Comparison of Error Probability and Signal-to-Noise Ratio between a Coherent Heterodyne and a Photon-Limited Laser Communications System.

The error probability for a coherent heterodyne laser digital communications system is calculated for Poisson signal and local oscillator photon distributions and compared to a photon counting system. It is shown that under optimum conditions, the coherent heterodyne system requires more average signal photons per detection interval than the photon counting system for equal probabilities of error. For a binary communications system with equal zero or one transmit probability, an error probability of </= 10(-3) requires a power S/N approximately 24 for the coherent heterodyne system while only a S/N approximately 3.5 for the photon counting system.