Signal-dependent noise for b-modulation NFT-based transmission

The nonlinear Fourier transform (NFT) is a potentially promising way to mitigate nonlinear signal distortions in fiber-optic communication systems [1-4]. Recently, the new approach named the b-modulation was introduced [1] that allows to control the temporal duration of NFT-generated signals. In the 'traditional' NFT-based communication, the nonlinear spectrum, r (ξ) is used to modulate data. Then the signal duration depends on the signal energy and is not predetermined and controlled. The utilisation of the NFT scattering coefficient b (ξ) gives a possibility to control the pulse duration in time domain under condition that the Fourier spectrum of b (ξ) is localized. In particular, the OFDM format satisfies that condition. It was already shown that the properties of the effective noise in the NFT domain differ from a circular Gaussian noise. More specifically, such a noise is signal-dependent and non-circular [2, 3]. It was shown in [4] that the covariance B ₁ and pseudo-covariance B ₂ characteristics related to b-coefficient of NFT spectrum depend on the propagation distance. Here, we extend our previous work and examine noise characteristics for a novel b-modulation transmission introduced in [1]. We demonstrate that the variances behaviour is generic and do not depend on a specifics of NFT modulation. The presence of amplifier spontaneous emission in the optical link translates into the effective noise in the nonlinear spectral domain as an effective additive term N (ξ, b (ξ, 0)): e{-4 i \xi{2L}b}(\xi, L) = b(\xi, 0) + N(\xi, b(\xi, 0), L), where \xi is the 'nonlinear frequency' (NFT spectral parameter): \langle N (\xi)N (\xi ')\rangle = 2DL\pi \delta (\xi -\xi')B{1}(\xi, L), \langle N (\xi)N(\xi')\rangle = 2DL\pi \delta (\xi - \xi ')B {2}(\xi, L).