Beamforming Design for MIMO DFRC Systems with Transmit Covariance Constraints

This paper develops the optimal beamforming design in a downlink multi-user multi-input-multi-output (MIMO) dual-function radar-communication (DFRC) system, which max-imizes the weighted sum-rate of communicating users under the prescribed transmit covariance constraint for radar performance guarantee. Specifically, we exploit the connection between weighted sum-rate and weighted minimum-mean-squared-error (MMSE) to reformulate the problem, and develop a block-coordinate-descent (BCD) type algorithm to iteratively compute the transmit beamforming and receive beamforming solutions. Using this approach, we reveal that the optimal receive beam-forming is the classic MMSE one and the optimal transmit beamforming design solves an orthogonal Procrustes problem (OPP), thereby allowing for closed-form solutions to subproblems in each BCD step and fast convergence of the proposed algorithm to a high-quality overall beamforming design. Numerical results validate the effectiveness of our proposed scheme.