重尾衰落中的多用户分集缩放
Multi-User Diversity Scaling in Heavy-Tailed Fading
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中文总结 AI 辅助
研究重尾复合衰落中多用户分集缩放定律的转变，证明最大信干噪比按$K^{1/m_s}$多项式缩放，给出遍历容量缩放，指出在特定阴影条件下该增益相关，确定收获增益条件并经模拟验证。
中文摘要 AI 辅助
经典多用户分集理论预测瑞利衰落信道上的吞吐量随$\log_2\!\log_2 K$增长。本文证明了在重尾复合衰落情况下这种缩放定律的根本转变。具体而言，在费希尔 - 斯内德科尔$\mathcal{F}$复合衰落中，信道功率有规则变化的上尾，使极值统计从耿贝尔域转变为弗雷歇域。我们证明$K$个用户中的最大信干噪比按多项式缩放为$K^{1/m_s}$，其中$m_s$是阴影严重度参数，导致遍历容量缩放为$\frac{1}{m_s}\log_2 K$。关键的是，这种缩放在干扰受限的泊松网络中持续存在，其中总同信道干扰改变缩放常数但不改变指数。这种多项式增益在严重到中等阴影（$m_s \leq 3$）时最相关，如在体域网、车辆/工业物联网和密集室内环境中遇到的情况，在实际用户数量下弗雷歇渐近超越行业标准对数正态模型。最后，我们确定收获此增益所需的条件，并通过蒙特卡罗模拟验证所有分析结果，包括MIMO随机波束成形。
英文摘要
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.
