Fluid Antennas and Stacked Intelligent Metasurfaces Enabled Multi-User ISAC for Low-Altitude Wireless Networks

In emerging low-altitude wireless networks (LAWNs), conventional stacked intelligent metasurfaces (SIM) assisted integrated sensing and communication (ISAC) systems with fixed position antennas, exhibit limited capability to adjust antenna positions within predefined regions of the transceiver aperture, thereby reducing the flexibility of beamforming and spatial interference suppression. To address this problem, we investigate a SIM-aided ISAC system, where fluid antennas (FAs) are employed to provide extra spatial degrees of freedom, enabling adaptive antenna repositioning to enhance beamforming performance and suppress interference. To evaluate the integrative performance gain provided by FAs and SIM, we derive the Cram´ er-Rao bound (CRB) for estimating the two-dimensional direction of arrival of the sensing target. We aim to maximize the user sum rate by jointly optimizing the covariance matrix at the base station (BS), the phase shifts at the SIM, and the positions of the FAs, subject to the power budget at the BS and the sensing constraints of the target. However, the CRB constraint induces a highly complex non-convexity with respect to the optimization variables. Thus, we obtain an inverse relationship between the CRB and the beampattern gain and replace the CRB constraint with an equivalent beampattern gain constraint at the target direction. To tackle the non-convex optimization problem, we employ an alternating optimization algorithm based on successive convex approximation, semidefinite relaxation and gradient ascent. Extensive simulation results validate the considerable benefits of the proposed FA-SIM-enabled LAWN-ISAC system in enhancing communication performance compared to traditional ISAC systems and reveal the trade-offs associated with principal system parameters of FAs and SIM.