Perturbative discrete-time multivariate fiber channel model with finite memory

Abstract

We introduce a discrete-time fibre channel model that provides an accurate analytical description of signalsignal and signal-noise interference with memory defined by the interplay of nonlinearity and dispersion. Also the conditional pdf of signal distortion, which captures non-circular complex multivariate symbol interactions, is derived providing the necessary platform for the analysis of channel statistics and capacity estimations in fibre optic links. Keywords: discrete-time channel model, channel memory, nonlinear interference, Shannon capacity INTRODUCTIONAccurate description of fibre channel models is critically important for information theory analysis, coding, and digital signal processing techniques in future high capacity transmission systems [1]. Existing channel models [2][3][4][5] are based on averaging signal distortions via an infinite memory approximation [6] of the signal interactions, where they are considered to be nonlinear noise. As averaging leads to information loss about the signal interference, it results in a degraded lower bound of the system capacity in the highly nonlinear regime. More accurate channel capacity estimations will require accurate modelling approaches that take into account the finite response of the nonlinear channel [7][8]. These can be also used for other applications such as coding [6] or pre/post-distortion [9-10] compensation, and suggest system designs that can improve significantly the transmission capacity [11][12].Here we developed a perturbative discrete-time channel model with finite memory based on the nonlinearity compensation technique proposed in [10] and experimentally demonstrated in [11][12]. The resulted multivariate channel model allows us to describe memory effects analytically, including both signal-signal and signal-noise effects. Its accuracy has been compared against numerical simulations and the traditional Gaussian noise model approach, showing high accuracy in every operating regime of the transmission system. Finally, we derive an analytical expression of the conditional pdf that describes signal-interference in fiber-optic channels..