Higher Order Moments of Error Rates of Digital Modulations

Statistics of the conditional error rates of digital modulations over fading channels are considered. The probability density function and the higher order moments of the conditional error rates are obtained using the Prony approximation. For a Ricean distributed channel fading amplitude at the detector input, non-monotonic behavior of the moments of the conditional bit error rates versus some channel model parameters is observed. Furthermore, the Bollinger bands for the first order non-central moment of the conditional bit error rate are obtained as an application of the second order moment of the conditional bit error rate. Our results indicate that, in line-of-sight communications links, smaller transmission powers can be used to reduce the average bit error rate as well as to reduce the variance of the conditional bit error rate.