Technical Research On High-Efficiency Nonlinear Frequency Division Multiplexing Systems

Nonlinear frequency division multiplexing(NFDM),as a possible technique to overcome the limit imposed by Kerr nonlinearity in conventional coherent optical communication systems,has attracted widespread attention in the communication community in recent years.The highlight of NFDM is that it takes the nonlinearity in the optical fiber as the design factor of the system,and through the mathematical tool of nonlinear Fourier transform(NFT),the time domain nonlinear transmission of the signal in the optical fiber is transformed into the linear transmission in the nonlinear spectral domain,thus fundamentally solving the problem of capacity limitation caused by fiber nonlinearity.The signal can be decomposed into two types of nonlinear spectra in the nonlinear spectral domain by NFT:discrete spectrum and continuous spectrum.Therefore,according to which part of the nonlinear spectra is exploited,NFDM systems can be categorized as discrete-spectrum modulation,continuous-spectrum modulation and full-spectrum modulation,that is,joint modulation of discrete spectrum and continuous spectrum.NFDM technology has opened up a new paradigm of encoding,modulating and processing data in optical communication.Therefore,it is of great significance to carry out related research on NFDM systems.Although NFDM systems theoretically solve the capacity limitation problem caused by nonlinear effects in high-speed long-distance optical fiber communication,the transmission performance and spectral efficiency(SE)of NFDM verification experiments reported in the literature are generally low,and there is no significant advantage over traditional wavelength-division multiplexing(WDM)or orthogonal frequency division multiplexing(OFDM)systems.The main reason is that the noise problem restricts the performance improvement of NFDM systems.The noise problem of the NFDM system mainly comes from the following two aspects:(1)processing noise,mainly from the calculation error of NFT/INFT algorithm,truncation error caused by the non-satisfaction of zeroing condition in the NFDM signal waveform design process,and the approximation error of system model.(2)physical noise,mainly from the amplified spontaneous emission(ASE)noise introduced by amplifiers in the optical fiber link.The existence of ASE noise destroys the integrability of the channel transmission equation,resulting in non-orthogonal nonlinear spectra and crosstalk.In addition,since NFT is a nonlinear transformation mathematically compared to the linear fourier transform(FT),ASE noise no longer appears as additive white Gaussian noise(AWGN)in the nonlinear spectral domain,but exhibits characteristics that are strongly related to signal power and interact with signals,which further limits the transmission performance and SE of NFDM systems.This article conducts the following research on the problems in the NFDM system mentioned above:(1)Research on noise problems in the continuous-spectrum NFDM system This part of the research starts from solving the noise problem of the NFDM system.First,through optimizing the waveform shaping stage of the NFDM system,the NFDM signal is made to meet the zero-boundary condition as much as possible,thereby reducing the processing noise of the system and improving system performance.Then,by introducing the probabilistic shaping(PS)technology at the transmitting end,the tolerance of the NFDM signal to ASE noise is improved by using the characteristics that the probability of the inner circle of the probabilistic shaping constellation is large and that of the outer circle is small under bmodulation.Finally,considering that there is a certain correlation between the subcarriers at the receiving end under the influence of noise factors,a neural network equalizer module is introduced at the receiving end of the NFDM system to learn the correlation between subcarriers,thereby further improving system performance.(2)Research on discrete-spectrum partial modulation and demodulation scheme in the full-spectrum NFDM systemIn order to fully utilize the available degrees of freedom in nonlinear spectral domain to improve data rate and SE,the most direct and effective way is to use full spectrum modulation.There are two common problems with full-spectrum systems in existing literature:(1)using q-modulation instead of b-modulation which has better performance;(2)discrete spectrum in full spectrum generally uses low-order modulation formats and lacks corresponding optimization and equalization schemes.Starting from the above problems,this part of the research constructs a full-spectrum NFDM system under b-modulation.Through simulation performance analysis,it was proved that under non-ideal channel conditions,the continuous spectrum and discrete spectrum will interact with each other,resulting in a decrease in the system performance.In order to improve the performance of the continuous spectrum part,PS technology was used in the modulation module of continuous spectrum.At the same time,geometric shaping(GS)combined with the linear minimum mean square error(LMMSE)estimator was used in the modulation and demodulation module of discrete spectrum to improve its performance.By optimizing the above scheme,a total rate of 103.75 Gbps was achieved with a bit error rate(BER)lower than the hard decision forward error correction(HD-FEC)threshold of 1620 km full-spectrum system transmission.Compared with traditional full-spectrum modulation,the achievable transmission distance of the system has increased by 500 km.(3)Research on the optimization of eigenvalue distribution of discrete spectrum part in the full-spectrum system In view of the current situation of few discrete spectrum eigenvalues and low modulation efficiency in the existing full-spectrum modulation scheme,the selection of eigenvalue distribution is optimized by studying the influence of discrete spectrum parameters on the temporal characteristics of multi-soliton signals and their influence on continuous spectrum in the full spectrum modulation,so as to maximize the data rate of discrete spectrum part.Then,combined with PS and LMMSE estimator,the transmission of full-spectrum NFDM system with BER lower than hard-decision FEC threshold was realized for 1120 km.Among them,13 eigenvalues were multiplexed in discrete spectrum part(currently the most),which can improve the data rate by about 12% compared with pure continuous-spectrum modulation system.This work provides direction for improving the modulation efficiency of discrete spectrum part in the fullspectrum system.To sum up,this paper focuses on the noise problem and modulation mode in the NFDM system,and improves the performance and spectral efficiency of the NFDM system by designing the modulation and demodulation strategies at the transceiver end of the system.The research work provides the direction for realizing high-efficiency nonlinear frequency division multiplexing systems.