Weighted-Sum Energy Efficiency Maximization in User-Centric Uplink Cell-Free Massive MIMO

TL;DR

This paper proposes a weighted-sum energy efficiency metric for user-centric uplink CF-mMIMO systems, along with optimization algorithms that improve energy use and spectral efficiency.

Contribution

It introduces the WSEE metric for more accurate energy efficiency assessment and develops QT-based algorithms for its maximization in CF-mMIMO systems.

Findings

WSEE provides a more precise energy efficiency measure for individual UEs.

The proposed algorithms outperform GEE-based methods in energy consumption and spectral efficiency.

Optimization convergence is stable and accelerated with the approximate QT variant.

Abstract

This paper introduces the weighted-sum energy efficiency (WSEE) as an advanced performance metric designed to represent the uplink energy efficiency (EE) of individual user equipment (UE) in a user-centric Cell-Free massive MIMO (CF-mMIMO) system more accurately. In a realistic user-centric CF-mMIMO context, each UE may exhibit distinct characteristics, such as maximum transmit power limits or specific minimum data rate requirements. By computing the EE of each UE independently and adjusting the weights accordingly, the system can accommodate these unique attributes, thus promoting energy-efficient operation. The uplink WSEE is formulated as a multiple-ratio fractional programming (FP) problem, representing a weighted sum of the EE of individual UEs, which depends on each UE's transmit power and the combining vector at the central processing unit (CPU). To effectively maximize WSEE, we develop optimization algorithms based on the quadratic transform (QT), which is effective for multiple-ratio FP. By applying QT sequentially to each user's EE and the uplink SINR, the method converts the nonconvex WSEE objective into tractable subproblems and ensures stable, monotone convergence. We further introduce an approximate variant that alleviates QT's inherent nonlinearities to accelerate convergence. Compared with global energy efficiency (GEE)-oriented baselines, the proposed algorithms yield simultaneous improvements in user power consumption and spectral efficiency, while also reducing optimization time. Overall, the framework provides a foundation for designing operational strategies tailored to specific system requirements.