Unified Manifold Optimization for Double-IRS-Aided MIMO Communication

Multiple collaborative intelligent reflecting surfaces (IRS) can address the blockage effect and improve channel capacity in multiple-input multiple-output (MIMO) communication systems. Most existing methods optimize the system via block coordinate descent (BCD) methods with relaxation of the objective function, which leads to performance gaps. To directly solve the channel capacity maximization problem in a double-IRS aided system, we propose a unified manifold optimization (UMO) framework to rephrase the problem as an unconstrained Riemannian problem. Specifically, a unified manifold space (UMS) is constructed to satisfy the constraints of the IRS and the precoding matrix, and a parallel conjugate gradient algorithm is derived to solve the problem over the UMS. Compared with existing approaches, the proposed method achieves higher channel capacity with less computational cost.