Integrating Linear-Law Detector Performance Simulation Using Gram-Charlier Expansion

In numerous RF communication applications there is a need to analyze detector performance in noise, interference and fading environments. In detection usually multiple pulses or signal samples are integrated to improve performance. A Gram-Charlier expansion is often used to approximate the probability density function (PDF) with known moments. In this study, Linear-law detector performance is simulated using a Gram-Charlier series and the results are compared with the results obtained by direct multiple - PDF convolution. Numerical calculations for the case of Gaussian White Noise show comparable performance results, although direct signal plus noise Rician PDF convolution is faster computationally and doesn´t have Gram-Charlier series computational sensitivity to the number of terms used in the series expansion.