Unifying Performance and Equity via Percentile Optimization and Cell-Free Massive MIMO

Abstract

Improving the throughput of the weakest users is a central objective of wireless resource allocation, and the objective around which the user-centric cell-free massive multiple-input multiple-output (UC-mMIMO) architecture is built. This paper brings the two together by formulating and solving percentile programs for UC-mMIMO networks. We maximize the sum-least-qth-percentile (SLqP) rate via downlink power control, a utility that targets the user equipments (UEs) in the lowest q percentile of the rate distribution and subsumes max-min-rate and sum-rate maximization as special cases. The problem is non-convex, non-smooth and NP-hard. The cyclic maximization approach of one of the previous percentile optimization series does not carry over: the coherent joint transmission technique introduces cross terms in the powers that destroy the block-concavity on which it relies. We develop a change of variables that restores block-concavity, yielding an algorithm with closed-form auxiliary updates and a concave power update, and we give a self-contained proof of non-decreasing convergence to a directional stationary point. Simulations establish two facts: first, percentile optimization retains its value in an architecture with no cell edges; relative to the weighted minimum mean-square error benchmark, it raises the average rate of the lowest-10th-percentile UEs by 56--72% and Jain's fairness index from below 0.92 to above 0.99. Second, compared directly with massive MIMO and small cells under the same SLqP utility, UC-mMIMO delivers the highest lower-percentile rates at every access point density tested, by up to 62% and 2.7$\times$ respectively, at the same fairness, and its advantage widens with densification.