Approximations of EESM Effective SNR Distribution

The Probability Density Function (PDF) or Cumulative Distribution Function (CDF) of the effective Signal to Noise Ratio (SNR) is an important statistical characterization in the performance analysis of an Orthogonal Frequency Division Multiple Access (OFDMA) system using Exponential Effective SNR Mapping (EESM). However, the exact closed form of PDF is extremely difficult to obtain. A general approximation method known as Moment Matching Approximating (MMA) is used to approximate the distribution of effective SNR by a simple expression. In this paper, the approximation by Gaussian, Generalized Extreme Value (GEV) and Pearson distribution are studied. Results show that Gaussian approximation is very useful when the number of sub-carriers is sufficiently large. Both GEV and Pearson approximation are accurate enough in approximating the distribution of effective SNR in a general case.