Robust Beamforming Design for Cell-Free MIMO ISAC Systems With Imperfect CSI

Abstract

Cell-Free MIMO integrated sensing and communication (CF-ISAC) systems can improve the capabilities of communication and sensing by utilizing distributed access points (APs). However, the imperfect channel state information (CSI) weakens the efforts of beamforming designs, resulting in performance degradation of CF-ISAC systems. To address this issue, this letter proposes a robust beamforming design algorithm for CF-ISAC systems. Specifically, we first formulate an optimization problem that maximizes the weighted sum rate (WSR) of user equipments (UEs) and leverages thresholds to fine-tune the communication performance of UEs and the sensing performance of the target, respectively. To deal with the non-convexity of the problem, the Lagrangian dual transform and the quadratic transform are utilized to convert the objective function into a convex form. Additionally, the S-procedure, Schur’s complement, and Taylor’s expansion are employed to convert the constraints into convex forms. Finally, the original optimization problem is transformed into a set of tractable semidefinite programming (SDP) subproblems. Simulation results demonstrate that the proposed robust algorithm exhibits a higher probability of satisfying each UE’s communication rate constraint under imperfect CSI.