Description
Optimal-Peak-Sidelobe Polyphase Code is an in-depth guide to efficiently designing optimal-peak-sidelobe polyphase codes. The search for low-sidelobe polyphase codes has challenged researchers since World War II, but the exponential computational complexity of the problem ensures that new insights and algorithms continue to emerge. This resource provides working algorithms and computer code to find ways to build optimal peak sidelobe polyphase codes and code sets. The goal of this book is to narrow the focus to optimal polyphase codes, so as to give a practical limit to the topic, and then to provide readers with the most valuable insights and most efficient algorithms available.
Given the demanding timelines of radar and communication system development, this book serves as a practical guide to implementing efficient search methods without starting from scratch. Readers will encounter intriguing connections to Algebraic Group Theory, Combinatorics, and advanced mathematical techniques that drive efficiency in code search and optimization.
Whether developing cutting-edge radar waveforms or refining signal processing techniques, this book delivers the tools and knowledge needed to push the boundaries of performance and efficiency. Beyond radar waveform design, the principles explored in this book hold significant relevance for professionals in communications, radio astronomy, and laser optics, where signal integrity and sidelobe suppression are critical. includes combinatorics, quantum sensing, cognitive architectures, and interference mitigation in sensor systems.
Table Of Contents
1 Preface
1.1 References
2 Introduction
2.1 Elements of the History of Radar
2.2 Radar Signals
2.3 Pulse Compression
2.4 References
3 Building the Framework
3.1 Background and Fundamentals
3.2 The Phase-Coded Pulse
3.3 Computing the Discrete Ambiguity Function
3.4 References
4 Binary Code Classes and Properties
4.1 The Binary Barker Codes
4.2 Minimum Peak Sidelobe (MPS) Codes
4.3 Legendre Sequences
4.4 m-Sequences
4.5 Rudin-Shapiro Sequence
4.6 Skew-Symmetric Codes
4.7 Some Properties of Binary Codes
4.8 Binary Phase Code Issues
4.9 References
5 The Search of Optimal-PSL Binary Codes
5.1 Computational Complexity
5.2 Search Approaches
5.3 Results to Date
5.4 Low-Level Operations
5.5 Littlewood Polynomials
5.6 The Coupon Collector Problem
5.7 Understanding the Binary Phase PSL Optimization Space
5.8 References
6 Polyphase Code Classes and Properties
6.1 Moving Beyond Binary
6.2 Some Constructible Polyphase Code Classes
6.3 Polyphase Code Properties
6.4 References
7 The Search for Optimal-PSL Polyphase Codes
7.1 Computational Effort
7.2 Cases for Which Search is Obviated
7.3 Algorithms for Optimal-PSL Searches
7.4 Success From an Atypical Approach
7.5 Generalized Barker Sequences
7.6 Issues With Polyphase Codes
7.7 Appendix
7.8 References
8 Beyond the Single Code – Complementary Code Sets
8.1 Motivation
8.2 Need for Separation
8.3 Some History
8.4 Definitions and Properties
8.5 Algebraic Formulation and Golay Pairs
8.6 Binary Complementary Code Matrices (CCMs)
8.7 The Row-Correlation Function
8.8 Necessary Condition Involving Sum of Squares
8.9 Construction Techniques for CCMs
8.10 Hadamard Matrices
8.11 Orthogonality Versus Complementarity
8.12 Swap Sets
8.13 Doppler Sensitivity
8.14 Applications
8.15 References
9 Polyphase Complementary Code Sets
9.1 Polyphase Complementary Code Sets
9.2 Polyphase Complementary Code Matrices
9.3 The Row-Correlation Function
9.4 Search Space and Equivalence Classes
9.5 Search Algorithm
9.6 Constructions
9.7 Polyphase Golay Pairs
9.8 Quad-phase CCMs - Search Results
9.9 Butson Hadamard Matrices
9.10 References
10 Developments Impacting Future Searches
10.1 Introduction
10.2 Evolving Design Tradeoffs
10.3 Optimization Options
10.4 References
10.5 Appendix – Codes for the PSLs in Table IV