Accurate Evaluation of Bit-Error Rates of Optical Communication Systems Using the Gram–Charlier Series

Accurate Evaluation of Bit-Error Rates of Optical Communication Systems Using the Gram–Charlier Series The probability densities and cumulative distribution functions of decision statistics of optical communications systems are expanded as a Gram–Charlier series, leading to arbitrarily accurate systematic evaluation of bit-error rates and optimal decision thresholds of optical communication systems. The method displays negligible computational complexity, and is applicable whenever the moment or cumulant generating function of the decision statistics are analytically available. We applied the technique to a birth-and-death Markoffian model of a direct-detection receiver with optical preamplifier in a two-level amplitude-shift keying system. The modal expansion series rapidly converged, whereas the alternative saddlepoint approximation method predicted a bit-error rate which deviated by 7% from the Gram–Charlier result.