A b-modulated nonlinear frequency division multiplexing system based on gaussian mixture clustering

Abstract

This invention proposes a b-modulation nonlinear frequency division multiplexing system based on Gaussian mixture clustering, belonging to the field of optical fiber communication system technology. It creatively applies the Gaussian mixture clustering algorithm to the b-modulation nonlinear frequency division multiplexing system, replacing the original hard decision and soft decision algorithms of the b-modulation nonlinear frequency division multiplexing system, to equalize the phase rotation of the received constellation diagram caused by noise, thereby eliminating the influence of spontaneous emission noise from the EDFA amplifier and various adverse factors in the optical fiber channel. At the same time, it performs clustering decision on the demodulated 16QAM constellation diagram data, reducing the bit error rate of the system and improving the system performance.

Description

Technical Field

[0001] This invention relates to the field of optical fiber communication system technology, and in particular to a b-modulation nonlinear frequency division multiplexing system based on Gaussian mixture clustering. Background Technology

[0002] Fiber nonlinearity is a major factor limiting the performance of fiber optic communication systems, and various compensation methods have been proposed, such as digital backward transmission, optical phase conjugation, and phase conjugated dual-wavelength transmission. However, these methods all treat nonlinearity as a system impairment and attempt to mitigate its adverse effects in transmission systems based on linear channel designs. Nonlinear frequency division multiplexing (NFDM), based on nonlinear Fourier transform (NFT), incorporates nonlinear effects into the design of optical communication systems, making dispersion and nonlinearity no longer limitations on the transmission system, but rather integral components of the system.

[0003] Nonlinear frequency division multiplexing technology relies on the principle of eigenvalue soliton communication. After encoding information into a nonlinear spectrum, the time-domain signal obtained by inverse nonlinear Fourier transform (INFT) is transmitted in optical fiber. The evolution of its nonlinear spectrum is only a phase rotation related to the eigenvalue and transmission distance. Only corresponding phase compensation is needed at the receiving end to recover the nonlinear spectrum carrying the encoded information.

[0004] Modulated nonlinear frequency division multiplexing (NFDM) systems are a newly proposed continuous spectrum NFDM system (Gui T, Zhou G, Lu C, et al. Nonlinear frequency division multiplexing with b-modulation:shifting the energy barrier[J]. Optics express, 2018, 26(21): 27978-27990), which encodes information in the scattering coefficients. up instead Up, and prove Modulated NFDM fiber optic communication systems compared to The modulated system exhibits a lower bit error rate and superior transmission performance. It overcomes the signal-noise correlation effect caused by the increase in factor carriers.

[0005] In a nonlinear frequency division multiplexing optical fiber communication system based on improved K-Means polarization division multiplexing, the bit error rate of the system is compared by applying different decision methods such as improved K-Means, hard decision, and soft decision at the receiver. The results show that the K-Means algorithm can equalize the data at the receiver and then make a decision, thereby reducing the bit error rate of the system.

[0006] In practical applications of nonlinear frequency division multiplexing (NFDM) optical fiber communication systems, EDFA amplifiers are used to periodically compensate for fiber loss during signal transmission. The spontaneous emission noise of the amplifier causes eigenvalue fluctuations. Due to the correlation between eigenvalues ​​and scattering coefficients, this further leads to random fluctuations in the scattering coefficients, causing phase rotation issues at the receiver. This introduces demodulation problems into the receiver's digital signal processing, increasing the system's bit error rate and reducing system performance. Existing systems based on... Modulated nonlinear frequency division multiplexing optical fiber communication systems often fail to perform equalization or achieve poor equalization when making decisions on signals that have passed through various channels and amplifier noise at the receiving end. For example, hard decision-making and soft decision-making without equalization, as well as K-Means clustering equalization, can lead to problems such as random initial centroids causing clustering to get trapped in local optima, resulting in a high bit error rate and affecting the system performance during actual signal transmission. Summary of the Invention

[0007] This invention addresses the problem of high demodulation bit error rate caused by signal phase rotation at the receiver in existing technologies. It proposes a b-modulation nonlinear frequency division multiplexing system based on Gaussian mixture clustering to improve system performance and reduce the system bit error rate.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A b-modulated nonlinear frequency division multiplexing system based on Gaussian mixture clustering, wherein:

[0010] At the transmitting end, a pre-compensation mechanism is used to modulate the NFDM signal, and the continuous spectrum is obtained after reconstruction. Pre-compensation The mechanism is designed as follows:

[0011]

[0012] Where m is the block index and A is the power control parameter. It is the normalized useful block duration. Due to pre-compensation tasks The normalized total block duration resulting from signal broadening, where N is the number of modulated subcarriers and L is the normalized transmission distance. It is a high-order QAM symbol sequence;

[0013] At the receiving end, the time domain signal Restored to nonlinear continuous spectrum Afterwards, phase compensation is performed, and the constellation diagram data is demodulated from the continuous spectrum and imported into the Gaussian mixture clustering algorithm model for clustering and decision-making.

[0014] The Gaussian mixture clustering algorithm model is as follows:

[0015]

[0016] Among them, Gaussian mixture distribution has a total of It consists of several mixture components, each corresponding to a Gaussian distribution, with a mean vector. Covariance Matrix It is the first Parameters of a Gaussian mixture component For the corresponding mixing coefficient Assume that all data samples are generated by a Gaussian mixture distribution.

[0017] Furthermore, the transmitter encodes the data into... After the subcarrier is on, the following formula is used. and Reconstruction:

[0018]

[0019]

[0020] in, This represents the Hilbert transform.

[0021] Furthermore, the Gaussian mixture clustering algorithm model parameters The solution is obtained by maximizing the likelihood estimation, i.e., maximizing the log-likelihood function. :

[0022] .

[0023] Furthermore, the Gaussian mixture clustering algorithm model includes the following steps:

[0024] First, the parameters of the Gaussian mixture clustering algorithm model are initialized;

[0025] Then the EM algorithm was used to optimize the model parameters. Perform iterative updates; in each iteration, first calculate the posterior probability of each sample belonging to each Gaussian component based on the current parameters. Then, the model parameters are updated based on the obtained posterior probabilities. The process continues until the stopping condition of the EM algorithm or the likelihood function is met. Slow growth or even cessation of growth;

[0026] Finally, each sample is assigned to its corresponding cluster according to the following formula, and the final result is returned:

[0027] .

[0028] Furthermore, the signal transmission process at the transmitting end includes:

[0029] Modulate the signal to After reconstruction, a continuous spectrum was obtained. ;

[0030] For continuous spectrum The problem of recovering the original time-domain signal from scattering data of a nonlinear continuous spectrum by performing a nonlinear inverse Fourier transform is transformed into solving the GLME equations, which are obtained using the TIB algorithm. .

[0031] The time-domain digital signal generated by the digital signal processing at the transmitting end is converted into an analog signal by a DAC, and then loaded onto an optical wave by a laser and an IQ modulator and sent into an optical fiber for transmission.

[0032] Furthermore, the signal processing at the receiving end includes:

[0033] A coherent detector is used to receive optical signals and convert them into electrical signals, which are then converted into digital signals by an ADC.

[0034] The signal is then fed into the digital signal processing module at the receiving end. After time synchronization and normalization, a nonlinear Fourier transform is used to convert the time-domain signal into a digital signal. Restore to nonlinear continuous spectrum data ;

[0035] Continuous spectrum NFT is transformed into numerically solving the Zakharov-Shabat system;

[0036] Then, post-phase compensation is performed to demodulate the data from the continuous spectrum and import it into the Gaussian mixture clustering algorithm model for equalization and decision-making to obtain the final data.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0038] The present invention proposes a b-modulated nonlinear frequency division multiplexing system based on Gaussian mixture clustering, which creatively applies the Gaussian mixture clustering algorithm to traditional... In modulated nonlinear frequency division multiplexing systems, it replaces the original Hard decision (HD) and soft decision (SD) algorithms are used in the modulation nonlinear frequency division multiplexing system to equalize the phase rotation of the received constellation diagram caused by noise, so as to eliminate the influence of spontaneous emission noise of EDFA amplifier and various adverse factors in optical fiber channel. At the same time, clustering decision is performed on the demodulated 16QAM constellation diagram data to reduce the bit error rate of the system and improve the system performance. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0040] Figure 1 The flowchart of the Gaussian mixture clustering algorithm model provided in the embodiment of the present invention is shown.

[0041] Figure 2 This is an architecture diagram of a b-modulated nonlinear frequency division multiplexing system based on Gaussian mixture clustering, provided in an embodiment of the present invention.

[0042] Figure 3 This is a flowchart of digital signal processing at the transmitting end provided in an embodiment of the present invention.

[0043] Figure 4 This is a flowchart of digital signal processing at the receiving end provided in an embodiment of the present invention. Detailed Implementation

[0044] To better understand this technical solution, the method of the present invention will be described in detail below with reference to the accompanying drawings.

[0045] The b-modulation nonlinear frequency division multiplexing system based on Gaussian mixture clustering proposed in this invention applies the Gaussian mixture clustering algorithm to traditional... In a modulated nonlinear frequency division multiplexing system, a Gaussian mixture clustering algorithm model is first built. Based on the principle of the Gaussian mixture clustering algorithm, the model is built using Python.

[0046] Specifically, we define the Gaussian mixture distribution:

[0047]

[0048] This distribution has a total of It consists of several mixture components, each corresponding to a Gaussian distribution. The mean vector is... Covariance Matrix It is the first The parameters of a Gaussian mixture component, and For the corresponding "mixing coefficient", Assume that all data samples are generated by a Gaussian mixture distribution.

[0049] Gaussian mixture distribution model parameters The solution is obtained by maximizing the likelihood estimation, i.e., maximizing the log-likelihood function. :

[0050]

[0051] The EM algorithm is used for iterative optimization and solution.

[0052] The Gaussian mixture clustering algorithm model process is as follows: Figure 1 As shown, the model parameters of the Gaussian mixture distribution are first initialized, and then the EM algorithm is used to iteratively update the model parameters. In each iteration, the posterior probability of each sample belonging to each Gaussian component is calculated based on the current parameters. (E-step), and then update the model parameters based on the obtained posterior probabilities. (M steps) until the stopping condition of the EM algorithm is met (e.g., the maximum number of iterations has been reached, or the likelihood function has been satisfied). (Growth is minimal or even ceases), then according to Each sample is assigned to its corresponding cluster, and the final result is returned.

[0053] Substitute the model When modulating a nonlinear frequency division multiplexing system, the demodulated 16QAM constellation data and the number of hyperparameter Gaussian mixture components are included in the simulation process. The input model is processed by the Gaussian mixture clustering algorithm to complete clustering, make decisions, and finally calculate the bit error rate.

[0054] Next, we will build a Gaussian mixture clustering-based clustering model. Specifically, a modulated nonlinear frequency division multiplexing system was constructed using a combination of Python and the commercial software VPI-Photonics, based on Gaussian mixture clustering. The system flow of a modulated nonlinear frequency division multiplexing system is as follows: Figure 2 As shown.

[0055] First, design the pre-compensation. Modulated NFDM symbols:

[0056]

[0057] Where m is the block index and A is the power control parameter. It is the normalized useful block duration. This is in consideration of the pre-compensation task The normalized total block duration resulting from signal broadening, where N is the number of modulated subcarriers and L is the normalized transmission distance. It is a high-order QAM symbol sequence.

[0058] Encode the data After the subcarrier is on, the following formula is used. and Reconstruction:

[0059]

[0060]

[0061] in, This represents the Hilbert transform.

[0062] Modulate the signal to After reconstruction, a continuous spectrum was obtained. .

[0063] For continuous spectrum The problem of recovering the original time-domain signal from scattering data of a nonlinear continuous spectrum by performing a nonlinear inverse Fourier transform (INFT) can be transformed into solving the GLME (Gelfand-Levitan-Marchenko) equation, which can be obtained using the Toeplitz inner bordering (TIB) algorithm. .

[0064] The time-domain digital signal generated by the digital signal processing at the transmitting end is converted into an analog signal by a DAC, and then loaded onto an optical wave by a laser and an IQ modulator and sent into an optical fiber for transmission.

[0065] At the receiving end, a coherent detector receives the optical signal and converts it into an electrical signal. This electrical signal is then converted into a digital signal by an ADC and sent to the receiver's digital signal processing module. After time synchronization and normalization, a nonlinear Fourier transform (NFT) is used to convert the time-domain signal into an electrical signal. Restore to nonlinear continuous spectrum data The continuous spectrum NFT is transformed into a numerical solution to the Zakharov-Shabat system, which is achieved using the Layer-peeling method.

[0066] Then, post-phase compensation is performed, the data is demodulated from the continuous spectrum and imported into the Gaussian mixture clustering module for equalization and decision-making to obtain the final data, and the performance such as bit error rate is judged.

[0067] Gaussian Mixture Clustering (GMM) is a probability-based clustering algorithm that assumes each cluster conforms to a different Gaussian distribution. It seeks to find the parameters of each Gaussian distribution so that it can effectively characterize the data distribution within its corresponding cluster. This invention considers the advantages of machine learning in solving various impairment problems in fiber optic communication systems, and the superior clustering performance, higher fitting accuracy, and more flexible application of GMM in unsupervised learning compared to other machine learning algorithms. It creatively proposes applying GMM to traditional... In modulated nonlinear frequency division multiplexing systems, this is used to equalize the phase rotation caused by noise, replacing the original... Hard decision (HD) and soft decision (SD) algorithms for modulated nonlinear frequency division multiplexing systems are used to perform clustering decisions on the demodulated 16QAM constellation diagram data, thereby improving system performance and reducing the system's bit error rate.

[0068] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. However, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A b-modulated nonlinear frequency division multiplexing system based on Gaussian mixture clustering, characterized in that: At the transmitting end, a pre-compensation mechanism is used to modulate the NFDM signal, and the continuous spectrum is obtained after reconstruction. Pre-compensation The mechanism is designed as follows: ， Where m is the block index and A is the power control parameter. It is the normalized useful block duration. Due to pre-compensation tasks The normalized total block duration resulting from signal broadening, where N is the number of modulated subcarriers and L is the normalized transmission distance. It is a high-order QAM symbol sequence; The transmitter encodes the data into After the subcarrier is on, the following formula is used. and Reconstruction: ， ， in, Represents the Hilbert transform; At the receiving end, the time domain signal Restored to nonlinear continuous spectrum Afterwards, phase compensation is performed, and the constellation diagram data is demodulated from the continuous spectrum and imported into the Gaussian mixture clustering algorithm model for clustering and decision-making. The Gaussian mixture clustering algorithm model is as follows: ， Among them, Gaussian mixture distribution has a total of It consists of several mixture components, each corresponding to a Gaussian distribution, with a mean vector. Covariance Matrix It is the first Parameters of a Gaussian mixture component For the corresponding mixing coefficient Assume that all data samples are generated by a Gaussian mixture distribution; Gaussian mixture clustering algorithm model parameters The solution is obtained by maximizing the likelihood estimation, i.e., maximizing the log-likelihood function. : ， The Gaussian mixture clustering algorithm model includes the following steps: First, the parameters of the Gaussian mixture clustering algorithm model are initialized; Then the EM algorithm was used to optimize the model parameters. Perform iterative updates; in each iteration, first calculate the posterior probability of each sample belonging to each Gaussian component based on the current parameters. Then, the model parameters are updated based on the obtained posterior probabilities. The process continues until the stopping condition of the EM algorithm or the likelihood function is met. Slow growth or even cessation of growth; Finally, each sample is assigned to its corresponding cluster according to the following formula, and the final result is returned: 。 2. The b-modulation nonlinear frequency division multiplexing system based on Gaussian mixture clustering according to claim 1, characterized in that, The signal transmission process at the transmitting end includes: Modulate the signal to After reconstruction, a continuous spectrum was obtained. ; For continuous spectrum The problem of recovering the original time-domain signal from scattering data of a nonlinear continuous spectrum by performing a nonlinear inverse Fourier transform is transformed into solving the GLME equations, which are obtained using the TIB algorithm. ; The time-domain digital signal generated by the digital signal processing at the transmitting end is converted into an analog signal by a DAC, and then loaded onto an optical wave by a laser and an IQ modulator and sent into an optical fiber for transmission.

3. The b-modulation nonlinear frequency division multiplexing system based on Gaussian mixture clustering according to claim 1, characterized in that, The signal processing at the receiving end includes: A coherent detector is used to receive optical signals and convert them into electrical signals, which are then converted into digital signals by an ADC. The signal is then fed into the digital signal processing module at the receiving end. After time synchronization and normalization, a nonlinear Fourier transform is used to convert the time-domain signal into a digital signal. Restore to nonlinear continuous spectrum data ; Continuous spectrum NFT is transformed into numerically solving the Zakharov-Shabat system; Then, post-phase compensation is performed to demodulate the data from the continuous spectrum and import it into the Gaussian mixture clustering algorithm model for equalization and decision-making to obtain the final data.

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