Riemannian Product Manifold Methods for Joint Design of Transmit Waveform and Receive Filter on MIMO Radar under Multiple Constraints

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In this paper, we investigate the joint design of transmit waveforms and receive filters for multiple-input multipleoutput radar, where the waveforms satisfy both constant modulus and similarity constraints. To address the resulting nonconvex optimization problem, we propose two efficient algorithms based on the Riemannian product manifold framework to maximize the signal-to-interference-plus-noise ratio (SINR). By reformulating the multi-constrained nonconvex problem from Euclidean space into an unconstrained optimization over the constructed product manifolds, the proposed algorithms leverage conjugate gradient descent for efficient and effective computation. Simulation results demonstrate that the proposed algorithms outperform state-of-the-art methods in SINR performance, while maintaining lower computational complexity.

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