Multi-Target Beamforming Optimization for Fluid Antenna-Enabled Multi-Static ISAC

This study investigates a fluid antenna (FA)-enabled multi-static integrated sensing and communication (ISAC) system. Within this system, multiple transmit access points (TAPs) are employed to transmit ISAC signals, enabling simultaneous downlink communication and target sensing. At the same time, there is a receive access point (RAP) to capture the reflected sensing signals for target detection. All of the TAPs are equipped with FAs to leverage the spatial degree of freedom. We formulate a maximization problem of the worst-case detection probability of designated targets subject to the communication constraints of the users, to optimize both the beamforming matrix and antenna position vector (APV) of each TAP. To address the non-convexity of the problem, we use an alternating optimization approach over two subproblems: (1) beamforming optimization, and (2) optimization of APVs. For the first subproblem, we use the semi-definite relaxation (SDR) method to derive the optimal beamforming vectors given fixed APVs. Then the latter is solved by the second-order Taylor series expansion to approximate the function related to the APVs in a convex form. Simulation results demonstrate that the adoption of FA significantly enhances the sensing performance of our proposed system. Also, the proposed cooperative multi-static ISAC system coordinates communication and sensing tasks across various TAPs effectively, underscoring its potential for improving overall system performance.