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

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.