The problem of average error probability evaluation for direct detection binary optical communications in the presence of avalanche gain, intersymbol interference, and colored additive Gaussian noise is considered. Tight new upper and lower bounds, together with a modified Gaussian quadrature rule based on approximate moments, are derived and evaluated. The bounds are found to be much tighter than the Chernoff bound though only slightly more complex to evaluate, and can be used as approximations to the error probability in most cases of practical interest. Taken together the new bounds and the modified Gaussian quadrature rule form a comprehensive set of performance evaluation tools offering a judicious balance between complexity and accuracy.

A technique for optimizing the performance of directdetection optical communication receivers for binary signaling in the presence of signal dependent noise, additive noise, and intersymbol interference by minimizing a Chernoff bound on the average error probability is extended to accommodate timing jitter. Receivers are identified which provide significantly improved performance compared to conventional designs, and the performance of a jitter-optimized receiver is shown to be relatively insensitive to variations in the jitter level.

A technique is developed for optimizing communication receivers by minimizing a Chernoff bound (CB) on the Bayes cost function. Being couched in terms of moment generating functions, the procedure is well suited to optical systems. Optimal CB receivers are derived and shown to coincide exactly with known minimum cost Bayes receivers for certain special cases of both electrical and optical communications for which closed form analytic solutions are possible. This provides endorsement for the method, which is then applied to more complex practical cases of linear optical fiber receivers in which both colored Gaussian noise and intersymbol interference play a part. The CB receivers are shown to offer some improvement compared with a zero forcing raised cosine equalizing receiver such as is commonly adopted, and all the evidence suggests that CB receivers achieve performance very close to the best possible with a linear receiver.