Envelope statistics for filtered optical signals corrupted by phase noise

The authors consider the case of an optical pulse containing phase noise passed through either an optical filter or (following heterodyne lightwave detection) an electrical filter. Because of the phase noise, the envelope of the filter output at any instant is a random variable. The authors have developed an analytical method for estimating the probability density function (PDF) of this envelope for different kinds of filters and for realistic combinations of phase noise severity and filter bandwidth. Applications are to detection analyses of coherent lightwave systems, where broad laser linewidths can be an important impairment. For each of several filter types, it is found that the envelope PDF can be accurately fitted by an exponential function with a decay that is simply related to system parameters. It is noted that the present findings provide a critical element in work toward a complete analysis of FDMA (frequency division multiple access) networks