Optimum Direct Detection for Digital Fiber-Optic Communication Systems

In recent years much attention has been focused on communication over optical channels.1-2 Most early work was concerned with the physics of the electromagnetic transmission phenomena associated with various optical media and with the devices needed to change electrical signals to optical ones, and vice versa. In this paper, we are concerned with the optimum (maximum likelihood) reception of digital data transmitted over the fiber-optic channel. Our work was motivated by the many invaluable discussions we have had with S. D. Personick on this subject. 1389 We shall not dwell on the quantum mechanical limitations imposed on the measurements of signals in the optical frequency range. Instead, we adopt a practical approach and assume at the outset that direct detection is used to convert optical energy to an electrical signal. This is accomplished by using a photodetector prior to any signal processing. Thus, we study a classical optical reception problem with the understanding that the photodetector output can be examined in every detail so as to extract all relevant information. In a fiber-optic communication system, information is conveyed by modulating the intensity of a light source, such as a light-emitting diode. This is manifested in a photon stream whose arrival times form a Poisson process with a time-varying intensity function. The photodetector output current can then be modeled as a noisy filtered Poisson process whose intensity function is the sum of a dispersed version of the modulating wave and a background dark current.