Receiver Selection and Transmit Beamforming for Multi-static Integrated Sensing and Communications

Next-generation wireless networks are expected to develop a novel paradigm of integrated sensing and communications (ISAC) to enable both the high-accuracy sensing and high-speed communications. However, conventional mono-static ISAC systems, which simultaneously transmit and receive at the same equipment, may suffer from severe self-interference, and thus significantly degrade the system performance. To address this issue, this paper studies a multi-static ISAC system for cooperative target localization and communications, where the transmitter transmits ISAC signal to multiple receivers (REs) deployed at different positions. We derive the closed-form Cram\'er-Rao bound (CRB) on the joint estimations of both the transmission delay and Doppler shift for cooperative target localization, and the CRB minimization problem is formulated by considering the cooperative cost and communication rate requirements for the REs. To solve this problem, we first decouple it into two subproblems for RE selection and transmit beamforming, respectively. Then, a minimax linkage-based method is proposed to solve the RE selection subproblem, and a successive convex approximation algorithm is adopted to deal with the transmit beamforming subproblem with non-convex constraints. Finally, numerical results validate our analysis and reveal that our proposed multi-static ISAC scheme achieves better ISAC performance than the conventional mono-static ones when the number of cooperative REs is large.