effects of the major transmission impairments and provide higher data rates, improved error rates, or longer repeaterless spans.

For an ana&s of equalization techniques in multimode fiber ystems, see [I]. ost current multigigabit-per-second digital fiber optic systems use simple modulation and detection techniques, such asonoff keying with matched-filter receiver techniques. However, morecomplex techniques, such asequalization, coding, and/or multilevel signaling, can be used in lightwave systems to significantly increase the data rate and/or reduce the effect of transmission impairments and improve performance, and in many casescan be easily implemented. The purpose of this article is to provide an overview of these techniques, which become increasingly important as device technology matures, in which case substantial increases in performance (especially for in-place systems) may only be achieved through these techniques. There are numerous sources of transmission impairments in lightwave systems. These include chromatic and polarization dispersion in the fiber, laser and fiber nonlinearities, nonideal receiver response, echo, and distortion caused by semiconductor optical amplifiers. Fortunately, there are also numerous techniques to reduce these impairments, including coding, equalization, and modulation techniques with multilevel signaling. The main problem facing the system designer is to determine the appropriate techniques for specific impairments, and for which systems these techniques will have the most significant impact on performance. Here, we offer guidelines for selecting signal processing techniques and present several examples of the potential use of these guidelines in both direct- and coherent-detection lightwave systems. Our goal is to determine performance bounds and find important applications for impairment reduction techniques in which the improvement is large and the implementation relatively simple. We are primarily interested in single-mode fiber systems.' These techniques can be used for upgrading existing systems (e.g., reducing chromatic and polarization dispersion in