Hybrid Beamforming for Millimeter-Wave ISAC System with Multi-Static Cooperative Localization

Beamforming is a key technique for achieving integrated sensing and communication (ISAC). However, most existing works focus on mono-static sensing, which can only provide limited sensing accuracy and range. In this paper, we investigate hybrid beamforming design for millimeter-wave (mmWave) multipleinput multiple-output (MIMO) ISAC system with multi-static cooperative localization, where one access point (AP) simultaneously transmits communication beams to serve multiple user equipments (UEs) and transmits a sensing beam towards a target, and other nearby APs perform cooperative localization on the target by estimating the angle-of-arrivals (AOAs) of received echo signals. To characterize the target localization accuracy, we derive the squared position error bound (SPEB) of AOA-based cooperative localization by using the equivalent Fisher information matrix (EFIM). Then, the hybrid beamforming design problem is formulated to minimize the SPEB of target localization, while satisfying the signal-to-interference-plus-noise ratio (SINR) requirements of individual communication UEs, transmit power budget, and constant modulus constraints. To solve the non-convex problem, a semidefinite relaxation (SDR)-based alternating optimization algorithm is proposed. Simulation results demonstrate that the proposed hybrid beamforming can achieve localization accuracy close to fully-digital beamforming and outperform the baseline schemes.