Fluctuating Line-of-Sight Fading Distribution: Statistical Characterization and Applications

TL;DR

The paper introduces the fluctuating LoS (fLoS) fading model to capture LoS component fluctuations in 6G scenarios, parameterized by $K$, $k$, $\lambda$, and $\Omega$. It derives exact MGFs, PDFs, CDFs, and moments for the fLoS SNR using multivariate confluent hypergeometric functions, and shows that for integer $k$ the model simplifies to a finite mixture of $κ$-$μ$ components. Outage probability and ergodic capacity are analyzed, with a tailored Prony's method used to approximate $\ln(1+x)$ for EC computation. The work also demonstrates an application to MISO systems under channel aging, highlighting a persistent diversity order of 1 and providing insights into system performance under aging in dynamic environments.

Abstract

We introduce the fluctuating Line-of-Sight (fLoS) fading model, characterized by parameters $K$, $k$, $λ$, and $Ω$. The fLoS fading distribution is expressed in terms of the multivariate confluent hypergeometric functions $Ψ_2$, $Φ_3^{(n)}$, and $Φ_3 = Φ_3^{(2)}$ and encompasses well-known distributions, such as the Nakagami-$m$, Hoyt, Rice, and Rician shadowed fading distributions as special cases. An efficient method to numerically compute the fLoS fading distribution is also addressed. Notably, for a positive integer $k$, the fLoS fading distribution simplifies to a finite mixture of $κ$-$μ$ distributions. Additionally, we analyze the outage probability and Ergodic capacity, presenting a tailored Prony's approximation method for the latter. Numerical results are presented to show the impact of the fading parameters and verify the accuracy of the proposed approximation. Moreover, we illustrate an application of the proposed fLoS fading distribution for characterizing wireless systems affected by channel aging.

Figures (5)

• Figure 1: PDF of the SNR over the fLoS fading with different values for the d.o.f., $k$, where $\bar{\gamma} = 0$ dB, $\lambda = 5$ and $K = 10$ dB.
• Figure 2: SNR PDF over fLoS fading versus $\lambda$ with $k = 1$ and $K = 10$ dB. Solid lines correspond to the $\bar{\gamma} = 1$ case. Dashed lines correspond to the $\bar{\gamma} = 2$ case.
• Figure 3: OP as a function of the normalized $\bar{\gamma}$ for fLoS fading with $k = 1.5$, $K = 13$ dB and different values of $\lambda$.
• Figure 4: EC per unit bandwidth, $\overline{C}$, as a function of $\bar{{\gamma}}$ for fLoS fading with $K = 13$ dB and $\lambda = 0$
• Figure 5: Coverage probability as a function of the time index, $n$, for fLoS fading with $N = 4$, $\kappa = 10$ dB, $\bar{\gamma} / {\gamma}_{\rm th} = 10$ dB, and different values of the normalized Doppler shift, $f_d T_s$.

Theorems & Definitions (6)

• Remark 1
• Lemma 1
• Lemma 2
• Theorem 1
• Theorem 2
• Corollary 1