A Unified Analysis of Fox H-Fading With Beam Misalignment: Theory and Applications

This paper presents a unified analysis of the Fox H-fading channel with beam misalignment. A statistical framework is introduced that includes new expressions for the probability density function, cumulative distribution function, higher-order moments of the envelope/instantaneous signal-to-noise ratio (SNR), and moment generating function of the instantaneous SNR. The analysis also derives expressions for important metrics such as the bit error probability, outage probability, and ergodic channel capacity, as well as an asymptotic analysis of these metrics. Moreover, this work investigates several special cases and provides a detailed examination of the relationship between the Nakagami-
$m$
,
$\alpha$
-
$\mathcal {F}$
, and extended generalized-
$K$
fading models and the Fox H-fading distribution. As a result, this analysis facilitates an understanding of how existing work in the literature can be obtained as particular cases of this study. Furthermore, Monte Carlo simulations are conducted to corroborate several curves for different values that characterize the channel and beam misalignment parameters. This presentation helps to extend our understanding of the behavior of the Fox H-fading channel under beam misalignment, which has potential applications in wireless communications and other fields.