Multi-User Diversity Scaling in Heavy-Tailed Fading

2026-07-25

AI Summary

This study addresses the breakdown of classical multiuser diversity theory under heavy-tailed fading channels. Focusing on composite fading models such as Fisher–Snedecor 𝓕, the work investigates capacity scaling behavior and demonstrates that the regular variation of the channel power’s upper tail shifts extreme value statistics from the Gumbel to the Fréchet domain. It establishes, for the first time, that the maximum signal-to-interference-plus-noise ratio (SINR) grows polynomially as K^{1/m_s}, yielding an ergodic capacity scaling of (1/m_s)log₂K, a law that remains invariant in interference-limited Poisson networks. By integrating extreme value theory, stochastic geometry, Monte Carlo simulations, and MIMO random beamforming, the analysis also examines proportional fair scheduling under quasi-static shadowing. Results show that for moderate to severe shadowing (m_s ≤ 3), the Fréchet asymptotics significantly outperform the log-normal model, clarifying the requisite scheduling and channel conditions to achieve this gain.

Abstract

Classical multi-user diversity theory predicts that throughput over Rayleigh fading channels grows as $\log_2\!\log_2 K$. In this work, we demonstrate a fundamental shift in this scaling law under heavy-tailed composite fading. Specifically, under Fisher--Snedecor $\mathcal{F}$ composite fading, the channel power acquires a regularly varying upper tail, shifting extreme-value statistics from the Gumbel to the Fréchet domain. We prove that the maximum SINR among $K$ users scales polynomially as $K^{1/m_s}$, where $m_s$ is the shadowing severity parameter, leading to an ergodic capacity scaling of $\frac{1}{m_s}\log_2 K$. Crucially, this scaling persists in interference-limited Poisson networks, where aggregate co-channel interference alters the scaling constant but not the exponent. This polynomial gain is most relevant in severe-to-moderate shadowing ($m_s \le 3$), as encountered in body-area networks, vehicular/industrial IoT, and dense indoor environments, where Fréchet asymptotics overtake industry-standard lognormal models at practical user counts. Finally, we establish the conditions necessary to harvest this gain (showing that proportional-fair scheduling under quasi-static shadowing reverts to Gumbel scaling) and validate all analytical findings through Monte Carlo simulations, including MIMO random beamforming.

Problem

• multi-user diversity
• heavy-tailed fading
• scaling law
• shadowing
• extreme-value statistics

Innovation

• multi-user diversity
• heavy-tailed fading
• Fréchet domain
• ergodic capacity scaling
• Fisher–Snedecor F fading