The {\kappa}-{\mu} Shadowed Fading Model with Integer Fading Parameters

TL;DR

This paper demonstrates that the {\kappa}-{\mu} shadowed fading model with integer parameters can be represented as a mixture of Nakagami distributions, simplifying performance analysis and approximation of fading channels.

Contribution

The paper introduces a closed-form mixture representation of the {\kappa}-{\mu} shadowed fading model with integer parameters, enabling easier analysis and approximation.

Findings

Performance evaluation becomes as simple as for Nakagami channels.

The {\kappa}-{\mu} shadowed distribution can approximate the {\kappa}-{\mu} distribution with large m.

Integer parameters have limited impact on fitting real measurements.

Abstract

We show that the popular and general {\kappa}-{\mu} shad- owed fading model with integer fading parameters {\mu} and m can be represented as a mixture of squared Nakagami (or Gamma) distributions. Thus, its PDF and CDF can be expressed in closed-form in terms of a finite number of elementary functions (powers and exponentials). The main implications arising from such connection are then discussed, which can be summarized as: (1) the performance evaluation of communication systems operating in {\kappa}-{\mu} shadowed fading becomes as simple as if a Nakagami fading channel was assumed; (2) the {\kappa}-{\mu} shadowed distribution can be used to approximate the {\kappa}-{\mu} distribution us- ing a closed-form representation in terms of elementary functions, by choosing a sufficiently large value of m; and (3) restricting the parameters {\mu} and m to take integer values has limited impact in practice when fitting the {\kappa}-{\mu} shadowed fading model to field measurements. As an application example, the average channel capacity of communication systems operating under {\kappa}-{\mu} shadowed fading is obtained in closed-form.