Radar Waveform Design based on Optimization Theory (Radar, Sonar and Navigation)

This book provides an overview of radar waveform synthesis obtained as the result of computational optimization processes and covers the most challenging application fields. The book balances a practical point of view with a rigorous mathematical approach corroborated with a wealth of numerical study cases and some real experiments. Additionally, the book has a cross-disciplinary approach because it exploits cross-fertilization with the recent research and discoveries in optimization theory. The material of the book is organized into ten chapters, each one completed with a comprehensive list of references. The following topics are covered: recent advances of binary sequence designs and their applications; quadratic optimization for unimodular sequence synthesis and applications; a computational design of phase-only (possibly binary) sequences for radar systems; constrained radar code design for spectrally congested environments via quadratic optimization; robust transmit code and receive filter design for extended targets detection in clutter; optimizing radar transceiver for Doppler processing via non-convex programming; radar waveform design via the majorization-minimization framework; Lagrange programming neural network for radar waveform design; cognitive local ambiguity function shaping with spectral coexistence and experiments; and relative entropy based waveform design for MIMO radar. Targeted at an audience of radar engineers and researchers, this book provides thorough and up-to-date coverage of optimisation theory for radar waveform design. Contents About the editors Foreword Notation 1. On recent advances of binary sequence designs and their applications | Ronghao Lin and Jian Li 1.1 Introduction 1.2 Algebraic methods 1.2.1 Barker sequences 1.2.2 Legendre sequences 1.2.3 m-Sequences 1.2.4 Gold sequences 1.2.5 Almost perfect autocorrelation sequences 1.2.6 Summary 1.3 Computation algorithms 1.3.1 Iterative twisted approximation 1.3.2 CD algorithm 1.3.3 CAN(PeCAN) family of algorithms 1.3.4 Summary 1.4 Conclusions References 2. Quadratic optimization for unimodular sequence synthesis and applications | Guolong Cui, Xianxiang Yu, Goffredo Foglia, Yongwei Huang, and Jian Li 2.1 Introduction 2.2 Problem formulation 2.3 Iterative algorithms for both the continuous and discrete phase cases 2.3.1 Iterative algorithm for continuous phase case 2.3.2 Iterative algorithm for discrete phase case 2.3.3 Power method-like approaches for both the continuous and discrete phase cases 2.4 Numerical examples 2.4.1 Code design to optimize radar detection performance 2.4.2 Spectrally compatible waveform design 2.5 Conclusions Acknowledgments References 3. A computational design of phase-only (possibly binary) sequences for radar systems | Mohammad Alaee-Kerahroodi, Augusto Aubry, Mohammad Mahdi Naghsh, Antonio De Maio, and Mahmoud Modarres-Hashemi 3.1 Introduction 3.1.1 Background and previous works 3.1.2 Contribution and organization 3.2 Problem formulation 3.3 CD code optimization 3.3.1 Continuous phase code design 3.3.2 Discrete phase code design 3.4 Numerical examples 3.4.1 Sequence design with good PSL 3.4.2 Sequence design with good ISL 3.4.3 Pareto-optimized solution and designing binary sequences 3.5 Conclusions Appendix A: Proof of Lemma 3.1 Appendix B: Derivation of the feasibility set Appendix C: Proof of Lemma 3.2 References 4. Constrained radar code design for spectrally congested environments via quadratic optimization | Marco Piezzo, Yongwei Huang, Augusto Aubry, and Antonio De Maio 4.1 Introduction 4.2 System model 4.3 Figures of merit and constraints 4.3.1 Detection probability 4.3.2 Energy and similarity constraints 4.3.3 Spectral compatibility constraint 4.3.4 Bandwidth priority constraint 4.4 QCQP’s solution methods via rank-one matrix decomposition 4.5 Radarwaveformdesign in a spectrally crowded environment under similarity and spectral coexistence constraints 4.5.1 Code design optimization problem 4.5.2 Performance analysis 4.6 Radar waveform design in a spectrally crowded environment under similarity, energy modulation, and spectral coexistence constraints 4.6.1 Code design optimization problem 4.6.2 Performance analysis 4.7 Radar waveform design under similarity, bandwidth priority, and spectral coexistence constraints 4.7.1 Code design optimization problem 4.7.2 Performance analysis 4.8 Conclusions A.1 Proof of Theorem 4.1 A.2 Proof of Theorem 4.2 A.3 Proof of Theorem 4.3 A.4 Proof of Proposition 4.1: SDP relaxation tightness for (4.36) References 5. Robust transmit code and receive filter design for extended targets detection in clutter | Seyyed Mohammad Karbasi, Augusto Aubry, Antonio De Maio, Mohammad Hassan Bastani, and Alfonso Farina 5.1 Introduction 5.2 Target and signal model 5.2.1 Target model 5.2.2 Signal model 5.3 Problem formulation 5.3.1 Filter matrix optimization 5.3.2 Code matrix optimization 5.4 Filter and code synthesis 5.4.1 Filter synthesis 5.4.2 Code synthesis 5.5 Special case of practical importance: spherical uncertainty set 5.6 Numerical results 5.6.1 TAA uncertainty set size analysis 5.6.2 TAA uncertainty set for different target types 5.6.3 Spherical uncertainty set 5.7 Conclusions Appendix A: Proof of Lemma 5.1 Appendix B: Proof of Proposition 5.1 References 6. Optimizing radar transceiver for Doppler processing via non-convex programming | Augusto Aubry, Mohammad Mahdi Naghsh, Ehsan Raei, Mohammad Alaee-Kerahroodi, and Bhavani Shankar Mysore 6.1 Introduction 6.2 Radar system operation 6.2.1 Transmit waveform 6.2.2 Receiver processing and signal model 6.2.3 Clutter and signal independent disturbance characterization 6.2.4 Performance metric for Doppler processing 6.3 Problem formulation and design issues 6.3.1 Constraints and optimization problem 6.3.2 Filter bank optimization: solution to problemPw (n) 6.3.3 Radar code optimization: solution to problemPs (n) 6.3.4 Transmit–receive system design: optimization procedure 6.4 Performance analysis 6.4.1 Monotonicity of the proposed method and the impact of similarity constraint 6.4.2 Impact of colored interference 6.4.3 Effect of target Doppler shift interval 6.4.4 Impact of receive filter bank size 6.4.5 Impact of sequence length on performance 6.4.6 Performance comparison 6.5 Conclusions Appendix A: Proof of Proposition 6.1 Appendix B: Proof of Proposition 6.2 Appendix C: Proof of Lemma 6.1 References 7. Radar waveform design via the majorization–minimization framework | Linlong Wu and Daniel P. Palomar 7.1 Introduction 7.2 Preliminaries: the MM method 7.2.1 The vanilla MM method 7.2.2 Convergence analysis 7.2.3 Acceleration schemes 7.2.4 Extension to the maximin case 7.3 Joint design of transmit waveform and receive filter 7.3.1 System model and problem formulation 7.3.2 MM-based method for joint design with multiple constraints 7.3.3 Numerical experiments 7.4 Robust joint design for the worst-case SINR maximization 7.4.1 Problem formulation 7.4.2 MM-based method for robust joint design 7.4.3 Numerical experiments 7.5 Conclusion Appendix A: Proof of Lemma 7.1 Appendix B: Proof of Lemma 7.4 Appendix C: Proof of Lemma 7.5 Acknowledgment References 8. Lagrange programming neural network for radar waveform design | Junli Liang, Yang Jing, Hing Cheung So, Chi Sing Leung, Jian Li, and Alfonso Farina 8.1 Introduction 8.2 Basics of LPNN 8.2.1 Problem statement 8.2.2 Lagrange programming neural network 8.3 LPNN for waveform design with spectral constraints 8.3.1 Problem statement 8.3.2 Algorithm development 8.3.3 LPNN stability analysis 8.4 LPNN for designing waveform with low PSL 8.4.1 Problem statement 8.4.2 Algorithm description 8.4.3 LPNN stability analysis 8.4.4 Summary of proposed algorithm 8.5 Numerical examples 8.5.1 Experiment 1: Flat spectrum waveform design 8.5.2 Experiment 2: Spectrally constrained waveform design for radar 8.5.3 Experiment 3: Region of interest around main lobe 8.5.4 Experiment 4: Region of interest on one side of main lobe 8.5.5 Experiment 5: Low-sidelobe autocorrelation level 8.6 Conclusions A.1 Positive definiteness of Hessian matrix of (8.48) A.2 Solution to (8.58) A.3 Adaptive selection scheme of C0 A.3.1 On positive definiteness of ∇2 θθL ̄x A.3.2 On positive definiteness of Z0 A.3.3 On positive definiteness of Hessian matrix H of (8.49) References 9. Cognitive local ambiguity function shaping with spectral coexistence and experiments | Guolong Cui, Jing Yang, Xiangxiang Yu, and Lingjiang Kong 9.1 Introduction 9.2 Problem formulation 9.2.1 Weighted integrated sidelobe level 9.2.2 Spectral coexistence 9.2.3 Optimization problem 9.3 Iterative sequential quadratic optimization algorithm 9.4 Numerical results 9.4.1 Simulation results 9.4.2 Experimental results 9.5 Conclusions Appendix A: Proof of Proposition 9.1 Appendix B: Proof of (9.17) Appendix C: Proof of Proposition 9.2 Acknowledgments References 10. Relative entropy-based waveform design for MIMO radar | Bo Tang and Jun Tang 10.1 Introduction 10.2 Signal model and problem formulation 10.2.1 Signal model 10.2.2 Problem formulation 10.3 Two-stage algorithm design 10.3.1 Synthesis of energy-constrained waveforms 10.3.2 Convergence and computational complexity analysis 10.3.3 Extension to the synthesis of constant-moduluswaveforms 10.3.4 Extension to the synthesis of similarity-constrained waveforms 10.4 One-stage algorithm design 10.4.1 Minorizing Part A 10.4.2 Minorizing Part B 10.4.3 Minorizing Part C 10.4.4 The minorized problem at the (k + 1)th iteration 10.4.5 Convergence and computational complexity analysis 10.4.6 Extension to include other constraints 10.4.7 Accelerated schemes for the one-stage methods 10.5 Numerical examples 10.6 Concluding remarks Appendix A: Proof of (10.19) Appendix B: Proof of Lemma 10.1 Appendix C: Anintroduction to minorization–maximization Acknowledgment References Index