Simultaneous RIS Adjustment and Transmission Based on Markov Chain Monte Carlo and Simulated Annealing

Reconfigurable Intelligent Surface (RIS) is a promising solution for enhancing the coverage and capacity of current and future wireless systems. To fully exploit its potential, RIS requires a fast adjustment algorithm, which determines the optimal reflection phase for each RIS Unit Cell (UC) and provides rapid and reliable data transmission. Existing statistical RIS adjustment algorithms typically rely on extensive channel measurements obtained through uniform random sampling of RIS configurations. Namely, each UC phase is selected with equal probability independently of the other UC phases. However, these random configurations result in low RIS channel gains during the adjustment process, which hinders data transmission. This paper addresses this issue and proposes a statistical RIS adjustment algorithm using Markov Chain Monte Carlo and Simulated Annealing (MCMC-SA). MCMC-SA chooses RIS configurations during adjustment according to the transition probabilities of a Markov chain. This feature allows MCMC-SA to improve the system capacity and simultaneously harvest performance gains during RIS adjustment. MCMC-SA can be used in large RISs with hundreds of elements and its complexity does not depend on the number of possible phase shifts on each UC. Also, it exhibits flexible parameter variability, which allows it to be robust to noise. Numerical results demonstrate that MCMC-SA significantly outperforms existing statistical RIS adjustment algorithms in signal-to-noise ratio (SNR) during the adjustment.