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

Donghwi Kim, Liesbet Van der Perre, Wan Choi

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.

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

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.

Paper Structure

This paper contains 22 sections, 3 theorems, 43 equations, 7 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Outline
  3. Notations
  4. System Model
  5. AP-UE Association
  6. Uplink Channel Estimation
  7. Uplink Data Transmission
  8. Performance Metrics
  9. Weighted-Global Energy Efficiency
  10. Energy Efficiency of Each User
  11. Weighted-Sum Energy Efficiency
  12. Energy Efficiency Maximization
  13. WGEE Maximization
  14. WSEE Maximization
  15. Convergence Analysis
  16. ...and 7 more sections

Key Result

Lemma 1

demir2021foundations In a user-centric CF-mMIMO system with local MRC and LSFD combiner, the uplink SE of UE $k$ can be expressed as and $\mathsf{SINR}_k^{\mathrm{ul}}$ is given by where $\mathfrak{A}_{mk} = \left\lvert u_{m k}\right\rvert^2 \beta_{m k^{\prime}} \gamma_{m k}$, $\mathfrak{B}_{mk} = \left\lvert\sum_{m \in \mathcal{M}_k} u_{m k}^\dagger \gamma_{m k} \sqrt{\frac{\rho_{k^{\prime}}}{\

Figures (7)

  • Figure 1: Illustration of a user-centric CF-mMIMO system
  • Figure 2: The WSEE over iterations with different weighting factors.
  • Figure 3: Curves of WSEE versus $\omega$.
  • Figure 4: Average transmit power consumption.
  • Figure 5: Average EE and SE distribution by UE priorities over $\omega$.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Lemma 1
  • Remark
  • Proposition 1
  • proof
  • Proposition 2
  • proof