Manifold-Based Sum Rate Maximization for MIMO Radar Communication Coexistence

In this paper, we introduce a radar communication coexistence (RCC) system wherein a multiple input multiple output (MIMO) base station (BS) and a MIMO radar operate using the same frequency spectrum. We introduce a novel optimization technique based on the Riemannian manifolds that jointly optimizes the BS beamformer and the radar transmit waveform covariance matrix to maximize the communication system sum rate (SR). This is done while reducing the interference levels affecting the radar and keeping its performance close to its standalone one. Specifically, we employ the complex cone and the spectrahedron manifolds as search spaces for the beamforming and the radar transmit waveform covariance matrix, respectively. In addition and for comparison purposes, we solve the same problem using semidefinite programming (SDP) relaxation of the non-convex problem over Euclidean manifolds. Simulation results indicate that the proposed manifold-based optimization algorithm provides a substantial improvement in the SR, and a notable reduction in the algorithm complexity when compared to the traditional SDP method. These benefits highlight its efficiency and potential for practical implementation in spectrum-sharing scenarios.