A new methodology for designing long-haul fiber-optic communication systems is presented. We derive the overall Volterra series transfer function of the system including linear dispersion, fiber nonlinearities, amplified spontaneous emission (ASE) noise from the fiber amplifiers, and the square-law nature of the direct detection (DD) system. Since analytical expressions for the probability of error are difficult to derive for the complex systems being used, we derive analytical expressions for an upper bound on probability of error for integrate-and-threshold detection at the receiver. Using this bound as a performance criterion, we determine the optimal dispersion parameters of each fiber segment required to minimize the effects of linear dispersion, fiber nonlinearities and ASE noise from the amplifiers. We study the dependence of optimal dispersion parameters on the average power levels in the fiber by varying the peak input power levels and the amplifier gains. Analytical expressions give us the freedom to choose system parameters in a practical manner, while providing optimum system performance. Using a simple system as an example, we demonstrate the power of the Volterra series approach to design optimal optical communication systems. The analysis and the design procedure presented in this work can be extended to the design of more complex wavelength division multiplexed (WDM) systems.
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