Riemannian Geometric Optimization Methods for Joint Design of Transmit Sequence and Receive Filter on MIMO Radar

• Published in: IEEE transactions on signal processing Vol. 68; pp. 5602 - 5616
• Main Authors: Li, Jie, Liao, Guisheng, Huang, Yan, Zhang, Zhen, Nehorai, Arye
• Format: Journal Article
• Language: English
• Published: New York IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Complexity; constant envelope (CE) constraint; Constraints; Design optimization; Euclidean geometry; Euclidean space; Interference; Iterative methods; joint design; Linear programming; Manifolds; Manifolds (mathematics); MIMO (control systems); MIMO radar; Moving targets; Multiple-input multiple-output (MIMO) radar; Optimization; product manifold; Radar equipment; receive filter; Riemann manifold; Riemannian optimization; Signal processing algorithms; Target detection; transmit sequence; Waveforms
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2020.3022821

In this paper, we study the joint design of a transmit sequence and a receive filter for an airborne multiple-input multiple-output (MIMO) radar system to improve its moving target detection performance in the presence of signal-dependent interference. The optimization problem is formulated to maximize the output signal-to-noise-plus-interference ratio (SINR), subject to the waveform constant-envelope (CE) constraint. To address the challenge of this non-convex problem, we propose a novel optimization framework for solving the problem over a Riemannian manifold which is the product of complex circles and a Euclidean space. Manifold optimization views the constrained optimization problem as an unconstrained one over a restricted search space. The Riemannian gradient descent algorithms and the Riemannian trust-region algorithm are then developed to solve the reformulated problem efficiently with low iteration complexity. In addition, the proposed manifold-based algorithms provably converge to an approximate local optimum from an arbitrary initialization point. Numerical experiments demonstrate the algorithmic advantages and performance gains of the proposed algorithms.