Hybrid Beamforming for mmWave Integrated Sensing and Communication with Multi-static Cooperative Localization

Beamforming is a key technology for achieving integrated sensing and communication (ISAC). However, most existing works focus on mono-static sensing, which has limited sensing accuracy and strong self-interference. To address these issues, this paper investigates hybrid beamforming (HBF) design for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) ISAC system with multi-static cooperative localization. Specifically, one access point (AP) simultaneously forms communication beams to serve multiple user equipments (UEs) and a sensing beam towards one target, and other multiple distributed APs perform cooperative localization on the target by estimating the angle-of-arrivals (AOAs) of received echo signals. First, to characterize the target localization accuracy, we derive the squared position error bound (SPEB) of AOA-based multi-static cooperative localization. Then, two HBF optimization problems are formulated to investigate the performance tradeoff between sensing and communication. For the sensing-centric design, we aim to minimize the SPEB of target localization while ensuring the signal-to-interference-plus-noise ratio (SINR) requirements of individual UEs. To tackle this nonconvex problem, we propose a semidefinite relaxation (SDR)-based alternating optimization algorithm. For the communication-centric design, a fractional programming (FP)-based alternating optimization algorithm is proposed for solving the communication sum-rate maximization problem under the sensing SPEB constraint. Simulation results demonstrate that the proposed two HBF algorithms can achieve localization accuracy and sum-rate performance close to fully-digital beamforming counterparts and outperform other baseline schemes.