Extended α-η-μ Fading Distribution: Statistical Properties and Applications

In this paper, the impact of the non-linearity of the propagation medium on the extended
$\eta $
-
$\mu $
fading distribution is studied. In particular, the extended
$\alpha $
-
$\eta $
-
$\mu $
fading model in which the parameter
$\alpha $
represents the non-linearity of the propagation environment is presented via providing the exact and asymptotic of the statistical properties, namely, the probability density function (PDF), cumulative distribution function (CDF), and generalized-moment generating function (G-MGF). To this effect, exact closed-form mathematically tractable expressions of the outage probability (OP), average symbol error probability (ASEP), amount of fading (AoF), channel quality estimation index (CQEI) and effective rate (ER) are obtained. The asymptotic behaviour at high average signal-to-noise (SNR) values is also analysed to gain further insights into the influence of the index
$\alpha $
on the performance metrics of the wireless communication systems. Moreover, the average channel capacity (ACC) under different adaptive transmission techniques, such as, optimum rate and adaptation (ORA), capacity of the channel with inversion and fixed rate (CIFR), and truncated inversion and fixed rate (TIFR) are derived. The validation of the derived expressions is verified via comparing the numerical results with the Monte-Carlo simulations as well as some previous works for different scenarios.