Robust Transceiver Design for ISAC with Imperfect CSI

In this paper, we explore robust transceiver design for an integrated sensing and communications system with bounded channel estimation error. To maximize the minimum sensing performance of multiple targets while satisfying communications requirements, we study the worst-case robust op-timization problem by jointly optimizing the transmitter and receiver variables. The formulated problem is challenging due to the non-convexity arising from the semi-infinite constraints (SICs) and coupled variables. To overcome these difficulties, we adopt the S-procedure to convert the SICs into finite convex linear matrix inequalities (LMIs). Using the alternating opti-mization technique, we decouple the robust transceiver design problem into feasibility-checking subproblems. By exploiting matrix lifting, we transform the rank-one constraints into a set of LMIs, which is leveraged to further check the feasibility of the obtained beamforming scheme. Numerical results are provided to demonstrate the robustness and effectiveness of the proposed algorithm in combating channel errors and improving the performance of ISAC systems.