# Mitigating the Impact of Noise on Nonlinear Frequency Division Multiplexing +
## 6 System Performance  
First, we further investigate the performance gain that can be achieved by using the proposed power-tilt strategy. Figure 7b shows the NFDM performance as a function of the launch power \(P\), comparing the cases with and without the power-tilt strategy (\(\delta=0.9\) and \(\delta=0\), respectively) and considering different burst lengths \(N_{b}\). In both cases, the DF-BNFT detection strategy is employed, which provides the best performance among all the considered strategies. At low power, when the NFDM system tends to a conventional linearly modulated system, the performance is independent of \(N_{b}\). On the contrary, when the power increases, the curves increase up to a certain peak value, which depends on the burst length \(N_{b}\)--the shorter \(N_{b}\), the better the peak performance. This behavior, already shown for the standard NIS modulation [9; 13; 24] and discussed in Section 3, is maintained also when the power-tilt strategy (dashed line) is used. Nevertheless, the tilt strategy with 0.9 strength significantly improves the peak performance of NFDM-NIS with DF-BNFT compared to the case of a flat power allocation (solid lines), with a larger gain when the burst length is shorter. In this case, since the same tilt strength \(\delta=0.9\) is used for any launch power, the performance at low power worsens, as explained in Section 5. This undesired effect could be easily avoided by optimizing the tilt strength for each launch power. Moreover, we expect that further improvements can be obtained by optimizing the tilt strength and/or tailoring the applied power profile for each burst length. This optimization is left for a future study. Then, we present a summary comparison of the performance achievable with the various modulation and detection techniques considered in this work, comparing it with the performance achievable by a standard NFDM system (with NIS modulation and FNFT detection) and by a conventional linearly modulated system (with no NFT and employing electronic dispersion compensation (EDC)). Figure 8 shows the peak performance (obtained at the corresponding optimal launch power) of the different systems as a function of the rate efficiency \(\eta\). The proposed I-FNFT, DF-FNFT, and DF-BNFT strategies (in order of increasing complexity and performance) significantly improve the performance of the NIS-modulated NFDM system compared to the FNFT strategy, the DF-BNFT one providing a gain of about 6 dB for \(\eta\geq 20\%\). Nonetheless, even with the DF-BNFT strategy and differently from the linearly modulated system, the NFDM performance keeps decreasing  
Figure 7: **(a)**Performance of NFDM systems with DF-BNFT detection and NIS modulation, for \(N_{b}=1024\) and different tilt strength \(\delta\), **(b)** Performance of NFDM systems with DF-BNFT detection and NIS modulation without power tilt (solid lines) and with 0.9 tilt (dashed lines). with the increase of the rate efficiency \(\eta\). As shown in Section 3, this is an inherent limitation of the NIS modulation--in which the increase of the power (beyond a certain limit) or of the signal duration cause a decrease of the minimum Euclidean distance between the generated waveforms--which cannot be solved by improving the detection strategy. The only way in which the problem with the minimum Euclidean distance might be overcome is by modifying the modulation itself, that is, the rule with which the modulated signal is mapped to the nonlinear spectrum--for instance, by resorting to the different strategies discussed in Section 5. The b-modulation--implemented here simply by letting \(b(\lambda)=-S(\lambda/\pi)\)--performs worse than NIS; in this case, the peak performance is determined by the power limit discussed in Section 5.1, which is reached before a possible decay of the minimum Euclidean distance takes place; however, a proper shaping of the carrier pulses and of the modulation alphabet can increase the power limit and enhance its performance [17].