In this paper, we propose new closed-form approximations to the probability-density function (pdf) of the received signal in intensity-modulation/direct-detection (IM/DD) optical channels. These approximations greatly simplify the problem of channel estimation. This is an important problem in the implementation of maximum-likelihood sequence-estimation (MLSE) receivers for electronic dispersion compensation (EDC) of optical fibers, which has been a topic of great interest in recent years. The approximations proposed here are also useful in the analysis of the error rate of these receivers. It is well known that noise in IM/DD optical channels is strongly non-Gaussian and signal dependent. Except in the simplest situations, the pdf of the signal corrupted by noise does not have a closed-form expression. This leads to difficulties in the calculation of the probability of error on these channels and, more importantly, in the implementation of receivers that exploit knowledge of the signal pdf to minimize the error rate, for example, those based on MLSE techniques. To limit the complexity of channel estimation (an important requirement in real-time adaptive EDC receivers), it is important that the functional form assumed for the pdf be as simple as possible, while providing a good match with the actual statistical properties of the channel. In this paper, we introduce a new generic functional form for the pdf that accurately models the behavior of the received signal. Based on this expression, we introduce a channel-estimation approach that dramatically simplifies the analysis and design of MLSE receivers for IM/DD channels. Simulations show an excellent agreement between the results based on the approximations proposed here and the exact expressions for the pdf.
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