Phase-Amplitude Design for Energy-Efficient Active RIS-aided Massive MIMO System

In this paper, we solve the energy efficiency (EE) optimization problem in active reconfigurable intelligent surface (RIS)-assisted massive multiple-input multiple-output (mMIMO) communication systems. By exploring different optimization techniques, we derive closed-form expressions for both the amplitude and phase of each RIS element, proposing a novel flexible iterative algorithm for active RIS scenarios. The numerical results reveal how the proposed analytical amplitude/phase beamforming design can be promising since it has proven to be of low complexity, providing up to ≈ 42% higher EE compared to the completely passive RIS with a lower running time of ≈ 93.6% lower compared to the semidefinite relaxation (SDR) technique. The paper contributes to the design and optimization of active RIS in mMIMO systems, highlighting the importance of both EE and computational feasibility in future wireless communication technologies.