Approximation of SINR and rate distributions in the presence of path-loss, shadowing and fast-fading

This paper studies the distribution of Signal-to-Interference-plus-Noise Ratio (SINR) for the downlink of cellular networks taking into account the joint impact of path-loss, shadowing and fast-fading. We show that the calculation of the probability density function (PDF) of the SINR is not tractable. We propose two approaches for deriving the analytical expressions of the statistics of the SINR using two different approximations and we compare the results to Monte Carlo simulations. In the first approach, the interfering signals are approximated to their means, the PDF of SINR approximates well the one obtained by simulation only when the variances of the shadowing signals are small. In the second approach, only the fast-fading is averaged for the interfering signals. We give a closed form expression of the distribution of the SINR. We show, by comparing to simulations, that this approximation is more accurate than the first one for any value of the shadowing variance. We also deduce a closed form for the average data rate expression.