Fairness-Oriented Multiple RISs-Aided MmWave Transmission: Stochastic Optimization Methods

In millimeter wave (mmWave) systems, it is challenging to ensure the reliable connectivity of communications due to its sensitivity to the presence of blockages. In order to improve the robustness of the mmWave system under the presence of the random blockages, multiple reconfigurable intelligent surfaces (RISs) are deployed to enhance the spatial diversity gain, and robust beamforming is then designed based on a stochastic optimization for minimizing the maximum outage probability among multiple users to ensure the fairness. Under the stochastic optimization framework, we adopt the stochastic majorization--minimization (SMM) method and the stochastic successive convex approximation (SSCA) method to construct deterministic surrogate problems at each iteration for new channel realizations, and obtain the closed-form solutions of the precoding matrix at the base station (BS) and the passive beamforming vectors at the RISs. Both stochastic optimization methods have been proved to converge to the set of stationary points of the original stochastic problems. Finally, simulation results show that the proposed robust beamforming in the RIS-aided system can effectively compensate for the performance loss caused by the presence of the random blockages, especially at high blockage probability, compared with the benchmark solutions.