Riemannian Product Manifold-Based Approach for MIMO Radar Joint Constrained Transmit Beampattern Design

This paper explores the waveform design problem for multiple-input multiple-output radar, focusing on minimizing the mean square error between the idealized beampattern and its actual implementation. The optimization respects two practical non-convex constraints: constant modulus and similarity. To address this non-convex optimization challenge, we propose a solution based on the Riemannian Product Manifold Conjugate Gradient (RPM-CG) framework. The RPM-CG framework transforms the multi-constrained non-convex problem in Euclidean space into a straightforward unconstrained one on the product manifold. Specifically, we leverage the conjugate gradient method to perform a descent search on the developed product manifold. Simulations demonstrate that RPM-CG outperforms other candidate beampattern design methods, enhancing the matching performance of the beampattern, reducing computational complexity, and maintaining waveform ambiguity properties.