# The {\alpha}-{\kappa}-{\mu} Shadowed Fading Distribution: Statistical Characterization and Applications

## TL;DR

This paper introduces the { extalpha}-{ extkappa}-{ extmu} shadowed ({ extalpha}-KMS) fading distribution, a comprehensive model unifying many classical fading distributions, and analyzes key performance metrics for wireless channels.

## Contribution

It proposes the { extalpha}-KMS distribution as a unifying fading model and derives analytical expressions for performance metrics like outage probability and capacity.

## Key findings

- { extalpha}-KMS includes many classical fading models as special cases.
- Performance metrics can be derived using existing { extalpha}-{ extmu} results.
- Finite mixture representation simplifies analysis for integer parameters.

## Abstract

We introduce the {\alpha}-{\kappa}-{\mu} shadowed ({\alpha}-KMS) fading distribution as a natural generalization of the versatile {\alpha}-{\kappa}-{\mu} and {\alpha}-{\eta}-{\mu} distributions. The {\alpha}-KMS fading distribution unifies a wide set of fading distributions, as it includes the {\alpha}-{\kappa}-{\mu}, {\alpha}- {\eta}-{\mu}, {\alpha}-{\mu}, Weibull, {\kappa}-{\mu} shadowed, Rician shadowed, {\kappa}-{\mu} and {\eta}- {\mu} distributions as special cases, together with classical models like Rice, Nakagami-m, Hoyt, Rayleigh and one-sided Gaussian. Notably, the {\alpha}-KMS distribution reduces to a finite mixture of {\alpha}-{\mu} distributions when the fading parameters {\mu} and m take positive integer values, so that performance analysis over {\alpha}-KMS fading channels can be tackled by leveraging previous (existing) results in the literature for the simpler {\alpha}-{\mu} case. As application examples, important performance metrics like the outage probability and average channel capacity are analyzed.