This paper discusses the investigation of maximum-likelihood sequence estimation (MLSE) receivers operating on intensity-modulated direct-detection optical channels. The study focuses on long-haul or metro links spanning several hundred kilometers of single-mode fiber with optical amplifiers. The structure of MLSE-based optical receivers operating in the presence of dispersion and amplified spontaneous emission (ASE), as well as shot and thermal noise, are discussed, and a theory of the error rate of these receivers is developed. Computer simulations show a close agreement between the predictions of the theory and simulation results. Some important implementation issues are also addressed. 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 noise is often non-Gaussian and signal dependent. For example, in optically amplified single-mode fiber links, the dominant source of noise is ASE noise, which after photodetection is distributed according to a noncentral chi-square probability density function. In addition, optical fibers suffer from chromatic and polarization-mode dispersion (PMD). Although the use of MLSE in optical channels has been discussed in previous literature, no detailed analysis of optical receivers using this technique has been reported so far. This motivates the study reported in this paper.

Abstract-Chromatic dispersion (CD) and polarization mode dispersion (PMD) severely limit the performance of optical transmission systems operating at data rates of 10 Gb/s and beyond. Electrical equalization techniques have been proposed to compensate dispersion in both coherent and intensity modulation/directdetection (IM/DD) systems. The former benefit from the fact that a complete compensation with zero penalty is possible, at least in principle, whereas in the latter the loss of phase information caused by the direct detection process results in a nonzero dispersion penalty even when optimal equalizers are used. In this paper, we investigate the combined adaptive digital equalization of all-order PMD, CD, and laser phase noise in highspeed coherent optical transmission systems. Although electrical equalization in coherent optical transmission systems has been addressed by previous literature [1]-[3], equalization of the combined effects of CD, PMD, and laser phase noise has not been reported so far. Simultaneous equalization of these impairments is particularly important in modulation systems that exploit polarization to increase the modulation efficiency, such as the joint polarization modulation and M-ary differential phase shift keying (JPMDPSK) system described in [4]. We propose a novel 4-dimensional equalizer structure for JPMDPSK systems. The specific example considered in this paper is 40 Gb/s transmission with a 10 GBaud symbol rate, using DQPSK modulation on each axis of polarization. Our results show that the new fourdimensional equalizer can compensate channel dispersion of up to 1000 km of standard single-mode fiber, with less than 3 dB penalty in signal to noise ratio (SNR). This is a dramatic improvement over 40 Gb/s IM/DD systems, even when they use electrical [5] or optical [6] equalization. The feasibility of the very large scale integration (VLSI) of coherent receivers in current technology is also discussed.

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