Alternative Formulations for the Fluctuating Two-Ray Fading Model

We present two alternative formulations for the popular fluctuating two-ray (FTR) fading model, which largely simplify its statistical characterization and subsequent use for performance evaluation. The new formulations are based on the observation that the FTR fading distribution can be expressed in terms of a finite continuous mixture of simpler distributions, also popular in the context of wireless channel modeling. In the general case with arbitrary $m$, the FTR fading model is described as an underlying Rician Shadowed (RS) distribution with continuously varying parameter $K$; hence, the chief statistics of the FTR fading model are expressed in terms of a finite-range integral over the equivalent RS statistic. In the special case of integer $m$, the FTR fading model is described in terms of a finite number of underlying squared Nakagami-$m$ distributions; again, the chief statistics of the FTR fading model are expressed in terms of a number of finite-range integrals over the equivalent Nakagami-$m$ statistic. In all instances, previous existing results in the literature for those simpler distributions can be extended to the case of FTR fading. Alternative expressions for the probability density function and cumulative distribution function of the FTR model are obtained, as well as new expressions for some Laplace-domain statistics of interest; these are used to exemplify the practical relevance of this new formulation for performance analysis.