Performance analysis and design of WDM based optical communication systems using a Volterra series method

Future broadband fiber optic communication systems must be based on wavelength division multiplexing (WDM) techniques, which will push the capacity of a single fiber link to the order of 10 Terabits per second. Traditionally, most of the performance analysis and system design for a single wavelength channel system is based on over-simplified analytical expressions or intensive simulations. This is not feasible for WDM based systems due to increase in bandwidth, more pronounced fiber nonlinearity and enhanced system complexity. The task of this dissertation is to develop effective analytical tools for performance analysis and system design of such systems, with a goal to reduce or equalize the combined effect of group-velocity dispersion (GVD) and fiber nonlinearities.; A Volterra series method, developed by Peddanarappagari and Brandt-Pearce, can give a closed-form Volterra series transfer function (VSTF) solution to the nonlinear Schrödinger (NLS) equation, which describes optical pulses propagating through a single mode optical fiber. In this dissertation, a modified NLS equation is derived to model systems with a much broader transmission bandwidth. By using a total field formulation the modified NLS equation is shown to be proper for WDM based systems without a need to change the equation form. Therefore, the VSTF solution for WDM based systems keeps the same form as for single wavelength channel systems. System parameters can be easily included into this VSTF solution. Thus many performance analysis and system design problems can be solved analytically.; Due to analytical and computational complexity, the VSTF solution must be truncated to the third order. This truncated third order solution is equivalent to the first order perturbation solution, which means that a small signal approximation is assumed. Thus the accuracy of this truncated VSTF solution becomes worse when fiber nonlinearities become more pronounced, as in WDM based systems. Therefore, it is necessary to investigate the accuracy systematically. After evaluating the third order model accuracy and inspecting various nonlinear effects, the truncation of the VSTF to third order is found sufficient for future broadband WDM based terrestrial applications when measures have been taken to suppress such nonlinear effects. Furthermore, application range characteristics are given as performance analysis and system design guide lines.; The applications for performance analysis and system design by using the third order VSTF method are illustrated by a nonlinear equalizer design example. A unified system equalization theory is given, which can explain several practical applications. An optimal equalizer is obtained, and the parameter mismatch sensitivity for such an optimal equalizer is analyzed. Another equalization scheme which uses optical phase conjugation (OPC) and Raman amplification is discussed. System optimization and design criteria, such as eye opening penalty (EOP), Q factor, and bit error rate (BER), are summarized. Using the third order Volterra series method, a BER upper bound for a channel of interest in a WDM system is discussed for the GVD optimization problem. The discussion shows that to apply the third order VSTF solution to the field of performance analysis and design for WDM based systems, signal dependent inter-channel interaction has to be studied carefully in the future. Finally, after a summary of major results of the dissertation, possible research directions using the Volterra series method for performance analysis and system design for WDM based systems are introduced as future work.