Cramér-Rao Bound Minimization for IRS-Aided Multi-User Multi-Target MIMO ISAC Systems

The joint active and passive beamforming for intelligent reflecting surface (IRS)-aided integrated sensing and communication (ISAC) systems is investigated in this paper. The multi-user multiple-input multiple output (MU-MIMO) communication and the sensing task of multi-target directions of arrival (MT-DOA) estimation are performed simultaneously within the system. Specifically, we formulate the joint beamforming as a min-max problem, aiming to minimize the maximum Cramér-Rao bound (CRB) for the MT-DOA estimations while ensuring a threshold of the MU-MIMO communication rates. Existing methods have not been successful in the beamforming design for such systems, and we propose a product Riemannian manifold optimization (PRMO) framework for solving the problem. Within the PRMO, a product Riemannian manifold space (PRMS) is constructed as the solution space, where the constraints of the precoding matrix and IRS phase shifts are naturally satisfied. The problem is transformed via the penalty method, and the parallel Riemannian Broyden–Fletcher–Goldfarb–Shanno (P-RBFGS) algorithm and the Riemannian exact penalty (REP) method are exploited to find a feasible solution over the PRMS. Simulation results demonstrate the performance gain brought by the optimized IRS and verify the effectiveness of the proposed PRMO compared with other schemes for the CRB minimization problem with communication rate constraints.