On the Maximum Achievable Sum-rate of the RIS-aided MIMO Broadcast Channel

Reconfigurable intelligent surfaces (RISs) represent a new technology that can shape the radio wave propagation and thus offers a great variety of possible performance and implementation gains. Motivated by this, we investigate the achievable sum-rate optimization in a broadcast channel (BC) in the presence of an RIS. We solve this problem by exploiting the well-known duality between the Gaussian multiple-input multiple-output (MIMO) BC and the multiple-access channel (MAC), and we correspondingly derive three algorithms which optimize the users' covariance matrices and the RIS phase shifts in the dual MAC. The optimal users' covariance matrices are obtained by a dual decomposition method with block coordinate maximization (BCM), or by a gradient-based method. The optimal RIS phase shifts are either computed sequentially by using a closed-form expression, or are computed in parallel by using a gradient-based method. We present a computational complexity analysis for the proposed algorithms. Furthermore, we extend the use of these methods to the case of a system with multiple RISs. Simulation results show that the proposed algorithms converge to the same achievable sum-rate, although the gradient-based optimization methods are generally more time efficient. In addition, we demonstrate that the proposed algorithms can provide a gain in the RIS-assisted BC assisted by multiple RISs and that the gain depends on the placement of the RISs.