Downlink Average Rate and SINR Distribution in Cellular Networks

The statistical characteristics of the signal-to-interference plus noise ratio (SINR) are closely related to many performance metrics of cellular networks. In this paper, the downlink average rate and SINR distribution are studied for orthogonal frequency division multiple access (OFDMA)-based cellular networks subject to the distance-dependent path loss and shadow fading (SF). With the analytical approximate mean and moment generating function (MGF) of the SINR in the logarithmic domain, the closed-form approximation for the lower and upper bounds of the average rate is obtained. Then the distribution of the SINR in the logarithmic domain is proposed to be approximated as the normal inverse Gaussian (NIG) distribution whose parameters are computed explicitly through moment matching. Also, the closed-form expression for the cumulative distribution function (CDF) of the SINR based on the NIG approximation is derived. Simulation results not only verify the tightness of the bounds, but also show that the NIG approximation is up to one order of magnitude more accurate than the Pearson type IV approximation and at least one order of magnitude more accurate than the lognormal approximation when the SF correlation coefficient is small or the standard deviations of the SF are large or different.