A semi-analytical method to model effective SINR spatial distribution in WiMAX networks

The stationary probabilities of different modulation and coding schemes (MCS) are required for dimensioning an OFDMA based network. In this paper, we introduce a semi-analytical approach to find out these stationary probabilities for a WiMAX network in downlink (DL) with users served by the best base station (BS). Using Monte Carlo simulations, we find the spatial distributions of effective signal to interference-plus-noise ratio (SINReff) for different values of shadowing standard deviation (σSH). With the help of distribution fit, we show that generalized extreme value (GEV) distribution provides a good fit for different frequency reuse schemes. Furthermore, by applying curve fitting, we demonstrate that the parameters of GEV distributions, as a function of (σSH) values, can be expressed using polynomials. These polynomial can then be used off-line (in place of time consuming simulations) to find out GEV cumulative distribution function (CDF), and hence the stationary probabilities of MCS, for any desired value of (σSH). We further show that these polynomials can be used for other cell configurations with acceptable deviation and significant time saving.