Riemannian geometric optimization methods for joint design of transmit sequence and receive filter of MIMO radar

To maximize the signal-to-interference-plus-noise ratio (SINR) under a constant-envelope constraint, an efficient joint design of the transmit waveform and the receive filter for multiple-input multiple-output (MIMO) radars is essential. In this paper, we propose a novel optimization framework to solve the resultant non-convex problem on a Riemannian product manifold. Based on the Riemannian structure of the formulated manifold, three Riemannian gradient-based methods are proposed to deal with the reformulated problem efficiently. The proposed algorithms provably converge to a local optimum from an arbitrary initialization point. Numerical experiments demonstrate the algorithmic advantages and performance gains of the proposed algorithms.