  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.
