Optimal Beamforming for MIMO DFRC Systems with Transmit Covariance Constraints

This paper optimizes the beamforming design of a downlink multiple-input multiple-output (MIMO) dual-function radar-communication (DFRC) system to maximize the weighted communication sum-rate under a prescribed transmit covariance constraint for radar performance guarantee. In the single-user case, we show that the transmit covariance constraint implies the existence of inherent orthogonality among the transmit beamforming vectors in use. Then, leveraging Cauchy's interlace theorem, we derive the globally optimal transmit and receive beamforming solution in closed form. In the multi-user case, we exploit the connection between the weighted sum-rate and weighted minimum mean squared error (MMSE) to reformulate the intended problem, and develop a block-coordinate-descent (BCD) algorithm to iteratively compute the transmit beamforming and receive beamforming solutions. Under this approach, we reveal that the optimal receive beamforming is given by the classic MMSE one and the optimal transmit beamforming design amounts to solving an orthogonal Procrustes problem, thereby allowing for closed-form solutions to subproblems in each BCD step and fast convergence of the proposed algorithm to a high-quality (near-optimal) overall beamforming design. Numerical results demonstrate the superiority of our approach to the existing methods, with at least 40% higher sum-rate under a multi-user MIMO setting in the high signal-to-noise regime.