Cover
Contents
About the editors
Foreword
References
Notation
1 On recent advances of binary sequence designs and their applications
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
1.3.1.1 Aperiodic case
1.3.1.2 Periodic case
1.3.2 CD algorithm
1.3.2.1 Aperiodic case
1.3.2.2 Periodic case
1.3.3 CAN(PeCAN) family of algorithms
1.3.3.1 Cyclic algorithm-new
1.3.3.2 Periodic cyclic algorithm-new
1.3.3.3 CANARY
1.3.3.4 PeCANARY
1.3.3.5 1bCAN
1.3.3.6 1bPeCAN
1.3.4 Summary
1.4 Conclusions
References
2 Quadratic optimization for unimodular sequence synthesis and applications
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
2.4.1.1 Impact of initial codes
2.4.1.2 Analysis of different Doppler frequencies
2.4.1.3 Impact of dividing block and M
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
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
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 Radar waveform design 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
Appendix A
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
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
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 problem Pw(n)
6.3.3 Radar code optimization: solution to problem Ps(n)
6.3.4 Transmitโreceive 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 majorizationโminimization framework
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
7.3.2.1 Majorized iteration method for joint design
7.3.2.2 Four waveform constraint cases
7.3.2.3 Summary of algorithm and complexity analysis
7.3.3 Numerical experiments
7.3.3.1 Joint design with the constant modulus constraint
7.3.3.2 Joint design with the similarity constraint
7.3.3.3 Joint design with the PAR constraint
7.3.3.4 Joint design with the spectrum compatibility constraint
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
7.4.2.1 Minorizer construction
7.4.2.2 Maximization solution pursuit
7.4.2.3 Computational complexity
7.4.2.4 Robust design with the uncertainty of Doppler
7.4.3 Numerical experiments
7.4.3.1 Experiment settings
7.4.3.2 Monotonic property of the proposed algorithms
7.4.3.3 Robust versus non-robust design
7.4.3.4 Comparison with existing methods
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
8.1 Introduction
8.2 Basics of LPNN
8.2.1 Problem statement
8.2.2 Lagrange programming neural network [44]
8.2.2.1 Principle of LPNN
8.2.2.2 Theoretical aspects
8.2.2.3 Procedure of LPNN
8.3 LPNN for waveform design with spectral constraints
8.3.1 Problem statement
8.3.1.1 Flat spectrum waveform design
8.3.1.2 Generalized spectrally constrained waveform design
8.3.2 Algorithm development
8.3.3 LPNN stability analysis
8.3.3.1 Regular point
8.3.3.2 Positive definiteness of A
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
8.4.3.1 Regular point
8.4.3.2 Positive definiteness of Hessian matrix
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
Appendix A
A.1 Positive definiteness of Hessian matrix of
A.2 Solution to (8.58)
A.3 Adaptive selection scheme of C0
A.3.1 On positive definiteness of โ200lx
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
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
9.4.1.1 Performance for ฮฒ โ [0.1, 1]
9.4.1.2 Optimization of both the WISL and the frequency stopband energy for ฮฒ = 0.5
9.4.1.3 Optimization of the WISL only for ฮฒ =1
9.4.1.4 Application: detection of multiple high-speed targets
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
Acknowledgment
References
10 Relative entropy-based waveform design for MIMO radar
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-modulus waveforms
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 An introduction to minorizationโmaximization
Acknowledgment
References
Index
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