Achieving $α$-Fairness in Clustered Cell-Free Networking: A Tight Relaxation Approach

2026-05-16

AI Summary

This work addresses the trade-off between inter-cluster fairness and system spectral efficiency in clustered cell-free networks by proposing a tunable α-fairness optimization framework. By establishing, for the first time, the equivalence between the continuous relaxation and the original integer programming formulation, and leveraging closed-form deterministic equivalents of ergodic capacity together with convexity analysis of the α-fair objective, the combinatorial clustering problem is transformed into a tractable continuous optimization problem. A customized algorithm is then developed to solve it efficiently, with guaranteed convergence. The framework unifies four representative fairness criteria within a single formulation. Numerical results demonstrate that, at the cost of only about 5% loss in total throughput, the proposed approach improves the Jain’s fairness index by up to 11% and enhances the minimum cluster capacity by as much as 45%.

Abstract

Clustered cell-free networking has emerged as a promising architecture to balance the high performance of cell-free massive MIMO and the scalability of traditional cellular systems. However, achieving fairness across subnetworks remains a critical yet largely unsolved challenge. This paper investigates the fairness problem in clustered cell-free networking and proposes a unified and tunable alpha-fairness scheme that effectively balances overall spectral efficiency and inter-subnetwork fairness. Using the closed-form deterministic equivalent of the ergodic sum capacity, we reformulate the combinatorial clustering problem as a continuous optimization problem. Leveraging the concavity/convexity properties of the alpha-fair objective, we classify the problem into four distinct cases according to the value of alpha. For each case, we establish the exact equivalence between the original integer program and its continuous relaxation, and develop efficient algorithms with guaranteed convergence. Extensive simulations show that the proposed scheme achieves up to 11% improvement in Jain's fairness index and 45% gain in minimum subnetwork capacity, with only a negligible 5% reduction in aggregate throughput.

Problem

• alpha-fairness
• clustered cell-free networking
• inter-subnetwork fairness
• spectral efficiency
• fairness

Innovation

• alpha-fairness
• clustered cell-free networking
• continuous relaxation
• deterministic equivalent
• convex-concave analysis