  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\'{e}r-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.
