  Nonlinear Fourier transform (NFT) and eigenvalue communication with the use
of nonlinear signal spectrum (both discrete and continuous), have been recently
discussed as a promising transmission method to combat fiber nonlinearity
impairments. However, because the NFT-based transmission method employs the
integrability property of the lossless nonlinear Schr\"odinger equation (NLSE),
the original approach can only be applied directly to optical links with ideal
distributed Raman amplification. In this paper, we investigate in details the
impact of a non-ideal Raman gain profile on the performance of the nonlinear
inverse synthesis (NIS) scheme, in which the transmitted information is encoded
directly onto the continuous part of the nonlinear signal spectrum. We propose
the lossless path-averaged (LPA) model for fiber links with non-ideal Raman
gain profile by taking into account the average effect of the Raman gain. We
show that the NIS scheme employing the LPA model can offer a performance gain
of 3 dB regardless of the Raman gain profiles
