On Optimally Shaped Signals for Nonlinear Frequency Division Multiplexed Fiber Systems

An approximated channel model is proposed for direct signaling on the continuous spectrum of a nonlinear frequency division multiplexed (NFDM) communication system, describing the effect of noise and nonlinearity at the receiver. The optimal input distribution that maximizes the mutual information of the proposed approximated channel under the peak amplitude constraint is then studied. We present that, considering the input-dependency of the noise, the conventional amplitude-constrained constellation designs can be geometrically shaped to provide significant mutual information gains. However, it is observed that further probabilistic shaping and constellation size optimization can provide only limited additional gains beyond the best geometrically shaped benchmark scheme, i.e., 64 Amplitude Phase Shift Keying. Then, an approximated channel model that neglects the correlation between subcarriers is proposed for the matched filtered signaling system, based on which the input constellation is geometrically shaped. We demonstrate that although the inter-subcarrier interference in the filtered case is neglected in the channel model, the shaping of the matched filtered case can provide promising gains in mismatch capacity over the unfiltered scenario.