Single-Threshold Processing for Orthogonal Likelihood-Ratio Detection with Application to FSK Fiber-Optic Communications

The conditions under which processing reduces to a single threshold comparison is derived for the binary orthogonal likelihood-ratio; detection of a signal embedded in additive, independent noise. The range of the signal and noise is assumed to be discrete. Optimal processing of the observation vector, as well as two commonly used ad hoc processing schemes, are discussed. It is shown, in all three cases, that single-threshold processing is optimal, provided a weak condition on the noise is satisfied, independent of the signal. The results are presented in the context of a PCM/FSK photocounting fiber-optic communication system in which the noise is considered to be of the Poisson or avalanche types. Although single-threshold processing is shown to be optimal in most cases, examples are presented where single-threshold processing is not optimal.