M.Sc Thesis

M.Sc StudentLivshitz Betty
SubjectOptically Pre-amplified and Pre-filtered Detection with
Electric Post-filtering - a Semi-analytic
Volterra Series Based Approach
DepartmentDepartment of Electrical and Computer Engineering
Supervisors PROFESSOR EMERITUS Moshe Nazarathy
PROF. Moshe Horowitz


We present an alternative quasi-analytic model for an optically amplified receiver, comprising an optical pre-amplifier, an optical pre-filter, a photo-detector and an electrical post-filter. Due to the square-law non-linearity and its interaction with the linear pre- and post- filters, the understanding of this seemingly simple structure has been elusive, gradually evolving over a succession of stud­ies, culminating in the models by Lee-and-Shim and Forestieri. Here we adopt a new approach to this old problem, applying Volterra non-linear theory to obtain fresh insight, deriving a simplified model streamlining the pseudo-analytic simulations. 

Volterra series is a powerful mathematical tool for simulating non-lin­ear systems. The method is applied here to quadratic optical detection in an unconventional way: by using an equivalent bilinear system, a mixed frequency-time formulation is derived, leading to representation of the output in a compact quadratic form.

Applications of the new method include: (i) Accurate determination of the bit-error rate of an amplitude shift keying (ASK) transmission system in the linear optical link propagation regime, including dispersion effects and fully accounting for inter-symbol interference. (ii) Simpler yet more gen­eral derivations of the second-order noisy signal statistics (autocorrelations and power spectral densities) at several points in the optically amplified receiver. (iii) Optimization of the electrical filter in order to maximize the signal-to-noise ratio at the sampler, for specified input signal and optical filter. The theory developed here is naturally extensible to advanced optical equalization tech­niques, involving Volterra non-linear opto-electronic equalizers.