Maximizing Geometric Mean Rate in RIS-Assisted Integrated Sensing and Communication Systems

This paper investigates the reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) system, wherein an ISAC base station (BS) serves multiple users with the aid of an RIS and detects multiple radar targets (RTs), simultaneously. Specifically, we consider the geometric mean (GM) rate as the communication performance metric to achieve both rate fairness among users and a high sum rate. To this end, we formulate the optimization problem for jointly designing the transmit precoder (TPC) and RIS phase shift matrix, aiming to maximize the GM rate of the users while ensuring minimum radiated power towards the RTs for their sensing, Additionally, the problem incorporates the maximum transmit power at the ISAC BS and unity modulus (UM) constraints on the elements of the RIS phase shift matrix. To solve this highly non-convex problem, we propose a majorization and minimization (MM)-based block coordinate descent (BCD) algorithm. In this algorithm, we first decouple the tightly coupled optimization variables and formulate the sub-problems via the BCD approach. Subsequently, each sub-problem is efficiently solved via employing the MM technique. Finally, the simulation results are presented and compared with benchmark schemes, which demonstrates the efficacy of the proposed algorithm in improving GM rate performance.