# Mitigating the Impact of Noise on Nonlinear Frequency Division Multiplexing +
## 7 Discussion
### Discrete Spectrum Modulation  
This manuscript considers NFDM systems in which only the continuous nonlinear spectrum is modulated: the discrete nonlinear spectrum is left empty by construction when the signal is generated at the TX, and is assumed to be still empty at the RX--if some discrete components arise during propagation because of ASE noise, they are simply neglected. Nevertheless, also the discrete spectrum can be employed to encode information, either on the eigenvalues \(\lambda_{i}\in\mathbb{C}^{+}\) or, most commonly, on their components \(\rho_{i}=b(\lambda_{i})/a^{\prime}(\lambda_{i})\) or \(b(\lambda_{i})\)[3; 14; 16]. The modulation of the discrete spectrum can be either associated with the modulation of the continuous spectrum or employed alone.  
In principle, adding some discrete components for information transmission comes for free, i.e., it should have no impact on the continuous spectrum and simply increase the information rate. Unfortunately, introducing discrete components has some drawbacks. Indeed, just a single discrete component brings a lot of energy (proportional to the imaginary part of \(\lambda_{i}\)), which strongly affects the accuracy of the numerical algorithms, so that the numerical methods usually employed for the BNFT cannot be used directly but should be combined with the Darboux transform [16; 35]. Furthermore, the information carried by a few discrete components is negligible with respect to that carried by the continuous nonlinear spectrum. To the best of our knowledge, the highest number of modulated discrete components demonstrated experimentally is seven without continuous spectrum and in single polarization [22], and two combined with continuous spectrum and two polarizations [16]. Similarly to the continuous spectrum, the b-modulation has been shown to provide significant advantage with respect to the conventional \(\rho_{i}\)-modulation, also for the discrete spectrum, by avoiding the noise on \(a^{\prime}(\lambda_{i})\). As far as it concerns the detection strategy, the conventional FNFT has been mostly used, except for the MAP strategy in time employed in [22], and a detection based on machine learning [25]. An NFT domain equalizer for discrete spectrum NFDM has been proposed in [36].  
An interesting but still unexplored possibility is that of using the discrete spectrum, jointly with the continuous one, not to carry additional information, but to control the Euclidean distance between the generated waveforms, trying to solve the noise problem discussed in Section 3. Indeed, though it is theoretically possible to create a large set of high-energy waveforms with an empty discrete spectrum--for instance by using NIS modulation--there is no guarantee that these waveforms will have a large enough minimum Euclidean distance. In fact, the conventional linear modulations that are commonly used in optical fiber systems--which guarantee the desired behavior in terms of minimum Euclidean distance--give rise to optical waveforms that, at typical launch powers, do contain discrete spectral components (solitons) with a very high probability [37].