Analysis of Nonlinear Phase Noise in Single-Carrier and OFDM Systems

Abstract

The amplified spontaneous emission (ASE) of inline amplifiers gives rise to amplitude fluctuations of the optical field envelope and the fiber nonlinearity translates them into phase fluctuations. This is known as nonlinear phase noise. This type of noise is first studied by Gordon and Mollenauer [1] and hence, this noise is also called “Gordon–Mollenauer phase noise.” The nonlinear phase noise leads to performance degradation in fiberoptic systems based on phase-shift keying (PSK) or differential phase-shift keying (DPSK) [1–4]. Gordon and Molleneuer pointed out that two degrees of freedoms (DOFs) of the noise field are of importance [1]. These noise components have the same form as the signal pulse. One of the noise components is in phase with the signal and the other in quadrature. The in-phase component of the noise changes the amplitude of the signal pulse and hence, leads to energy change while the quadrature component leads to a linear phase shift. The energy change is translated into an additional phase shift due to fiber nonlinearity. Gordon and Mollenauer argued that the noise components other than the above-mentioned modes have less significant effects if the optical bandwidth is not too large and they derived a simple analytical expression for the variance of nonlinear phase noise by ignoring fiber dispersion. When the receiver filter bandwidth is larger than the signal bandwidth, it has been found that two DOFs are not sufficient to describe the noise process [5]. Analytical expressions for the probability density function of nonlinear phase noise have been derived in [6–8] by ignoring fiber dispersion. The interaction between the nonlinearity and ASE is the strongest when the dispersion is zero because of phase matching and therefore, the analyses of [1, 5–8] over estimate the impact of nonlinear phase noise. Attempts have been made to calculate the impact of nonlinearphase noise in the presence of dispersion [–23]. By assuming that the signal is CW and using the approach typically used in the study of modulational instability, it has been found that the variance of nonlinear phase noise becomes quite small in dispersion-managed transmission lines when the absolute dispersion of the transmission fiber becomes large [9]. Later in [10], the variance of nonlinear phase noise is calculated for a Gaussian pulse in a dispersion-managed transmission line and results showed that variance of nonlinear phase noise due to self-phase modulation (SPM) is quite small as compared to the case of no dispersion.