Robust Spectral and Energy Efficiency Tradeoff for RIS‐Aided Multi‐User Communication

ABSTRACT Reconfigurable intelligent surface (RIS) holds potential for enhancing spectral efficiency (SE) and energy efficiency (EE). Nevertheless, the variations in these two metrics are not synchronous. Additionally, acquiring precise channel state information (CSI) presents substantial difficulties in actual implementations. In this work, an RIS‐aided multi‐user network with imperfect CSI is investigated. Correspondingly, we focus on balancing SE and EE through the collaborative design of the base station (BS)'s precoding matrix and the RIS's phase shifts, which consider the transmit power budget and the channel uncertainties constraints. The non‐convexity of the joint optimization problem motivates the use of two‐stage AO, which decouples the problem into tractable subproblems for BS beamforming and RIS phase‐shift design, ensuring convergence to a locally optimal solution. In the outer‐stage problem, the quadratic transformation (QT) method is applied to convert the fractional objective into a linear form. By introducing auxiliary variables, a closed‐form solution is obtained. In the inner‐stage problem, by employing successive convex approximation (SCA), introducing auxiliary variables, and utilizing S‐procedure, the SE with uncertain channels is transformed into a concave form and further converted into equivalent linear matrix inequalities (LMIs). Simulation results illustrate that the proposed design effectively attains a favorable tradeoff in both SE and EE, and demonstrate certain superiority compared to the baseline.