Energy-Efficient Power Control in Single-User M-MIMO-OFDM System with PA Nonlinearity

Although multiple works have proposed energy-efficient resource allocation schemes for Massive Multiple-Input Multiple-Output (M-MIMO) system, most approaches overlook the potential of optimizing Power Amplifier (PA) transmission power while accounting for non-linear distortion effects. Furthermore, most M-MIMO studies assume narrow-band transmission, neglecting subcarrier intermodulations at the non-linear PA for an Orthogonal Frequency Division Multiplexing (OFDM) system. Therefore, this work investigates the energy-efficient power allocation for a single-user equipment (UE) M-MIMO downlink (DL) system employing OFDM with nonlinear PAs. Unlike prior works, we model wide-band transmission using a soft-limiter PA model and derive a closed-form expression for the signal-to-distortion-and-noise ratio (SNDR) under Rayleigh fading and Maximal Ratio Transmission (MRT) precoding. Next, the Energy Efficiency (EE) function is defined considering two PA architectures and a distorted OFDM signal. We then propose a low complexity root-finding algorithm to maximize EE by transmit power adjustment. Simulation results demonstrate significant EE gains over a fixed PA back-off baseline, with over $100\%$ improvement under both low and high path loss. Our findings reveal how the optimal operating point depends on the antenna count, the PA model, and the propagation conditions.