Asynchronous Distributed Beamforming Optimization Framework for RIS-Assisted Wireless Communications

Reconfigurable intelligent surface (RIS) is a promising solution to enhance the spectral and energy efficiencies of future wireless networks. In this paper, we aim to maximize the sum rate of the RIS-Assisted multiuser system with different availabilities of channel state information (CSI) by jointly optimizing the transmit precoding matrix and the RIS reflection matrix. Considering the large-scale nature of the RIS and the potential large number of served users, the conventional centralized optimization framework suffers from huge computational and communication overheads, and does not scale well with the system size. To tackle this issue, we develop an efficient asynchronous alternating direction method of multipliers (AS-ADMM) framework to maximize the sum rate under both perfect and imperfect CSI. Specifically, we firstly reformulate the original optimization problem under perfect CSI into a tractable consensus problem and then apply the proposed AS-ADMM framework to find a locally optimal solution, in which both the central server (C-server) and distributed servers (D-servers) update their variables with semi-closed-form solutions. Whereas for tackling the worst-case sum rate maximization, we firstly convert it into an equivalent max-min-max counterpart and find its semidefinite programming (SDP) based conservative approximation using the well-known sign-definiteness lemma. To drive a low-complexity solution, we develop an alternating optimization (AO) procedure that alternates between the two layers of the equivalent max-min-max problem with semi-closed-form solutions. The global optimality under a simplified scenario and the convergence behavior of the AS-ADMM algorithm are also discussed. Numerical results demonstrate the good scalability and superior performance of our proposed AS-ADMM framework over the existing benchmark schemes.