Beyond Diagonal Reconfigurable Intelligent Surfaces Enable Near-Field ISAC Systems

This article explores a near-field integrated sensing and communication (ISAC) system enabled by a beyond diagonal reconfigurable intelligent surface (BD-RIS), where the target and users are located at the reflective and refractive space, respectively. In contrast to most existing RIS-aided ISAC systems that employ a single-connected architecture, we investigate group- and fully connected (FC) BD-RIS architectures. Moreover, depending on the availability of prior information about the extended target, we propose a parametric scattering model (PSM) and an unstructured channel model (UCM). For PSM and UCM, we derive the Cramér–Rao bound (CRB) of target positions and the response matrix, respectively. Both CRB minimization problems are investigated: 1) for CRB minimization in PSM, we develop the alternative optimization (AO) algorithm that leverages semidefinite relaxation (SDR) and penalty-based manifold optimization (PBMO) and 2) for CRB minimization in UCM, we prove that the optimal beamformers reside on a complex matrix sphere manifold and utilize the PBMO to jointly optimize. Finally, the numerical results show that: 1) the developed schemes consistently outperform the benchmark counterparts in sensing performance, irrespective of whether prior information is available, and 2) the additional prior information can effectively improve the sensing accuracy of the extended target.