A Formulation of the Log-Logistic Distribution for Fading Channel Modeling

Abstract

In some scenarios, the log-logistic (LL) distribution is shown to provide the best fit to field measurements in the context of wireless channel modeling. However, a fading channel model based on the LL distribution has not been formulated yet. In this work, we introduce the L-distribution as a reformulation of the LL distribution for channel modeling purposes. We provide closed-form expressions for its PDF, CDF, and moments. Performance analysis of wireless communication systems operating under L-fading channels is exemplified, providing exact and asymptotic expressions for relevant metrics such as the outage probability and the average capacity. Finally, important practical aspects related to the use of the L-distribution for channel fitting purposes are discussed in two contexts: (i) millimeter-wave links with misaligned gain, and (ii) air–ground channels in unmanned aerial vehicle communications.