Noise equalization method and device for high-order modulation double sideband continuous spectrum NFDM system

Abstract

The application provides a noise equalization method and device for a high-order modulation double offset continuous spectrum NFDM system, and belongs to the technical field of optical fiber communication. The method comprises the following steps: generating a distribution probability corresponding to a high-order modulation format constellation point by using an MB distribution at a transmitting end, and generating a PS symbol according to the distribution probability; modulating the PS symbol to a scattering coefficient to generate a time domain signal, and transmitting the time domain signal into an optical fiber after electro-optical conversion; recovering the PS symbol by using a receiving end in a DSP sequence opposite to that of the transmitting end, reorganizing the sequence order of the PS symbol, and obtaining input features of a c-ANN; taking ideal symbols of the transmitting end and the reorganized c-ANN input features of the receiving end as labels and input data of a c-ANN network, obtaining equalized data, and realizing suppression and equalization of ASE noise and processing noise. The application can effectively equalize noise and improve system performance.

Description

Technical Field

[0001] This invention belongs to the field of optical fiber communication technology, and particularly relates to a noise equalization method and apparatus for a high-order modulated dual-biased continuous spectrum NFDM system. Background Technology

[0002] With the booming development of cloud platforms, the Internet of Things, online high-definition video playback, and artificial intelligence, global data traffic demand is growing exponentially. This has driven fiber optic communication systems and networks, as the backbone of information transmission, to develop towards ultra-high speed and ultra-large capacity. To meet the ever-increasing capacity demands, various new technologies such as high-order modulation formats, wavelength division multiplexing (WDM), orthogonal frequency division multiplexing (OFDM), and space division multiplexing are widely used or researched. While the application of new technologies improves system transmission capacity and spectral efficiency, it also leads to increasingly higher input power to the fiber, and the impact of fiber nonlinearity on system performance is becoming increasingly severe. Nonlinear damage caused by fiber nonlinearity has become the most significant factor limiting the improvement of system capacity. The emerging nonlinear frequency division multiplexing (NFDM) technology treats nonlinearity as an inherent property of optical fiber communication systems. By designing a completely new communication system architecture, it theoretically avoids the adverse effects of optical fiber nonlinearity. Its core idea is to linearize the nonlinear optical fiber channel using the mathematical tool of nonlinear Fourier transform (NFT, also known as backscattering IST). Specifically, it utilizes the important characteristic that the nonlinear spectrum (NS) obtained by NFT evolves linearly in the nonlinear optical fiber channel to modulate information onto the nonlinear spectrum for transmission in the optical fiber. Depending on the type of nonlinear spectrum, NFDM systems can be divided into discrete spectrum modulation, continuous spectrum modulation, and full-spectrum modulation. Different modulation methods can be further subdivided into single-biased transmission and double-biased transmission.

[0003] While NFDM systems theoretically solve the capacity limitation problem caused by nonlinear effects in high-speed, long-distance fiber optic communication, their channel model requires lossless and noise-free conditions for the signal's NS (Neural Switching) to follow a linear evolution pattern. This allows the NFT algorithm at the receiver (Rx) to accurately recover the transmitter (Tx) signal. However, loss and noise are unavoidable in practical fiber optic links. For loss, NFDM systems can approximate the loss using a lossless path-averaged channel (LPA) model, with more accurate models for shorter fiber spans. Noise, due to its inherent randomness, cannot be addressed using a simple, uniform model in NFDM systems. The noise issues primarily stem from computational errors in the nonlinear forward / inverse Fourier transform (NFT / INFT) algorithm. Because this algorithm is inherently nonlinear, it suffers from high computational complexity and implementation difficulty. Furthermore, it exhibits significant computational errors when processing high-energy signals, hindering the modulation of multiple discrete spectra and large numbers of subcarrier continuous spectra, thus limiting the transmission performance and spectral efficiency of the NFDM system. Physical noise, mainly spontaneous emission noise (ASE) introduced by the fiber amplifier (EDFA), violates the integrability condition of the nonlinear Schrödinger equation, causing crosstalk as the nonlinear spectrum becomes non-orthogonal. Additionally, ASE in the nonlinear frequency domain (NSD) is no longer a Gaussian white noise model but exhibits a strong correlation with signal power and interacts with the signal, further limiting the transmission performance and spectral efficiency of the NFDM system.

[0004] To address noise processing, existing technologies propose using the Wiener-Hopf method to perform CS INFT calculations, avoiding the error propagation problem inherent in the classic Ablowitz-Ladik algorithm in the frequency domain. Existing technologies also propose a "multi-exponential" algorithm, achieving fourth-order accuracy for NFTs. However, these methods still suffer from high computational complexity and large INFT / NFT algorithm errors when processing high-power signals. Existing technologies also directly use convolutional neural networks (CNNs) to demodulate information from the NFDM time-domain waveform, replacing the original NFT demodulation and reducing numerical calculation errors; however, the CNNs in this scheme have high complexity. Currently, there is no solution that simultaneously reduces complexity and improves accuracy for noise processing. To address the combined impact of ASE noise and noise processing, existing technologies also use feedforward artificial neural networks (FFNNs) to equalize noise in the nonlinear frequency domain, demonstrating an order-of-magnitude improvement in bit error rate (BER) through numerical simulations. Subsequently, the team proposed a bidirectional long short-term memory recurrent neural network (BLSTM) equalization scheme, which significantly outperforms the previously proposed FFNN equalization scheme. However, this approach significantly increases complexity and is only applicable to SP-CS NFDM systems. Existing technologies propose a two-stage ANN that can equalize interference between NFDM pulses in the time domain and crosstalk between subcarriers in the nonlinear spectral domain. While this approach achieves joint noise equalization across multiple dimensions, its complexity increases significantly. Existing technologies propose introducing probabilistic shaping (PS) in Tx and utilizing a real-valued neural network (r-ANN) in Rx to implement a joint noise equalization scheme. However, this scheme only studies noise equalization in SP-CS NFDM systems, and the highest modulation order is 64QAM. Summary of the Invention

[0005] To address the aforementioned shortcomings in the prior art, this invention provides a noise equalization method and apparatus for a high-order modulated dual-biased continuous spectrum NFDM system, which solves the noise problem in the DP-CS NFDM system.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] In a first aspect, the present invention provides a noise equalization method for a high-order modulated dual-biased continuous spectrum NFDM system, comprising the following steps:

[0008] S1. At the transmitting end, the distribution probability corresponding to the constellation points of the high-order modulation format is generated using the MB distribution, and PS symbols are generated according to the distribution probability to reduce signal power.

[0009] S2. The PS symbol is modulated onto the scattering coefficient to generate a time-domain signal, and the time-domain signal is electro-optically converted and transmitted to the optical fiber;

[0010] S3. The PS symbols are recovered by the receiver in the reverse DSP order of the transmitter, and their sorting order is reorganized to obtain the input features of c-ANN.

[0011] S4. Use the ideal symbols from the transmitter and the reorganized c-ANN input features from the receiver as the labels and input data of the c-ANN network to obtain the equalized data.

[0012] The beneficial effects of this invention are as follows: This invention utilizes PS technology to reduce the distribution probability of high-power constellation points in high-order modulation format signals, reduces the peak-to-average power ratio of continuous spectrum subcarriers, and achieves suppression and equalization of ASE noise and processing noise. Furthermore, it utilizes c-ANN to effectively suppress the correlation between subcarriers caused by noise, thereby obtaining equalized data and achieving suppression and equalization of ASE noise and processing noise. This invention can effectively equalize noise and improve system performance.

[0013] Furthermore, the expression for the probability distribution in step S1 is as follows:

[0014]

[0015] Where, p i Re represents the probability distribution, v represents the integer factor, and Re(·) and Im(·) represent the QAM symbols x for each complex number, respectively. i The real and imaginary parts, χ denotes the complex number QAM symbol, x i Represents the QAM symbol for the i-th complex number;

[0016] The expression for the signal power is as follows:

[0017]

[0018] Among them, P i Indicates signal power.

[0019] The beneficial effects of the above-mentioned further scheme are: when the modulation format order increases, the signal power increases, and the ASE noise decreases. However, the increase in signal energy will cause the processing noise to increase sharply. Therefore, this invention introduces PS technology to reduce the distribution probability of high-power constellation points of high-order modulation format signals, thereby reducing the peak-to-average power ratio (PAPR) of continuous spectrum subcarriers and achieving suppression and equalization of processing noise.

[0020] Furthermore, step S2 includes the following steps:

[0021] S201. At the transmitting end, the PS symbol is modulated using OFDM to generate an NFDM symbol, the NFDM symbol is modulated to an intermediate variable, and then modulated using Γ. b The transformation is converted to scattering coefficients, where Γ bRepresents the GAMMA transform;

[0022] S202. The scattering coefficients are converted into time-domain signals using the nonlinear inverse Fourier transform (INFT) algorithm.

[0023] S203. Based on the time-domain signal, the electrical signal is converted into an optical signal using an IQ modulator, and the optical signal is transmitted to the optical fiber.

[0024] The beneficial effects of the above-mentioned further scheme are: for DP-CS NFDM systems, the present invention chooses to encode information on nonlinear coefficients, which can generate more compact time-domain signals and reduce the interaction between signals and noise compared with other encoding methods.

[0025] Furthermore, the expression for the intermediate variable is as follows:

[0026]

[0027] Among them, u m,n (λ) represents an intermediate variable, and A represents the input power of the control signal. This indicates phase rotation, used to achieve dispersion precompensation, where j represents an imaginary number and λ represents the nonlinear frequency, z represents the distance transmitted along the optical fiber, and N c T represents the number of subcarriers, k represents the k-th subcarrier, T0 represents the effective time of the time-domain signal, and T S The time-unified time parameter is represented by n, which represents the nth NFDM pulse, m, which represents the two polarizations x and y, and c. m,k,n This represents the QAM symbol on the k-th subcarrier with the m-th polarization, and is used to represent the transmitted n-th QAM symbol;

[0028] The expression for the scattering coefficient is as follows:

[0029] b m,n (λ)=Γ b u m,n (λ), m∈{x,y}

[0030] Among them, b i,n (λ) represents the scattering coefficient.

[0031] Furthermore, step S3 includes the following steps:

[0032] S301. Use a coherent receiver to convert the optical signal into a time-domain signal;

[0033] S302. Based on the converted time-domain signal, the scattering coefficient is calculated using the nonlinear Fourier transform (NFT) algorithm.

[0034] S303. Based on the scattering coefficients calculated in step S302, remove the fiber channel response through a one-step phase-shifting operation, and utilize Γ... b The inverse transform yields intermediate variables, and OFDM demodulation is used to recover the PS symbols, where Γ b Represents the GAMMA transform;

[0035] S304. Reorganize the sorting order of the recovered PS symbols to obtain the input features of c-ANN.

[0036] The beneficial effect of the above-mentioned further scheme is that, since inter-carrier crosstalk occurs between the previous subcarrier and the next subcarrier, the present invention reorganizes their arrangement order, and the middle subcarrier is the target to be equalized, thus obtaining the input features of c-ANN.

[0037] Furthermore, the expression for the input features of the c-ANN is as follows:

[0038] S m =[S -n ,S -n+1 ,...,S0,...,S n-1 ,S n ], m∈{x,y}

[0039] Among them, S m Let S0 represent the input features of c-ANN, and S represent the current symbol. -n S -n+1 S represents the symbol preceding the current symbol. n-1 and S n This indicates the symbol following the current symbol, n represents the nth symbol, and m represents the two polarizations x and y.

[0040] Furthermore, step S4 includes the following steps:

[0041] S401. The reorganized c-ANN input features at the receiving end are sent to the input layer of the c-ANN network, and the ideal symbol at the transmitting end is used as the ideal output of the c-ANN network.

[0042] S402. Calculate the real and imaginary parts of the c-ANN input features;

[0043] S403. Calculate the actual output z based on the real and imaginary parts of the c-ANN input features:

[0044] z = S m ×W+b=(S r ×W r -S i ×W i )+j(S r ×Wi +S i ×W r )+(b r +jb i )

[0045] Among them, S m This represents the input features of the c-ANN, where W and b represent the weights and biases of neurons in the complex-valued fully connected layer, respectively. W = W r +jW i ,b=b r +jb i j represents an imaginary number, b r and b i S represents the real and imaginary parts of the bias, respectively. r W represents the real part of the input feature. r S represents the weight of the real part. i W represents the imaginary part of the input feature. i The weights represent the imaginary part;

[0046] S404. Based on the actual output z, the weights of the neurons are trained using the backpropagation algorithm to minimize the error between the actual output of the c-ANN network and the ideal symbol at the transmitter, thus obtaining the equalized data.

[0047] The beneficial effects of the above-mentioned further scheme are as follows: In the low transmit power region (below the optimal transmit power), ASE noise plays a major role, and its impact on the signal tends to be additive. Therefore, there is a weak correlation between subcarriers, and c-ANN can only bring a small gain. However, in the high transmit power region (above the optimal transmit power), the impact of noise processing is severe, and the correlation between subcarriers is enhanced. Therefore, the noise equalization effect of c-ANN is significant.

[0048] Secondly, the present invention provides a noise equalization system for a noise equalization method of a high-order modulated dual-biased continuous spectrum NFDM system, comprising:

[0049] The first processing module is used to generate the distribution probability corresponding to the constellation points of the high-order modulation format using the MB distribution at the transmitting end, and generate PS symbols according to the distribution probability to reduce signal power;

[0050] The second processing module is used to modulate the PS symbol onto the scattering coefficient to generate a time-domain signal, and then transmit the time-domain signal to the optical fiber after electro-optic conversion.

[0051] The third processing module is used to recover the PS symbols at the receiving end according to the DSP order opposite to that at the transmitting end, reorganize their sorting order, and obtain the input features of c-ANN.

[0052] The fourth processing module is used to take the ideal symbols from the transmitter and the reorganized c-ANN input features from the receiver as the labels and input data of the c-ANN network to obtain the equalized data.

[0053] The beneficial effects of this invention are: This invention utilizes PS technology to reduce the distribution probability of high-power constellation points in high-order modulation format signals, reduces the PAPR of continuous spectrum subcarriers, achieves suppression and equalization of ASE noise and processing noise, and improves equalization performance by introducing c-ANN to effectively weaken the correlation between subcarriers caused by noise.

[0054] Thirdly, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the program to implement the noise equalization method for the high-order modulated dual-biased continuous spectrum NFDM system.

[0055] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that is executed by a processor to implement a noise equalization method for a high-order modulated dual-biased continuous spectrum NFDM system. Attached Figure Description

[0056] Figure 1 This is a flowchart of the method of the present invention.

[0057] Figure 2 This is a schematic diagram of the c-ANN equalizer provided by the present invention.

[0058] Figure 3 This is a block diagram of the DP-CS NFDM simulation system in this invention.

[0059] Figure 4 This is a performance comparison chart between the present invention and the traditional NFT scheme under different transmission powers.

[0060] Figure 5 The graph shows a performance comparison between the present invention and the traditional NFT scheme at different transmission distances, with the optimal transmission power.

[0061] Figure 6 The graph shows a performance comparison between the present invention and traditional NFT schemes, NFT schemes incorporating PS technology, and joint schemes based on PS and r-ANN at different transmit powers.

[0062] Figure 7 This is a schematic diagram of the device of the present invention. Detailed Implementation

[0063] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0064] Example 1

[0065] To address the noise problem in DP-CS NFDM systems, this invention provides a noise equalization method for high-order modulated dual-biased continuous-spectrum NFDM systems. This method utilizes PS technology to reduce the distribution probability of high-power constellation points in the high-order modulation format signal, thereby reducing the PAPR of continuous-spectrum subcarriers and achieving suppression and equalization of ASE noise and processing noise. Furthermore, by introducing c-ANN, it effectively weakens the inter-carrier correlation caused by noise, improving equalization performance. Figure 1 As shown, this invention provides a noise equalization method for a high-order modulated dual-biased continuous-spectrum NFDM system, the implementation of which is as follows:

[0066] S1. At the transmitting end, the distribution probability corresponding to the constellation points of the high-order modulation format is generated using the MB distribution, and PS symbols are generated according to the distribution probability to reduce signal power.

[0067] In this embodiment, the Maxwell-Boltzmann (MB) distribution is used at the transmitting end to generate the distribution probability corresponding to the constellation points of the high-order modulation format. PS symbols are generated according to the distribution probability. By reducing the peak-to-average power ratio of the continuous spectrum subcarriers, the suppression and equalization of ASE noise and processing noise are achieved.

[0068] In this embodiment, the distribution probability of constellation points can be obtained through the MB distribution, and its specific form is as follows:

[0069]

[0070] Where, p i Re represents the probability distribution, v represents the integer factor, and Re(·) and Im(·) represent the QAM symbols x for each complex number, respectively. i The real and imaginary parts, χ denotes the complex number QAM symbol, x i Let v represent the i-th complex QAM symbol. Given a v, we can obtain the corresponding probability distribution of the PS symbol.

[0071] The PS symbol is randomly generated using the probability distribution, and the signal power can be obtained from the following formula:

[0072]

[0073] Among them, P i χ represents the signal power, and χ represents the complex QAM symbol.

[0074] In this embodiment, since the power of the high-order modulation signal is large, the processing noise will increase sharply. The introduction of PS technology can reduce the distribution probability of the peripheral constellation points, thereby reducing the signal power and achieving noise suppression and equalization.

[0075] S2. The PS symbol is modulated onto the scattering coefficient to generate a time-domain signal, which is then electro-optically converted and transmitted into the optical fiber. The implementation method is as follows:

[0076] Step S2 includes the following steps:

[0077] S201, S201, at the transmitting end, the PS symbol is modulated using OFDM to generate an NFDM symbol, the NFDM symbol is modulated to an intermediate variable, and then modulated using Γ b The transformation is converted to scattering coefficients, where Γ b Represents the GAMMA transform;

[0078] The expression for the intermediate variable is as follows:

[0079]

[0080] Among them, u m,n (λ) represents an intermediate variable, and A represents the input power of the control signal. This indicates phase rotation, used to achieve dispersion precompensation, where j represents an imaginary number and λ represents the nonlinear frequency, z represents the distance transmitted along the optical fiber, and N c T represents the number of subcarriers, k represents the k-th subcarrier, T0 represents the effective time of the time-domain signal, and T S The time-unified time parameter is represented by n, which represents the nth NFDM pulse, m, which represents the two polarizations x and y, and c. m,k,n This represents the QAM symbol on the k-th subcarrier with the m-th polarization, and is used to represent the transmitted n-th QAM symbol;

[0081] The expression for the scattering coefficient is as follows:

[0082] b m,n (λ)=Γ b u m,n (λ), m∈{x,y}

[0083] Among them, b i,n (λ) represents the scattering coefficient.

[0084] S202. The scattering coefficients are converted into time-domain signals using the nonlinear inverse Fourier transform (INFT) algorithm.

[0085] S203. Based on the time-domain signal, the electrical signal is converted into an optical signal using an IQ modulator, and the optical signal is transmitted to the optical fiber.

[0086] S3. The PS symbols are recovered at the receiver in the reverse DSP order compared to the transmitter, and their sorting order is reorganized to obtain the input features of the c-ANN. A schematic diagram of the c-ANN equalizer is shown below. Figure 2 As shown, its implementation method is as follows:

[0087] S301. Use a coherent receiver to convert the optical signal into a time-domain signal;

[0088] S302. Based on the converted time-domain signal, the scattering coefficient is calculated using the nonlinear Fourier transform (NFT) algorithm.

[0089] S303. Based on the scattering coefficients calculated in step S302, remove the fiber channel response through a one-step phase-shifting operation, and utilize Γ... b The inverse transform yields intermediate variables, and OFDM demodulation is used to recover the PS symbols, where Γ b Represents the GAMMA transform;

[0090] S304. Reorganize the sorting order of the recovered PS symbols to obtain the input features of c-ANN.

[0091] In this embodiment, after receiving the optical signal transmitted through the optical fiber, the receiving end uses a coherent receiver to convert the optical signal into a time-domain signal, then obtains the scattering coefficients using a nonlinear Fourier transform (NFT) algorithm, removes the optical fiber channel response through a one-step phase shift operation, and utilizes Γ... b The inverse transform yields intermediate variables, which are then demodulated using OFDM to recover the PS symbols. The input features of the c-ANN are the symbols on the received terminal carrier, such as... Figure 2 As shown in (a), it is represented as:

[0092] S m =[S -n ,S -n+1 ,...,S0,...,S n-1 ,S n ], m∈{x,y}

[0093] Among them, S m =S r +jS i Both are complex numbers, representing the input features of c-ANN, S0 represents the current symbol, S -n S -n+1 S represents the symbol preceding the current symbol. n-1 and S n This indicates the sign following the current symbol, where m represents the two polarizations x and y, and S...r S represents the real part of the input feature. i Let j represent the imaginary part of the input feature. The number of nodes in the c-ANN input layer is related to the input feature consisting of the current symbol and the 2n adjacent symbols on both sides, so the number of nodes in the input layer is set to 2n+1.

[0094] S4. Using the ideal symbols from the transmitting end and the reorganized c-ANN input features from the receiving end as the labels and input data of the c-ANN network, the equalized data is obtained. The implementation method is as follows:

[0095] S401. The reorganized c-ANN input features at the receiving end are sent to the input layer of the c-ANN network, and the ideal symbol at the transmitting end is used as the ideal output of the c-ANN network.

[0096] S402. Calculate the real and imaginary parts of the c-ANN input features;

[0097] S403. Calculate the actual output z based on the real and imaginary parts of the c-ANN input features:

[0098] z = S m ×W+b=(S r ×W r -S i ×W i )+j(S r ×W i +S i ×W r )+(b r +jb i )

[0099] Among them, S m This represents the input features of the c-ANN, where W and b represent the weights and biases of neurons in the complex-valued fully connected layer, respectively. W = W r +jW i ,b=b r +jb i j represents an imaginary number, b r and b i S represents the real and imaginary parts of the bias, respectively. r W represents the real part of the input feature. r S represents the weight of the real part. i W represents the imaginary part of the input feature. i This represents the weight of the imaginary part. Figure 2 (c) gives the complex logic structure inside the c-ANN: First, the input feature S is obtained. m The real part S r And the imaginary part S i Then, for the real part operation, the real part S of the input feature...r Multiplied by the real part W of the weight r Similarly, the imaginary part operation is S. i Multiplied by W i Finally, subtract the two products and add the real part of the bias, b. r Similarly, the imaginary part of the actual output z can be obtained as the real part of the actual output z.

[0100] S404. Based on the actual output z, the weights of the neurons are trained using the backpropagation algorithm to minimize the error between the actual output of the c-ANN network and the ideal symbol at the transmitter, thus obtaining the equalized data.

[0101] In this embodiment, the input features S of the c-ANN are obtained through processing. m Then, it is fed into the input layer of the network, and the PS signal of the transmitter Tx is used as the actual output z of the c-ANN network, i.e., the label. The c-ANN network consists of an input layer, a hidden layer, and an output layer connected in sequence, which are responsible for feature input, feature extraction, and equalization signal output, respectively.

[0102] To verify the effectiveness of this invention, this embodiment verifies it from the perspective of a simulation system:

[0103] The block diagram of the DP-CS NFDM system built based on cross-simulation using VPI Transmission Maker 11.2 and MATLAB is shown below. Figure 3 As shown. Among them. Figure 3 (a) illustrates the specific DSP process at the transmitter. The PS signal is first modulated by OFDM to generate NFDM symbols, and then Γ is used... b The transformation is converted to the scattering coefficient, and T is reduced through dispersion pre-compensation techniques. GI Next, the INFT algorithm is used to generate the time-domain signal, where the effective time of the time-domain signal is set to 3.2 ns, the normalized time parameter is 1 ns, and T... GI The wavelength is 4.8 ns, and the bandwidth is 40 GHz. Finally, an I / Q modulator is used to perform electro-optical conversion to generate an optical signal, which is then fed into the optical fiber channel for transmission at a power calculated using denormalization. In the optical fiber link, the fiber span is set to 80 km, and the loss coefficient, dispersion coefficient, and nonlinear coefficient are set to 0.2 dB / km, 16.8 ps / (nm×km), and 1.3 W, respectively. -1 km -1 The EDFA is used to compensate for fiber loss, but it introduces ASE noise, with noise figures (NF) set to 4dB, 5dB, and 6dB. The optical bandpass filter (OBPF) is used to filter out out-of-band noise, with a bandwidth of 80GHz. The specific DSP flow of the receiver Rx is as follows... Figure 3As shown in (b), after converting the optical signal into an electrical signal using a coherent receiver, the received time-domain signal is first converted into a nonlinear frequency-domain signal using an NFT algorithm. Then, the fiber channel response is removed through a one-step phase-shift operation, followed by Γ... b The Q-factor is calculated by inverse transformation, OFDM decoding, and equalization via c-ANN network, followed by symbol demapping.

[0104] The parameters of the c-ANN network are set as follows: A c-ANN regression task is implemented using Python. The c-ANN consists of an input layer, one hidden layer, and an output layer. The hidden layer has 16 nodes, and the activation function is modReLU. The weight matrix is ​​optimized by minimizing the mean squared error (MSE) using the backpropagation (BP) algorithm. The noise equalization process of the c-ANN network is as follows: Figure 3 As shown in (c), during training, the received current symbol and its six adjacent symbols are taken as a sample and used as the input feature of the c-ANN. The PS signal of the transmitter Tx is used as the label of the c-ANN network. Datasets are typically divided into three categories: training, validation, and testing. The training dataset is used to fit the model, the validation dataset is used to observe whether the model fits well, and finally, the testing dataset is used to evaluate the model performance. In this invention, the dataset contains 128,000 samples, of which 89,600 samples are used to train the c-ANN model. The training and validation datasets are divided in a 3:1 ratio, and the remaining 38,400 samples are input into the training model for testing to obtain the equalized signal.

[0105] The parameters of the real-valued neural network (r-ANN) used for comparison are set as follows: For the fairness of the comparison, the r-ANN consists of an input layer, two hidden layers and an output layer. Each hidden layer has 16 nodes, the activation function is ReLU, the backpropagation algorithm is used, the error function is MSE, and the input features are taken as the current symbol and the 6 symbols on both sides to form a sample. The real part and imaginary part of each symbol are considered separately, and the number of samples is consistent with that of c-ANN.

[0106] In this embodiment, in order to evaluate the performance of the present invention, the following is defined: As a system performance indicator, erfc -1 Let represent the complementary error function, and BER represent the bit error rate. Simulation results are as follows: Figure 4 As shown, this invention delivers performance improvements of approximately 1.1 dB and 0.9 dB compared to traditional NFT schemes when the number of subcarriers is 128 and 256, respectively. Overall, this invention demonstrates significant performance advantages across the entire power range for different modulation formats and subcarrier numbers; simulation results are as follows. Figure 5As shown, under the same transmission distance, the Q factor of this invention is significantly higher than that of the traditional NFT scheme. Specifically, when the NF is 5dB and the 7% FEC (forward error correction, FEC) threshold is met, the PS-128QAM6 signal after c-ANN equalization can be transmitted for 1200km, while the uniform 64QAM signal can be transmitted for a maximum of 880km. Simulation results are as follows. Figure 6 As shown, the NFT scheme incorporating PS technology exhibits a significant performance improvement compared to the traditional NFT scheme. Therefore, PS technology has a clear advantage in noise suppression and equalization, while the use of a c-ANN equalizer can further enhance system performance. Under the same performance conditions, this invention outperforms the combined PS and r-ANN scheme.

[0107] In this embodiment, the present invention utilizes PS technology to reduce the distribution probability of high-power constellation points in high-order modulation format signals, reduces the peak-to-average power ratio of continuous spectrum subcarriers, achieves suppression and equalization of ASE noise and processing noise, and utilizes c-ANN to effectively suppress the correlation between subcarriers caused by noise.

[0108] Example 2

[0109] like Figure 7 As shown, the present invention provides a noise equalization system for implementing the noise equalization method of the high-order modulated dual-biased continuous spectrum NFDM system described in Embodiment 1, comprising:

[0110] The first processing module is used to generate the distribution probability corresponding to the constellation points of the high-order modulation format using the MB distribution at the transmitting end, and generate PS symbols according to the distribution probability to reduce signal power;

[0111] The second processing module is used to modulate the PS symbol onto the scattering coefficient to generate a time-domain signal, and then transmit the time-domain signal to the optical fiber after electro-optic conversion.

[0112] The third processing module is used to recover the PS symbols at the receiving end according to the DSP order opposite to that at the transmitting end, reorganize their sorting order, and obtain the input features of c-ANN.

[0113] The fourth processing module is used to take the ideal symbols from the transmitter and the reorganized c-ANN input features from the receiver as the labels and input data of the c-ANN network to obtain the equalized data.

[0114] like Figure 7 The noise equalization and registration system provided in the embodiment shown can execute the technical solution shown in the noise equalization and registration method of the above method embodiment. Its implementation principle and beneficial effects are similar, and will not be repeated here.

[0115] In this embodiment, the functional units can be divided according to a noise equalization registration method. For example, each function can be divided into its own functional units, or two or more functions can be integrated into one processing unit. The integrated unit can be implemented in hardware or as a software functional unit. It should be noted that the unit division in this invention is illustrative and represents only a logical division; in actual implementation, other division methods may be used.

[0116] In this embodiment, the noise equalization registration system, in order to realize the principle and beneficial effects of the noise equalization registration method, includes hardware structures and / or software modules corresponding to the execution of various functions. Those skilled in the art should readily recognize that, in conjunction with the illustrative units and algorithm steps described in the embodiments disclosed herein, this invention can be implemented in hardware and / or a combination of hardware and computer software. Whether a function is executed by hardware or computer software depends on the specific application and design constraints of the technical solution. Different methods can be used to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0117] In this embodiment, the present invention utilizes PS technology to reduce the distribution probability of high-power constellation points in high-order modulation format signals, reduces the peak-to-average power ratio of continuous spectrum subcarriers, achieves suppression and equalization of ASE noise and processing noise, and utilizes c-ANN to effectively suppress the correlation between subcarriers caused by noise.

[0118] Example 3

[0119] The present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the program to implement the noise equalization method of the high-order modulated dual-biased continuous spectrum NFDM system of Embodiment 1.

[0120] In this embodiment, the electronic device may include: a processor, a memory, a bus, and a communication interface. The processor, the communication interface, and the memory are connected via the bus. The memory stores a computer program that can run on the processor. When the processor runs the computer program, it executes some or all of the steps of the noise equalization method provided in the aforementioned embodiment 1 of this application.

[0121] Example 4

[0122] The present invention provides a computer-readable storage medium storing a computer program that is executed by a processor to implement the noise equalization method for a high-order modulated dual-biased continuous spectrum NFDM system described in Embodiment 1.

[0123] The aforementioned computer-readable storage medium can be implemented by any type of volatile or non-volatile storage device or combination thereof, such as static random access memory (SRAM), erasable and non-volatile read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer. The readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. The readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an application-specific integrated circuit (ASIC), or they can exist as discrete components in a noise equalization system.

[0124] The present invention can be provided as a method, apparatus, or computer program product. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) including computer-usable program code. Referring to the flowcharts and / or block diagrams of methods, apparatuses, and computer program products according to embodiments of the present invention, it should be understood that each flowchart and / or block diagram, and combinations thereof, can be implemented by computer program instructions. These computer program instructions can be provided to a computer-readable storage medium that operates in a particular manner on a general-purpose computer, special-purpose computer, embedded computer, or other programmable data processing device, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means implemented in the flowchart. Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes in the flowchart. These computer program instructions may also be accreted to a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing one or more processes and / or boxes in the flowchart. Figure 1 The steps of the function specified in one or more boxes.

[0125] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A noise equalization method for a high-order modulated dual-biased continuous-spectrum NFDM system, characterized in that, Includes the following steps: S1. At the transmitting end, the distribution probability corresponding to the constellation points of the high-order modulation format is generated using the MB distribution, and PS symbols are generated according to the distribution probability to reduce signal power. The expression for the probability distribution in step S1 is as follows: in, Represents the probability distribution. Represents the integer factor, and Re(·) and Im(·) represent the QAM symbols for each complex number, respectively. The real and imaginary parts, Represents the complex number QAM symbol. Indicates the first A complex QAM symbol; The expression for the signal power is as follows: in, Indicates signal power; S2. Modulate the PS symbol onto the scattering coefficient to generate a time-domain signal, and then convert the time-domain signal to electro-optical form before transmitting it into the optical fiber; this includes the following steps: S201. At the transmitting end, the PS symbol is modulated using OFDM to generate an NFDM symbol, the NFDM symbol is modulated to an intermediate variable, and then... The transformation is converted into scattering coefficients, where, Represents the GAMMA transform; S202. The scattering coefficients are converted into time-domain signals using the nonlinear inverse Fourier transform (INFT) algorithm. S203. Based on time-domain signals, an IQ modulator is used to convert electrical signals into optical signals, and the optical signals are transmitted to optical fibers. S3. The PS symbols are recovered by the receiver in the reverse DSP order of the transmitter, and their sorting order is reorganized to obtain the input features of c-ANN. S4. Using the ideal symbols from the transmitter and the reorganized c-ANN input features from the receiver as the labels and input data of the c-ANN network, the equalized data is obtained; this includes the following steps: S401. The reorganized c-ANN input features at the receiving end are sent to the input layer of the c-ANN network, and the ideal symbol at the transmitting end is used as the ideal output of the c-ANN network. S402. Calculate the real and imaginary parts of the c-ANN input features; S403. Calculate the actual output based on the real and imaginary parts of the c-ANN input features. : in, This represents the input features of c-ANN. and These represent the weights and biases of neurons in a complex-valued fully connected layer, respectively. , represents an imaginary number, and These represent the real and imaginary parts of the bias, respectively. Represents the real part of the input feature. The weights represent the real parts. Represents the imaginary part of the input features. The weights represent the imaginary part; S404, Based on actual output By using the backpropagation algorithm, the weights of neurons are trained to minimize the error between the actual output of the c-ANN network and the ideal symbol at the transmitter, thus obtaining the equalized data.

2. The noise equalization method for a high-order modulated dual-biased continuous-spectrum NFDM system according to claim 1, characterized in that, The expression for the intermediate variable is as follows: in, Indicates intermediate variables. This indicates the input power of the control signal. This indicates phase rotation, used to achieve dispersion pre-compensation. Represents an imaginary number and , Represents nonlinear frequency. Indicates the distance transmitted along the optical fiber. Indicates the number of subcarriers. Indicates the first k Subcarriers, Indicates the effective time of the time-domain signal. Indicates time-unified time parameters, Indicates the first One NFDM pulse, Represents two polarizations x and y , Indicates the first m The polarization of the first k The QAM symbols on the subcarrier are used to indicate the transmitted _th ... n One QAM symbol; The expression for the scattering coefficient is as follows: in, This represents the scattering coefficient.

3. The noise equalization method for a high-order modulated dual-biased continuous-spectrum NFDM system according to claim 1, characterized in that, Step S3 includes the following steps: S301. Use a coherent receiver to convert the optical signal into a time-domain signal; S302. Based on the converted time-domain signal, the scattering coefficient is calculated using the nonlinear Fourier transform (NFT) algorithm. S303. Based on the scattering coefficient calculated in step S302, remove the fiber channel response through a one-step phase-shift operation, and utilize... The inverse transform yields intermediate variables, and OFDM demodulation is used to recover the PS symbols, where, Represents the GAMMA transform; S304. Reorganize the sorting order of the recovered PS symbols to obtain the input features of c-ANN.

4. The noise equalization method for a high-order modulated dual-biased continuous-spectrum NFDM system according to claim 3, characterized in that, The expression for the input features of the c-ANN is as follows: in, This represents the input features of c-ANN. Indicates the current symbol, , Indicates the symbol preceding the current symbol. and Indicates the symbol following the current symbol. Indicates the first A symbol, Represents two polarizations x and y .

5. A noise equalization system for implementing the noise equalization method of any one of claims 1-4 for a high-order modulated dual-biased continuous-spectrum NFDM system, characterized in that, include: The first processing module is used to generate the distribution probability corresponding to the constellation points of the high-order modulation format using the MB distribution at the transmitting end, and generate PS symbols according to the distribution probability to reduce signal power; The second processing module is used to modulate the PS symbol onto the scattering coefficient to generate a time-domain signal, and then transmit the time-domain signal to the optical fiber after electro-optic conversion. The third processing module is used to recover the PS symbols from the receiver in the reverse DSP order of the transmitter, reorganize their sorting order, and obtain the input features of c-ANN. The fourth processing module is used to take the ideal symbols from the transmitter and the reorganized c-ANN input features from the receiver as the labels and input data of the c-ANN network to obtain the equalized data.

6. An electronic device, characterized in that, The system includes a memory, a processor, and a computer program stored in the memory and running on the processor, the processor executing the program to implement the noise equalization method for a high-order modulated dual-biased continuous-spectrum NFDM system as described in any one of claims 1-4.

7. A computer-readable storage medium storing a computer program, characterized in that, The computer program is executed by a processor to implement the noise equalization method for a high-order modulated dual-biased continuous spectrum NFDM system as described in any one of claims 1-4.

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