# Mitigating the Impact of Noise on Nonlinear Frequency Division Multiplexing +
## 8 Conclusions  
In this manuscript, we have first considered a standard NFDM system, discussing its weakness with respect to conventional linearly modulated systems. In particular, we have highlighted that both the modulation and the detection strategies have been directly inherited from conventional systems and simply reapplied in the nonlinear spectrum domain, with no check on their optimality in this new context. In fact, we have shown that the linear modulation of the continuous nonlinear spectrum yields a set of optical waveforms with a minimum distance that decays as the power increases, making the system very sensitive to noise. At the same time, the detection is optimized for an AWGN channel, but is applied in the nonlinear frequency domain, where the noise is signal-dependent. Both these issues are responsible for the severe performance limitations that affect NFDM systems and which prevent them from achieving high spectral efficiencies.  
In light of the above, we have investigated some improved modulation and detection strategies that can mitigate the detrimental impact of amplifier noise in NFDM systems. In particular, by combining the NIS modulation with a simple power-tilt strategy and the DF-BNFT detection strategy, we have obtained a performance improvement of more than 8 dB with respect to a standard NFDM system. The improved NFDM system outperforms a conventional linearly modulated system with EDC for a rate efficiency--the ratio between the effective signaling time and the total (signaling plus guard) time in which the channel is used--\(\eta\leq 30\%\). Unfortunately, when the rate efficiency is increased, the performance decays even for the improved system--exactly as for all NFDM systems and in contrast to linearly modulated systems. While we discussed other important aspects related to NFDM that should be properly accounted for before NFDM systems can be considered for practical applications, e.g., the modulation of the discrete spectrum or the impact of attenuation, in our opinion, the most important theoretical issue that needs to be solved is the unfavorable performance decay that characterize the current NFDM system. Indeed, the great variability of performance among the various strategies considered in this work suggests that we are still far from optimality, and that further improvements might be achievable, for instance by more finely tuning the proposed power-tilt strategy and optimizing the applied power profile beyond a simple linear tilt.  
A natural question that arises from the results presented in this work is whether we should keep investigating NFDM systems and, if so, in which direction. As we have seen, current NFDM systems have some fundamental limitations which make them not competitive with traditional systems--even in an ideal physical scenario and even considering the large gains provided by the improved modulation and detection strategies proposed in this work--unless one is interested in the transmission of very short bursts separated by long guard intervals. Nevertheless, we believe that a more appropriate mathematical treatment of the noise impact on NFDM, possibly favored by a joint exploitation of the continuous and discrete spectrum, could help to design optimal modulation and demodulation techniques to eventually overcome these limitations. Without such a major breakthrough, it is unlikely that we will ever be able to exploit the alleged tolerance of NFDM to fiber nonlinearity. This is, therefore, the main research direction that we recommend for future studies on NFDM.  
Conceptualization, S.C. and M.S.; methodology, S.C. and M.S.; software, S.C.; investigation, S.C. and M.S.; resources, M.S. and E.F.; writing--original draft preparation, S.C.; writing--review and editing, M.S. and E.F. ; supervision, M.S.; funding acquisition, M.S and E.F. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
The authors declare no conflict of interest.