An Exact Statistical Representation of $\alpha-\eta-\kappa-\mu$ Fading Model for THz Wireless Communication

The
$\alpha-\eta-\kappa-\mu$
is one of the most generalized and flexible channel models having an excellent fit to experimental data from diverse propagation environments. The existing statistical results on the envelope of
$\alpha-\eta-\kappa-\mu$
model contain an infinite series, prohibiting its widespread application in the performance analysis of wireless systems. This paper employs a novel approach to derive density and distribution functions of the envelope of the
$\alpha-\eta-\kappa-\mu$
fading channel without an infinite series approximation. The derived statistical results are presented using a single Fox's H-function for tractable performance analysis, especially for high-frequency mmWave and terahertz wireless transmissions. We also develop an asymptotic analysis using the Gamma function, which converges to the exact values within a reasonable range of channel parameters. To further substantiate the proposed analysis, we present the exact outage probability and average bit-error-rate (BER) performance of a wireless link subjected to the
$\alpha-\eta-\kappa-\mu$
fading model using a single trivariate Fox's H-function. We obtain the diversity order of the system by analyzing the outage probability at a high signal-to-noise (SNR) ratio. We use simulations to demonstrate the significance of the developed statistical results compared with the existing infinite series representation of the
$\alpha-\eta-\kappa-\mu$
model.