The κ−μ$$ \kappa -\mu $$/Gamma‐Rayleigh Fading Model: A Composite Fading Model for Powerline‐Wireless Communication Channels

ABSTRACT Statistical distributions are frequently used to model fading effects introduced by the communication channel on the received signal. Some distributions are directly derived from physical propagation models, while others are adapted from statistics and applied to model fading based on their goodness‐of‐fit to measurements or on account of their mathematical simplicity. In this paper, a line‐of‐sight (LOS) shadowed /gamma‐Rayleigh (/GR) is proposed and thoroughly investigated. The GR distribution was selected for its mathematical simplicity and flexibility. Closed‐form expressions for fundamental statistics such as the probability density function (PDF) and cumulative distribution function (CDF) are derived for the /GR fading model. Additionally, analytical expressions for higher‐order moments, including the amount of fading (AF) and the moment generating function (MGF), are provided in closed‐form expressions. Performance measures of interest, such as outage probability (OP), average symbol error probability (ASEP), and average channel capacity, are derived in closed‐form for communication systems operating under the /GR channel fading conditions. The validity and utility of the proposed composite fading model for characterizing composite fading behavior observed in hybrid powerline‐wireless communication (PLC‐WLC) channels are demonstrated through an extensive series of theoretical comparisons with experimental PLC‐WLC measurements. Hybrid PLC‐WLC channel measurements were performed in various environments, and PLC‐WLC propagation scenarios were classified according to the cable branching characteristics of the PLC segment of the hybrid PLC‐WLC channel. The goodness‐of‐fit of the proposed composite fading model was evaluated using the Kullback‐Leibler (KL) divergence test. The results revealed that the proposed composite fading model exhibited an excellent fit to the fading conditions encountered in hybrid PLC‐WLC channels. Compared with other existing composite fading models, the /GR model provided the most accurate fitting results for measurements in large indoor environments, for which the propagation conditions present strong LOS signal components and weak scattered signal components. Furthermore, it was concluded on the basis of the obtained results that increased branching and terminations in the PLC channel of a PLC‐WLC propagation environment lead to increased shadowing and multipath fading effects on the received signal and, consequently, to increased composite fading.