Multiple RIS-aided DF relaying for vehicular communication systems: a performance analysis

Abstract

This paper addresses the issue of outdated channel state information (CSI) caused by the coupling between Doppler frequency shift and CSI feedback delay in high-mobility internet of vehicles (IoV) scenarios. It establishes a multi-reconfigurable intelligent surface (RIS)-assisted decode-and-forward (DF) relaying communication system model for IoV and introduces a first-order auto-regressive (AR1) channel model to characterise the correlation between the estimated CSI and the actual channel. It also proposes a dynamic RIS selection mechanism. Under generalised-k fading channels, approximate closed-form expressions are derived for the system outage probability, bit error rate (BER) and ergodic capacity based on the statistical properties of the end-to-end signal-to-noise ratio. Furthermore, the problem of maximising system energy efficiency is formulated subject to constraints on total transmit power, minimum transmission rate and BER. Block coordinate descent and a phase matching technique are then employed to obtain a closed-form solution for the RIS phase shifts. The original problem is subsequently decoupled into a one-dimensional power allocation problem. Based on this, analytical solutions are derived for the piecewise stationary points and the feasible region pruning criterion via the Lambert W function. Simulation results demonstrate that, under outdated CSI conditions, the proposed multi-RIS-assisted DF relaying cooperative scheme significantly outperforms both the DF-only and multi-RIS-only schemes. Additionally, system performance improves as the number of RIS reflecting elements increases, in line with the law of diminishing marginal returns.