In this work, we address the energy efficiency (EE) maximization problem in a downlink communication system utilizing reconfigurable intelligent surface (RIS) in a multi-user massive multiple-input multiple-output (mMIMO) setup with zero-forcing (ZF) precoding. The channel between the base station (BS) and RIS operates under a Rician fading with Rician factor K1. Since systematically optimizing the RIS phase shifts in each channel coherence time interval is challenging and burdensome, we employ the statistical channel state information (CSI)-based optimization strategy to alleviate this overhead. By treating the RIS phase shifts matrix as a constant over multiple channel coherence time intervals, we can reduce the computational complexity while maintaining an interesting performance. Based on an ergodic rate (ER) lower bound closed-form, the EE optimization problem is formulated. Such a problem is non-convex and challenging to tackle due to the coupled variables. To circumvent such an obstacle, we explore the sequential optimization approach where the power allocation vector p, the number of antennas M, and the RIS phase shifts v are separated and sequentially solved iteratively until convergence. With the help of the Lagrangian dual method, fractional programming (FP) techniques, and Lemma 1, insightful compact closed-form expressions for each of the three optimization variables are derived. Simulation results validate the effectiveness of the proposed method across different generalized channel scenarios, including non-line-of-sight (NLoS) and partially line-of-sight (LoS) conditions. This underscores its potential to significantly reduce power consumption, decrease the number of active antennas at the base station, and effectively incorporate RIS structure in mMIMO communication setup with just statistical CSI knowledge.

翻译：本文研究了采用可重构智能超表面（RIS）的多用户大规模多输入多输出（mMIMO）下行通信系统中的能效（EE）最大化问题，其中基站采用迫零（ZF）预编码。基站与RIS之间的信道服从莱斯因子为K1的莱斯衰落。由于在每个信道相干时间间隔内系统性地优化RIS相位偏移具有挑战性且开销较大，本文采用基于统计信道状态信息（CSI）的优化策略来降低这一负担。通过将RIS相位偏移矩阵视为多个信道相干时间间隔内的恒定参数，可在保持可观性能的同时降低计算复杂度。基于遍历速率（ER）下界闭式表达式，建立了能效优化问题。该问题因变量耦合而呈现非凸特性，求解难度较大。为克服此障碍，本文采用序列优化方法，将功率分配向量p、天线数量M和RIS相位偏移v分离，并通过迭代求解直至收敛。借助拉格朗日对偶法、分数规划（FP）技术及引理1，推导出了三个优化变量的紧凑闭式表达式。仿真结果验证了所提方法在不同广义信道场景（包括非视距（NLoS）和部分视距（LoS）条件）下的有效性。这充分表明，仅需统计CSI知识，该方法即可显著降低功耗、减少基站活跃天线数量，并将RIS结构有效集成至mMIMO通信系统中。