SINR and Rate Distributions for Downlink Cellular Networks

Signal-to-Interference-plus-Noise Ratio (SINR) measures the quality of the radio link between a base station and a User Equipment (UE). This quality indicator is important for the operator as it is used to measure and to optimize network coverage and the maximum user bitrate (which can be deduced from the SINR using the Shannon formula). In this paper, we study the SINR distribution for the downlink assuming that the received signals from serving and interfering cells undergo a path-loss and log-normal shadowing fading. We show that SINR can be approximated by a log-normal random variable and we give analytical expressions of characteristics parameters of its distribution. We then derive the average SINR expression. Also, we give a closed-expression of the rate probability density function and the outage probability and we obtain closed expressions of the average rate and lower and upper bounds of the average rate. For validation, we first compare theoretical results to Monte-Carlo network simulations and show that all the theoretical curves approximate well those obtained by simulations. Then using real measurements obtained by a measurement campaign, we validate the SINR distribution assumption. Based on a test of normality, we find that the recorded SINR samples are normally distributed in the logarithmic domain. We also show that the theoretical probability density function curves and the histogram of the measured samples of SINR are close.