Energy Efficiency and Spectral Efficiency Tradeoff in RIS-Aided Multiuser MIMO Uplink Systems

We study the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in multiuser multiple-input multiple-output (MIMO) uplink communications aided by a reconfigurable intelligent surface (RIS) equipped with discrete phase shifters. For reducing the required signaling overhead and energy consumption, our design is based on the partial channel state information (CSI), including the statistical CSI between the RIS and user terminals (UTs) and the instantaneous CSI between the RIS and the base station. To investigate the EE-SE tradeoff, we develop a framework for the joint optimization of UTs' transmit precoding and RIS reflective beamforming to maximize a metric called resource efficiency. Based on the closed-form solutions of all UTs' optimal transmit subspace and an asymptotic objective expression, an optimization framework is proposed via exploiting the quadratic transformation, the homotopy, accelerated projected gradient, and majorization-minimization methods. Numerical results illustrate the effectiveness of our optimization framework for the considered RIS-aid communications.