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 (G-C) series, leading to arbitrarily accurate systematic evaluation of bit-error rates (BERs) and optimal decision thresholds of optical communication systems. The method displays negligible computational complexity and is applicable whenever the moment or cumulant generating functions of the decision statistics are analytically available. We applied the technique to a birth-and-death Markovian 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 BER which deviated by 7% from the G-C result.