Joint Robust Optimal Transmit and Receive Beamforming Designs for a DFRC System for the MIMO Radar and Secondary Multicast Communication in a Cognitive Radio Network

Consider a joint robust design problem for the transmit and receive beamvectors for a dual-functional radar and communication (DFR-C) system in the secondary communication of a cognitive radio (CR) network. The base station (BS) sends signals to detect a MIMO radar target while serving the secondary downlink users. Then a maximization problem of the worst-case radar output signal-to-interference-plus-noise ratio is formulated, subject to the total power constraint for the BS, the robust signal-to-noise constraints for the secondary users and the robust interference constraints for the primary users in the CR network, under the assumptions of imperfect CSI and uncertainty of the transmit and receive steering vectors for the radar sensing. To tackle the nonconvex problem, we derive the closed-form optimal values for two specific quadratic problems with a spherical constraint, and reexpress the robust constraints into quadratic constraints. Then an alternating optimization strategy is adopted to solve the problem. Specifically, when optimizing the transmit beamvector, a second-order cone programming (SOCP) approximation algorithm is proposed. On the other hand, when optimizing the receive beamvector, an SOCP problem is reformulated and solved. Then, simulation results demonstrate the improved performance of the DFRC system by the proposed algorithm, comparing with existing schemes.