Fluid-Antenna Enhanced ISAC: Joint Antenna Positioning and Dual-Functional Beamforming Design under Perfect and Imperfect CSI

Integrated sensing and communication (ISAC) emerges as an essential technique for overcoming spectrum congestion. However, the performance of traditional ISAC systems with fixed-position-antennas (FPA) is limited due to insufficient spatial degree of freedom (DoF) exploration. Recently, fluid antenna (FA) with reconfigurable antenna position is developed to enhance the sensing and communication performance by reshaping the channel. This paper investigates an FA-enhanced ISAC system where a base station is equipped with multiple FAs to communicate with multiple single-antenna users and with FPAs to sense a point target. In this paper, we consider both perfect and imperfect channel state information (CSI) of the communication channel and sensing channel. In two cases, we focus on the maximization of the sensing signal-to-noise (SNR) by optimizing the positions of FAs and the dual-functional beamforming under the constraints of the FA moving region, the minimum FA distance and the minimum signal-to-interference-plus-noise (SINR) per user. Specifically, for the ideal case of perfect CSI, an iterative alternating optimization (AO) algorithm is proposed to tackle the formulated problem where the dual-functional beamforming and the FA positions are obtained via semidefinite relaxation (SDR) and successive convex approximation (SCA) techniques. Then, for the imperfect CSI case, we propose an AO-based iterative algorithm where $\mathcal{S}-$Procedure and SCA are applied to obtain the dual-functional beamforming and the FA positions. Furthermore, we analytically and numerically prove the convergence of the proposed algorithms. Numerical results demonstrate the notable gains of the proposed algorithms in the respective cases.