Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise

This paper presents a novel method based on a parametric gain (PG) approach to study the impact of nonlinear phase noise in single-channel dispersion-managed differentially phase-modulated systems. This paper first shows through Monte Carlo simulations that the received amplified spontaneous emission (ASE) noise statistics, before photodetection, can be reasonably assumed to be Gaussian, provided a sufficiently large chromatic dispersion is present in the transmission fiber. This paper then evaluates in a closed form the ASE power spectral density by linearizing the interaction between a signal and a noise in the limit of a distributed system. Even if the received ASE is nonstationary in time due to pulse shape and modulation, this paper shows that it can be approximated by an equivalent stationary process, as if the signal were continuous wave (CW). This paper then applies the CW-equivalent ASE model to bit-error-rate evaluation by using an extension of a known Karhunen–Loéve method for quadratic detectors in colored Gaussian noise. Such a method avoids calculation of the nonlinear phase statistics and accounts for intersymbol interference due to a nonlinear waveform distortion and optical and electrical postdetection filtering. This paper compares binary and quaternary schemes with both nonreturn- and return-to-zero (RZ) pulses for various values of nonlinear phases and bit rates. The results confirm that PG deeply affects the system performance, especially with RZ pulses and with quaternary schemes. This paper also compares ON–OFF keying (OOK) differential phase-shifted keying (DPSK) systems, showing that the initial 3-dB advantage of DPSK is lost for increasing nonlinear phases because DPSK is less robust to PG than OOK.