Optimum direct detection for digital fiber-optic communication systems

We report on optimum direct detection of digital data signals that are transmitted over optical fibers. Direct detection is provided by a photodetector whose output current is modeled as a noisy filtered Poisson stream of pulses. In this model, the time-varying pulse arrival rate is proportional to a linearly distorted version of the modulating signal. We show how the photodetector output is processed to derive the minimum probability-of-error receiver. Special attention is given to certain practical limiting cases. When the average energy in the response of the photodetector to an individual photon is small compared to the additive thermal noise, the optimum detector is shown to be linear except for the use of precomputed bias terms. At the other extreme are the photomultiplier and the avalanche photodiode where the average energy in the response of the photodetector to a single photon is large compared with the additive noise. In this situation, we show that the optimum detector estimates the photon arrival times and then uses these estimates in a weighted counter. In both limiting cases, the detectors are specialized to one-shot M-ary and synchronous multilevel pulse-amplitude modulated (pam) signals with intersymbol interference. For pam signaling, we demonstrate that finite system memory allows application of dynamic programming to provide a detector implementation whose computational complexity does not increase with time.