Environment-based MIMO Radar Waveform Design Via Riemannian Geometric Approaches

Multiple-input multiple-output(MIMO)radar system which has been a hot topic of research for novel radar systems,can emit a different signal out of each transmitting antenna.Compared with phased-array radar systems,MIMO radar systems can provide extra degrees of freedom and the waveforms can be optimized to carry out a flexible radar power allocation and enhance the performance of radar systems.Focusing on the waveform design for MIMO radar,this dissertation studies the transmit beampattern matching design,the joint design of transmit waveform and receive filter,and the information-theoretic cognitive waveform design for multi-target detection.The main contents and contributions of the dissertation are summarized as follows:The first part focuses on the problem of transmit beampattern matching design for colocated MIMO radar with constant-envelope(CE)constraint.In order to solve the resultant non-convex optimization problem,a product-Riemannian-manifold-based beampattern matching design(PRM-BMD)method is proposed.The essential Riemannian geometric structure of the formulated manifold and the Riemannian gradient of the objective function are derived.Since the descent is achieved directly on the formulated product manifold while maintaining feasibility,the PRM-BMD improves the matching performance of the designed transmit beampattern and reduces the computational complexity.The second part focuses the joint design of transmit waveform and receive filter for an airborne colocated MIMO-STAP radar system in the presence of clutter.Aiming at maximizing the output signal-to-clutter-plus-noise ratio(SCNR)with CE constraint on the waveform,two manifold-based alternating optimization methods are proposed,i.e.,complex-circles-manifold-based joint design(JD-CCM)method,and fixed-rank-manifold-based joint design(JD-FRM)method.The JD-CCM algorithm formulates the CE constraint on the waveform as a complex-circles manifold and the JD-FRM algorithm formulates the fixed-rank constraint of the waveform covariance matrix as a fixed-rank manifold.Then alternating optimization method is leveraged to optimize the waveform and receive filter iteratively.The JD-CCM algorithm and JD-FRM algorithm which avoid the model errors caused by the relaxation and approximation in the existing methods,can improve the output SINR performance and reduce the computational complexity.The third part focuses on the joint design of transmit waveform and receive filter for an airborne colocated MIMO-STAP radar in the presence of clutter and interference.Three product-manifold-based algorithms,i.e.,product Riemannian manifold steepest descent(PRM-SD),product Riemannian manifold conjugate gradient(PRM-CG),and product Riemannian manifold trust-region(PRM-TR)algorithms are proposed to tackle the non-convex SINR maximization problem with CE constraint.The proposed algorithms leverage the geometric properties of the feasible region to formulate a product Riemannian manifold which is a Cartesian product of a complex-circles manifold and a Euclidean space.Then the essential Riemannian geometric structures and the explicit expressions of the Riemannian gradient and the Riemannian Hessian are strictly derived.Bo doing so,two first-order line-search methods(PRM-CG,PRM-SD)and a second-order method(RPM-TR)are developed on the product manifold.We also demonstrate the convergence of the proposed algorithms and analyze the computational complexities of the proposed algorithms.Compared to the counterparts solving the problem in Euclidean space,the proposed algorithms can achieve a superiority in terms of the output SINR and computational complexity.The fourth part addresses the information-theoretic cognitive waveform design of colocated MIMO radar systems.Aiming at improving the multi-target detection performance,a manifold-based adaptive waveform design(MAWD)method is proposed.The multi-target detection problem is formulated as a sequential multi-hypothesis testing problem.In order to improve the probability of multi-target detection,MAWD method tackles the maximizing of the J-divergence between distributions of the different hypotheses under CE constraint.Simulation results show that the proposed algorithm can achieve a dynamic cognition of the environment and improve the multi-target detection performance.