可爱却狡猾：有效闭合形式替代精确对数正态统计
Cute but Cunning: Effective Closed-Form Alternatives to the Exact Lognormal Statistics
AI总结：
本文提出两种闭合形式替代模型，用于高效近似对数正态分布的统计特性，适用于无线通信中的大尺度衰落建模。
摘要：
对数正态分布是一种基础的统计模型，在生物学、金融、经济学、工程等领域广泛应用。在无线通信中，它是最主要的大尺度衰落建模统计量。然而，其已知的解析不可行性持续带来信道特性和性能分析的挑战。本文介绍两种有效的、数学上可处理的替代模型，由纳卡吉米-$m$和逆纳卡吉米-$m$（I-Nakagami-$m$）变量的乘积构成。这些模型在渐近精确的闭合形式表达式中提供了关键性能指标——包括特征函数、误码率和香农容量——并允许对复合$α$-$μ$-对数正态衰落模型的概率密度函数和累积分布函数进行解析表达。为便于实现，开发了一种矩匹配框架，将对数正态参数映射到替代模型参数。此外，提出了一种随机混合方法，通过利用纳卡吉米-$m$和I-Nakagami-$m$分布的互补近似特性来增强收敛性。该方法进一步扩展到异质级联衰落通道，其中包含任意组合的$α$-$μ$、$κ$-$μ$和$η$-$μ$变量，对于这些情况，推导出到等效对数正态分布的矩映射。数值结果证实了所提方法的准确性和效率，将其定位为精确对数正态统计的实用且可靠的替代方案。
英文摘要：
The Lognormal distribution is a fundamental statistical model widely used in different fields of science, including biology, finance, economics, engineering, etc. In wireless communications, it is the primary statistic for large-scale fading modeling. However, its known analytical intractability presents persistent channel characterization and performance analysis challenges. This paper introduces two effective and mathematically tractable surrogate models for the Lognormal distribution, constructed from the product of Nakagami-$m$ and Inverse Nakagami-$m$ (I-Nakagami-$m$) variates. These models yield asymptotically exact closed-form expressions for key performance metrics -- including the characteristic function, bit error rate, and Shannon's capacity -- and enable analytically tractable expressions for the probability density function and cumulative distribution function of the composite $α$-$μ$-Lognormal fading model. To facilitate implementation, a moment-matching framework is developed to map the Lognormal parameters to the surrogate model parameters. In addition, a random mixture approach is proposed to enhance convergence by exploiting the complementary approximation properties of the Nakagami-$m$ and I-Nakagami-$m$ distributions. The methodology is further extended to heterogeneous cascaded fading channels comprising arbitrary combinations of $α$-$μ$, $κ$-$μ$, and $η$-$μ$ variates, for which moment-based mappings to the equivalent Lognormal distributions are derived. Numerical results confirm the accuracy and efficiency of the proposed approach, positioning it as a practical and reliable alternative to exact Lognormal statistics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
