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In millimeter wave (mmWave) systems, it is challenging to ensure the reliableconnectivity of communications due to its sensitivity to the presence ofblockages. In order to improve the robustness of the mmWave system under thepresence of the random blockages, multiple reconfigurable intelligent surfaces(RISs) are deployed to enhance the spatial diversity gain, and robustbeamforming is then designed based on a stochastic optimization for minimizingthe maximum outage probability among multiple users to ensure the fairness.Under the stochastic optimization framework, we adopt the stochasticmajorization--minimization (SMM) method and the stochastic successive convexapproximation (SSCA) method to construct deterministic surrogate problems ateach iteration for new channel realizations, and obtain the closed-formsolutions of the precoding matrix at the base station (BS) and the passivebeamforming vectors at the RISs. Both stochastic optimization methods have beenproved to converge to the set of stationary points of the original stochasticproblems. Finally, simulation results show that the proposed robust beamformingin the RIS-aided system can effectively compensate for the performance losscaused by the presence of the random blockages, especially at high blockageprobability, compared with the benchmark solutions.

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