On the Optimality of Inverse Gaussian Approximation for Lognormal Channel Models

IF 3.2 2区 工程技术 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC
Taoshen Li;Shuping Dang;Zhihui Ge;Zhenrong Zhang
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引用次数: 0

Abstract

Because of the equilibrium between mathematical tractability and approximation accuracy maintained by the inverse Gaussian (IG) distributional model, it has been regarded as the most appropriate approximation substitute for the lognormal distributional model for shadowed and atmospheric turbulence induced (ATI) fading in the past decades. In this paper, we conduct an in-depth information-theoretic analysis for the lognormal-to-IG channel model substitution (CMS) technique and study its parametric mapping optimality achieved by minimizing the Kullback-Leibler (K-L) divergence between the two distributional models. In this way, we rigorously prove that the moment matching criterion produces the optimal IG substitute for lognormal reference distributions, which has never been observed in other CMS techniques. In addition, we clarify a myth in the realm of CMS that the IG substitute outperforms the gamma substitute for approximating lognormal reference distributions; instead, the substitution superiority shall depend on the parametric mapping criterion and the scale parameter of the lognormal reference distribution. All analytical insights presented in this paper are validated by simulation results.
论对数正态信道模型的反高斯逼近最优性
由于反高斯(IG)分布模型在数学可操作性和近似精度之间保持平衡,在过去几十年中,它一直被认为是对数正态分布模型在阴影和大气湍流诱导(ATI)衰落方面最合适的近似替代模型。本文对对数正态-IG 信道模型替代(CMS)技术进行了深入的信息理论分析,并通过最小化两个分布模型之间的 Kullback-Leibler (K-L) 分歧,研究了其参数映射的最优性。通过这种方法,我们严格证明了矩匹配准则能产生对数正态参考分布的最佳 IG 替代,而这在其他 CMS 技术中从未观察到。此外,我们还澄清了 CMS 领域的一个神话,即 IG 替代在近似对数正态参考分布方面优于伽马替代;相反,替代的优劣取决于参数映射准则和对数正态参考分布的标度参数。本文提出的所有分析见解都得到了模拟结果的验证。
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来源期刊
IEEE Signal Processing Letters
IEEE Signal Processing Letters 工程技术-工程:电子与电气
CiteScore
7.40
自引率
12.80%
发文量
339
审稿时长
2.8 months
期刊介绍: The IEEE Signal Processing Letters is a monthly, archival publication designed to provide rapid dissemination of original, cutting-edge ideas and timely, significant contributions in signal, image, speech, language and audio processing. Papers published in the Letters can be presented within one year of their appearance in signal processing conferences such as ICASSP, GlobalSIP and ICIP, and also in several workshop organized by the Signal Processing Society.
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