The α-Lomax Distribution: A Compound Channel Model

Abstract: In this paper, we propose the {\alpha}-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 {\alpha}-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.