Higher Order Statistics of Sampled Fading Channels With Applications

In this paper, we present a novel analytical framework for the calculation of the level crossing rate (LCR) and the average fade duration (AFD) of fading channels sampled at a certain sampling period
$T_{S}$
. These expressions are valid for arbitrary fading distributions with arbitrary correlation and can be easily computed in terms of the cumulative distribution function (cdf) of the fading envelope and its bivariate cdf. This approach yields interesting insights into the effect of finite sampling in the higher order statistics of fading processes. We also demonstrate that the proposed expressions for sampled fading process converge with the existing expressions for continuous fading processes as the sampling period tends to zero. As a direct application, exact closed-form expressions are given for the LCR and AFD of sampled Rayleigh fading processes, which are suitable to characterize the higher order statistics of the equivalent frequency-domain fading process in multipath Rayleigh fading.