Coprime Array-Enhanced STAR-RIS for CRB Optimization in ISAC Systems

Simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) are widely adopted in integrated sensing and communication (ISAC) systems to sense users in non-line-of-sight (NLoS) scenarios. However, the uniform spacing of elements in the uniform linear array (ULA) imposes fundamental limitations on angular resolution. To address the challenge, we propose replacing the ULA with a coprime array in the sensor module of the STAR-RIS to enhance high-accuracy direction-of-arrival (DOA) estimation. Furthermore, we derive the Cramér-Rao bound (CRB) of the proposed architecture, and a joint optimization problem is formulated to minimize the CRB. To solve the problem, we introduce Schur complement to transform the non-convex problem into a Fisher information matrix (FIM) optimization problem, and an efficient dual-loop iterative algorithm based on the penalty dual decomposition method is adopted to resolve it. Numerical results demonstrate that the proposed coprime array structure can achieve higher theoretical sensing accuracy compared with the traditional ULA structure.