 Wirtinger Calculus 407 A.2.1 Examples 408 A.2.2 Discussion 410 A.3 Gradients 411 A.3.1 Examples 411 A.3.2 Discussion 412 References 413

6 CONTENTS ix Appendix В Parameters of the Numerical Examples 415 B.l Fundamentals of Digital Subscriber Lines 415 B. 2 Single-Pair Digital Subscriber Lines 417 B.3 Asymmetric Digital Subscriber Lines 418 References 420 Appendix С Introduction to Lattices 421 C.l Definition of Lattices 421 C.2 Some Important Parameters of Lattices 425 C.3 Modifications of Lattices 428 C.4 Sublattices, Cosets, and Partitions 430 C.5 Some Important Lattices and Their Parameters 434 References 437 Appendix D Calculation of Shell Frequency Distribution 439 D.l Partial Histograms 440 D.2 Partial Histograms for General Cost Functions 444 D.3 Frequencies of Shells 445 References 453 Appendix E Preceding for MIMO Channels 455 E.l Centralized Receiver 456 E.l.l Multiple-lnput/Multiple-Output Channel 456 E.l.2 Equalization Strategies for MIMO Channels 457 E.1.3 Matrix DFE 459 E.l.4 Tomlinson-Harashima Preceding 460 E.2 Decentralized Receivers 465 E.2.1 Channel Model 465 E.2.2 Centralized Receiver and Decision-Feedback Equalization 466 E.2.3 Decentralized Receivers and Preceding 466 E.3 Discussion 468 E.3.1 ISI Channels 468 E.3.2 Application of Channel Coding 469 E.3.3 Application of Signal Shaping 470 E.3.4 Rate and Power Distribution 470 References 471 Appendix F List of Symbols, Variables, and Acronyms 475

7 X CONTENTS F.l Important Sets of Numbers and Constants 475 F.2 Transforms, Operators, and Special Functions 476 F.3 Important Variables 478 F.4 Acronyms 479 Index 483