This chapter delves into the critical aspects of optimizing energy efficiency (EE) in active reconfigurable intelligent surface (RIS)-assisted massive MIMO (M-MIMO) wireless communication systems. We develop a comprehensive and unified theoretical framework to analyze the boundaries of EE within M-MIMO systems integrated with active RIS while adhering to practical constraints. Our research focuses on a formulated EE optimization problem aiming to maximize the EE for active RIS-assisted M-MIMO communication systems. Our goal is to strategically find the number of active RIS elements for outperforming the EE attainable by an entirely passive RIS. Besides, the proposed novel solution has been tailored to the innovative problem. The formulation and solution design consider analytical optimization techniques, such as lagrangian dual transform (LDT) and fractional programming (FP) optimization, facilitating the effective implementation of RIS-aided M-MIMO applications in real-world settings. In particular, our results show that the proposed algorithm can provide up to 120% higher EE than the entirely passive RIS. Besides, we found that the active RIS can operate with less than half of the reflecting elements for the entirely passive RIS. Finally, in view of active RIS achieving the complete utilization of amplification power available, it should be equipped with a reasonable number of reflecting elements above N = 49.

翻译：本章深入探讨了有源可重构智能表面（RIS）辅助的大规模MIMO（M-MIMO）无线通信系统中优化能量效率（EE）的关键问题。我们构建了一个全面且统一的理论框架，用于分析集成有源RIS的M-MIMO系统中EE的边界，同时考虑实际约束条件。研究聚焦于一个明确的EE优化问题，旨在最大化有源RIS辅助M-MIMO通信系统的EE。我们的目标是策略性地确定有源RIS单元的数量，以优于完全无源RIS可实现的EE。此外，所提出的新颖解决方案是针对该创新问题量身定制的。该问题的建模与求解设计采用了解析优化技术，例如拉格朗日对偶变换（LDT）和分数规划（FP）优化，从而促进了RIS辅助M-MIMO应用在实际场景中的有效实施。特别地，结果表明，所提算法相比完全无源RIS可提供高达120%的EE提升。此外，我们发现，有源RIS可在少于完全无源RIS一半反射单元数量的情况下工作。最后，鉴于有源RIS能充分利用可用放大功率，它应配备不少于N = 49个反射单元。