κ-μ衰落中独立非同分布SNR随机变量的第k个最大顺序统计量的分布及其在6G中的应用
Distribution of $k$-th Maximum Order Statistics of Independent, & Non-Identical SNR random variables in $κ-μ$ fading and its applications in $6G$
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中文总结 AI 辅助
研究κ-μ衰落中独立非同分布SNR随机变量第k个最大顺序统计量的分布，运用极值理论推导其渐近分布，还导出特殊情况，通过多应用展示意义，推导相关表达式，经蒙特卡罗模拟验证结果准确性。
中文摘要 AI 辅助
本文运用极值理论建立了具有独立非同分布参数的κ-μ衰落信道中信号与噪声比（SNR）的第k个最大顺序统计量的渐近分布。由于κ-μ包含如莱斯、瑞利和 Nakagami-m等著名分布，这些分布的顺序统计量也作为特殊情况导出。通过展示其在包括MIMO系统、反向散射系统、可重构智能表面和无人机辅助中继选择系统等多种应用中的适用性，证明了结果的实际意义。此外，利用第k个最大顺序统计量推导了中断概率和平均吞吐量的表达式。进行了全面的蒙特卡罗模拟以验证所提结果的准确性。
英文摘要
This paper employs extreme value theory to establish the asymptotic distribution of the $k$-th maximum order statistics of signal to noise ratio (SNR) for a $κ-μ$ fading channel with independent and non-identically distributed (i.n.i.d.) parameters. Since $κ-μ$ encompasses well-known distributions such as Rice, Rayleigh, and Nakagami-m, the order statistics for these are also derived as special cases. We demonstrate the practical significance of our results by showcasing their applicability in several applications, including antenna selection in MIMO systems, backscatter systems, reconfigurable intelligent surfaces, and UAV-assisted relay selection systems. Furthermore, by utilizing the $k$-th maximum order statistics, we derive expressions for outage probability and average throughput of $k$-th maximum order statistics. Comprehensive Monte Carlo simulations are carried out to verify the accuracy of the proposed results.
