Error probability bounds and approximations for the influence of crosstalk on wavelength division multiplexed systems

New methods are developed for evaluating the average error probability in the presence of crosstalk for direct detection wavelength division multiplexed systems. A specific objective is the identification of soundly based performance evaluation tools adequately accommodating signal dependent noise, or compound randomness, encountered with systems incorporating optical amplifiers or avalanche photodiode receivers. To this end, explicit moment generating functions (MGFs) for random processes, including crosstalk, are developed. Results indicate that signal to interference ratio (SIR) of some 15.2 dB is required for a PIN receiver if performance is to be maintained unimpaired by crosstalk with a bit error rate (BER) of 10^-9. In contrast, for an avalanche photodiode (APD) receiver a slightly greater SIR is required, an SIR of 16.4 dB being found to be necessary for an APD gain of 10, for example