Optically Amplified Direct Detection With Pre- and Postfiltering: A Volterra Series Approach

We present yet another quasi-analytic model for an optically amplified receiver, comprising an optical preamplifier, an optical prefilter, a photodetector, and an electrical postfilter. Due to the square-law nonlinearity and its interaction with the linear pre- and postfilters, 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 nonlinear theory to obtain fresh insight deriving a simplified model streamlining the pseudoanalytic simulations. Volterra series is a powerful mathematical tool for simulating nonlinear systems, applied here to quadratic optical detection in an unconventional way, by deriving a mixed frequency-time representation, leading to a simple and compact quadratic form in the combined signal-plus-noise signal spectra, albeit not computationally efficient. Next, Forestieri's results, which used distinct bases for the signal and noise, are rederived using the insightful Volterra formalism. Finally, we reformulate the model using an expansion of both signal and noise in a common harmonic basis over a sliding window of duration equal to the ISI system memory. This final version of the optically amplified receiver model is most computationally efficient, provides the most compact description, and lends itself to intuitive interpretation. Applications of the new method include accurate determination of the bit error ratio of amplitude-shift keying, frequency-shift keying, and differential phase-shift keying transmission systems in the linear optical link propagation regime, including the effects of dispersion and fully accounting for intersymbol interference. The theory developed here is naturally extensible to advanced optical equalization techniques, involving Volterra nonlinear optoelectronic equalizers.