Error probability evaluation with a limited number of moments

In digital communications systems the error probability can often be expressed as the expectation of a function of an interference random variable. To approximate such expectations a number of methods have been proposed such as series expansion methods, Gauss quadrature rules and maximum entropy and minimum relative entropy methods. The methods proposed to approximate the error probability expectations typically require knowledge of a large number of moments of the interference random variable which may not be always available. In this paper, we use the Pearson system of distributions to approximate the distribution of the interference random variable and we then use the approximate distribution to compute the error probability expectations. This system of distributions has been used in a variety of situations to model distributions whose behaviour deviates from Gaussian behaviour. Very good agreement is observed between the Pearson approximation and simulation in the intersymbol interference case. Very good agreement was also observed between the Pearson approximation and simulation in the intermodulation distortion case.