Abstract
An approximated channel model is proposed for signalling on the continuous spectrum of a nonlinear frequency division multiplexing 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 peak amplitude constraint is then studied. We show that, considering the input-dependency of noise, the conventional amplitude-constrained constellation designs can be shaped geometrically to show significant mutual information gains. However, it is observed that further probabilistic shaping and input distribution size optimization can only provide limited additional gains beyond the best geometrically shaped benchmark scheme, i.e., 64 Amplitude Phase Shift Keying.
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