The α-Lomax Distribution: A Compound Channel Model

TL;DR

The paper addresses the need for flexible fading models by introducing the α-Lomax distribution, which generalizes Lomax fading with a shaping parameter $α$ that controls unimodality versus decreasing behavior of the SNR. By modeling the instantaneous SNR as $Γ= ar{γ} Z$ with a derived PDF and CDF for $Γ$, it yields closed-form expressions for outage probability, average BER, and average capacity, plus a BLER expression for short packets, and it provides high-SNR approximations to simplify design insights. The α-Lomax framework includes a physical sampling model, demonstrates parameter-driven diversity gains with $G_d=α$, and is validated against empirical D2D data, showing superior fit over competing compound models. This work enables more accurate performance analysis and design of modern wireless systems, including URLLC and D2D scenarios, by offering a tunable, analytically tractable fading model and practical high-SNR approximations.

Abstract

In this paper, we propose the α-Lomax distribution as a new compound fading channel model. This new distribution generalizes the recently introduced Lomax fading channel model. It is worth noting that the Lomax distribution is a decreasing function, while the α-Lomax is a unimodal function, offering greater flexibility in modeling wireless fading channels. In particular, we derive closed-form expressions for the probability density function and cumulative distribution function for the instantaneous signal-to-noise ratio (SNR). Additionally, we provide closed-form expressions for several fundamental performance metrics, including outage probability, average bit error rate, and channel capacity. Furthermore, we derive closed-form expression for the average block-length error rate in short-packet communications. Moreover, we fit the PDF of the proposed channel model to empirical data obtained from a device-to-device communication system. We also offer simple and accurate approximations for these expressions in the high SNR regime.

Figures (7)

• Figure 1: Outdoor NLoS empirical and theoretical PDFs fitted to D2D communication systems 8270655n.
• Figure 2: $\alpha$-Lomax SNR PDF under varying $\alpha$ with $\lambda=1.25$.
• Figure 3: $\alpha$-Lomax SNR PDF under varying $\lambda$ with $\alpha=2$.
• Figure 4: Outage performance for different values of $\alpha$ and $\lambda$. $R_{0}=1$ [bps/Hz].
• Figure 5: Average BER performance for various modulation schemes with $\alpha=1.75$ and $\lambda=1.25$.