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In this paper we investigate maximum likelihood sequence estimation (MLSE) receivers operating on intensity modulated direct detection optical channels. Our study focuses on long haul or metro links spanning several hundred kilometers of single mode fiber with optical amplifiers. We describe the structure of MLSE-based optical receivers operating in the presence of dispersion and amplified spontaneous emission (ASE) noise, and we develop a theory of the error rate of these receivers. Computer simulations show a close agreement between the predictions of the theory and simulation results. We also address some important implementation issues. Optical channels suffer from impairments that set them apart from other channels and therefore they need a special investigation. Among these impairments are the facts that the optical channel is nonlinear, and the dominant source of noise is often ASE noise, which is distributed according to a noncentral chi-square probability density function (pdf). Additionally, optical fibers suffer from chromatic and polarization mode dispersion (PMD). Although the use of MLSE in optical channels has been discussed in earlier literature (J. H. Winter and R. D. Githin, Sept. 1990) (H.F. Haunstein et. al., 2001) no detailed analysis of optical receivers using this technique has been reported so far. This motivates the study reported in this paper.