RIS-assisted communications in correlated Rayleigh channels: Comparison of training overhead reduction schemes

Channel training in reconfigurable intelligent surface (RIS)-assisted communications is usually conducted in an on-off manner, resulting in unaffordable training time overhead when the number of RIS elements is large. In this paper, for correlated Rayleigh channels, we compare three typical training overhead reduction schemes, namely RIS element selection (Scheme 1), element grouping (Scheme 2), and statistical CSI-based phase shifts design (Scheme 3). For Scheme 1 and Scheme 2, we propose two algorithms to select RIS elements (or form element groups) and determine the optimal number of activated elements (or formed groups), based on the channel correlation information only; for Scheme 3, we consider a semi-definite programming-based approach in the literature, and propose an alternative dominant eigenvector-based method for determining the RIS phase shifts vector. Via extensive simulations, we compare the achievable ergodic rates of these schemes versus the signal-to-noise ratio, the channel correlation level, and the element number-to-coherent time ratio, respectively, and discuss possible switching of the three schemes over these system parameters. At last, operation regions of the considered training overhead reduction schemes are shown in the plane characterized by the system parameters, which provides useful guidelines for practical scheme determination.