Joint Beamforming for CRB-Constrained IRS-Aided ISAC System via Product Manifold Methods

In this paper, we focus on the joint beamforming for intelligent reflecting surface (IRS) aided integrated sensing and communication (ISAC) systems, where a multi-antenna base station (BS) performs multi-user multi-input single-output (MU-MISO) communication and radar sensing simultaneously. Specifically, the direction-of-arrival (DoA) estimation is considered as the task of radar sensing, and we aim to optimize the MU-MISO communication while enhancing the estimation accuracy by ensuring a Cramér-Rao bound (CRB) lower bound. First, for the CRB-constrained sum rate maximization problem, we propose a product Riemannian manifold optimization (PRMO) framework to solve the problems without relaxing the objective functions. Specifically, a product Riemannian manifold space (PRMS) is constructed to satisfy the constraints of the precoding matrix and IRS phase shifts, and the constraint of the CRB threshold is tackled by a Riemannian exact penalty (REP) method. A parallel Riemannian Broyden-Fletcher–Goldfarb-Shanno (P-RBFGS) algorithm is derived to update the parameters over the PRMS. Then, considering the fairness of the MU-MISO communication, the PRMO is further extended to tackle the CRB-constrained max-min optimization by maximizing the minimum rate among all users. Simulation results demonstrate that with the same CRB constraint, the PRMO outperforms the existing method in sum rate maximization with lower computational complexity, and the extended PRMO enables the users to obtain approximately equal rates, thus guaranteeing the fairness of the system.