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A theory of nonlinear signal propagation in multi-span wavelength divisionmultiplexed coherent transmission systems that employ the semiconductor opticalamplifier as in-line amplifiers is presented for the first time. The rigorousderivation, based on time-domain first-order perturbation theory, is developedin detail. The end result is the expressions for the signal-to-noise ratio ofthe received sampled photocurrent, including contributions from noise,fiber-induced nonlinear distortions, and amplified-induced nonlineardistortions.

Coherent WDM Systems Using in-Line Semiconductor Optical Amplifiers