Joint Beamforming Design for Hybrid RIS-Assisted mmWave ISAC System Relying on Hybrid Precoding Structure

In this paper, we investigate a millimeter wave integrated sensing and communication system with aid of the hybrid reconfigurable intelligent surface (HRIS), where the dual-function radar and communication station (DFBS) applies the hybrid precoding structure. On this basis, we consider the sensing and communication performance, respectively, and formulate two optimization problems. One is to maximize the worst-case illumination power while ensuring the communication quality, and another is to maximize the total achievable rate while satisfying the sensing performance. To solve them, we first decouple each nonconvex problem into three subproblems via the alternative optimization technique. For the former one, we transform DFBS and HRIS beamforming optimization subproblems into the convex ones by the quadratic constrained quadratic programming (QCQP) and semidefinite program relaxation (SDR) techniques, and obtain the solutions by standard convex optimization technique. For the later one, fractional programming is applied to decouple the objective function, and then we transform DFBS and HRIS beamforming design subproblems into the convex ones by QCQP and Taylor expansion techniques, and obtain the solutions by the alternating direction method of multipliers (ADMM). For the hybrid precoding design subproblems of DFBS in both problems, a manifold optimization-alternating minimization (MO-AltMin) algorithm based on minimizing the Euclidean distance is used to obtain the solutions. Simulation results show the effectiveness of the proposed schemes.