CRB Minimization for RIS-Aided mmWave Integrated Sensing and Communications

In this article, reconfigurable intelligent surface (RIS) is employed in a millimeter-wave (mmWave) integrated sensing and communications (ISAC) system. To alleviate the multihop attenuation, the semi-self sensing RIS approach is adopted, wherein sensors are configured at the RIS to receive the radar echo signal. Focusing on the estimation accuracy, the Cram $\acute {\text {e}}\text{r}$ -Rao bound (CRB) for estimating the direction of the angles is derived as the metric for sensing performance. A joint optimization problem on hybrid beamforming and RIS phase shifts is proposed to minimize the CRB, while maintaining satisfactory communication performance evaluated by the achievable data rate. The CRB minimization problem is first transformed as a more tractable form based on Fisher information matrix (FIM). To solve the complex nonconvex problem, a double layer loop algorithm is proposed based on penalty concave-convex procedure (penalty-CCCP) and block coordinate descent (BCD) method with two subproblems. The successive convex approximation (SCA) algorithm and second-order cone (SOC) constraints are employed to tackle the nonconvexity in the hybrid beamforming optimization. To optimize the unit modulus constrained analog beamforming and phase shifts, manifold optimization (MO) is adopted. Finally, the numerical results verify the effectiveness of the proposed CRB minimization algorithm and show the performance improvement compared with other baselines. Additionally, the proposed hybrid beamforming algorithm can achieve approximately 96% of the sensing performance exhibited by the full digital approach within only a limited number of radio frequency (RF) chains.