A Robust Design of a Transmit and Multiple Receive Beamforming Vectors in a System of Multistatic Radars for Target Sensing and Secure Communication

This paper addresses a robust design problem joint for a transmit and multiple receive beamforming vectors in a multistatic radars system that performs a target sensing and sends data to the multicast communication legitimate users in the presence of an eavesdropper, under the assumptions of imperfect channel state information of all channels and uncertainties for the transmit and receive steering vectors in the radar target sensing. Accordingly, a worst-case achievable secrecy date rate maximization problem is formulated, ensuring that the output robust signal-to-clutter-noise ratio (SCNR) for every radar receive array is not less than a threshold value and the transmit power budget constraint is satisfied. To solve the nonconvex problem, we utilize the closed-form optimal values for two special classes of robust least square problems to rewrite the original robust beamforming problem into two sub-problems. One of the sub-problems can be solved by a successively second-order cone programming (SOCP) approximation, and the other sub-problem is recast into an SOCP feasibility problem. Then, an alternating optimization method can be employed to solve the original robust beamformer problem for the system of multistatic radars by solving two sub-problems between, and eventually, a solution for the robust beamforming problem can be obtained. Simulation illustrates the effectiveness of the proposed method, with comparison to the known 5-lemma method (followed by a large-size semidefinite relaxation and a Gaussian randomization postprocess).