Weighted Sum-Rate Maximization With Transceiver and Passive Beamforming Design for IRS-Aided MIMO-BC Communications via Matrix Fractional Programming

This paper investigates the joint active transceiver and passive beamforming design to maximize the weighted sum-rate (WSR) of an IRS-aided multi-streams multiuser multiple-input multiple-output broadcast channel (MIMO-BC) downlink transmission system. Due to the coupling of the transceiver parameters, the considered WSR optimization problem is highly non-convex and thus challenging to solve. Different from the normally used methods, such as the weighted minimum mean-square error (WMMSE), we rely on the matrix fractional programming (MFP) theory to derive an effective algorithm to the WSR problem. Specifically, we reformulate the original problem into a tractable one by exploiting the special structure of the objective function, i.e., a MFP which involves a matrix ratio inside a logarithm in the objective function. An alternating optimization (AO) framework is then devised to decompose the reformulated problem into four subproblems, which optimize the introduced auxiliary variable, the transmit beamforming matrix, the receive matrix, and the reflecting beamforming matrix by fixing other variables respectively. Through the matrix quadratic transform, we reformulate the MFP problem as a convex one, and thus obtain the optimal transmit beamforming matrix. By leveraging the optimality conditions for unconstrained optimization problems, the optimal receive beamforming matrix and the introduced auxiliary variable are derived in closed form. For solving the passive beamforming subproblem, we propose an iterative algorithm based on successive convex approximation (SCA). Since the computational complexity of SCA is relatively high, we propose a computationally efficient method based on manifold optimization (MO) to optimize the passive beamforming matrix. Finally, we also consider the robust beamforming design when the system suffers from imperfect CSI. Simulation results demonstrate the effectiveness of the proposed methods.