  The Fisher-Snedecor $\mathcal{F}$ distribution has been recently proposed as
a more accurate and mathematically tractable composite fading model than
traditional established models in some practical cases. In this paper, we
firstly derive exact closed-form expressions for the main statistical
characterizations of the ratio of products of $\mathcal{F}$-distributed random
variables, including the probability density function, the cumulative
distribution function and the moment generating function. Secondly, simple and
tight approximations to the distribution of products and ratio of products of
$\mathcal{F}$-distributed random variables are presented. These analytical
results can be readily employed to evaluate the performance of several emerging
system configurations, including full-duplex relaying systems operating in the
presence of co-channel interference and wireless communication systems enhanced
with physical-layer security. The proposed mathematical analysis is
substantiated by numerically evaluated results, accompanied by equivalent ones
obtained using Monte Carlo simulations.
