arXiv subjects

Carlos Rafael Nogueira da Silva

Publications and source records attributed to Carlos Rafael Nogueira da Silva.

2 recordsLinked to original sources

arXiv2025

Cute but Cunning: Effective Closed-Form Alternatives to the Exact Lognormal Statistics

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.

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arXiv2019

On Shadowing the $κ$-$μ$ Fading Model

In this paper, we extensively investigate the way in which $κ$-$μ$ fading channels can be impacted by shadowing. A family of shadowed $κ$-$μ$ fading models are introduced and classified according to whether the underlying $κ$-$μ$ fading undergoes single or double shadowing. We discuss three types of single shadowed $κ$-$μ$ model (denoted Type I to Type III) and three types of double shadowed $κ$-$μ$ model (denoted Type I to Type III). The taxonomy of the single shadowed Type I - III models is dependent upon whether the fading model assumes that the dominant component, the scattered waves, or both experience shadowing. The categorization of the double shadowed Type I - III models is dependent upon whether a) the envelope experiences shadowing of the dominant component, which is preceded (or succeeded) by a secondary round of shadowing (multiplicative), or b) the dominant and scattered contributions are fluctuated by two independent shadowing processes, or c) the scattered waves of the envelope are subject to shadowing, which is also preceded (or succeeded) by a secondary round of multiplicative shadowing. Although the physical definition of the examined models make no predetermination of the statistics of the shadowing process, for illustrative purposes, two example cases are provided for each type of single and double shadowed model by assuming that the shadowing is shaped by a Nakagami-$m$ random variable (RV), an inverse Nakagami-$m$ RV or their mixture. The double shadowed $κ$-$μ$ models offer remarkable flexibility as they include the $κ$-$μ$, $η$-$μ$, and the various types of single shadowed $κ$-$μ$ distribution as special cases. Moreover, we demonstrate a practical application of the double shadowed $κ$-$μ$ Type I model by applying it to channel measurements obtained for body area networks operating at 2.45 GHz.

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