Self-adaptive equalization method of PON (Passive Optical Network)

Abstract

The invention provides an adaptive equalization method for a PON, and the method comprises the steps: decomposing an input unbalanced signal into a preset number of layers through employing a Mallat decomposition algorithm, and obtaining a high-frequency detail coefficient and a low-frequency approximation coefficient of each layer; performing denoising processing on the high-frequency detail coefficient of each layer: calculating a GCV score of the high-frequency detail coefficient of the current layer by using a generalized cross validation threshold method, determining an optimal denoising threshold value for denoising processing based on the GCV score, and performing denoising processing on the high-frequency detail coefficient based on the optimal denoising threshold value by using a nonlinear contraction function; based on the denoised high-frequency detail coefficient of each layer and the denoised low-frequency approximation coefficient of the corresponding layer, performing layer-by-layer iterative reconstruction by using a Mallat reconstruction algorithm to obtain a denoised data symbol sequence; and taking the denoised data symbol sequence as the input of a pre-trained embedded wavelet neural network, and outputting an equalized signal.

Description

Technical Field

[0001] This invention relates to the field of optical fiber communication technology, and in particular to an adaptive equalization method for PON. Background Technology

[0002] In modern high-speed broadband access technologies, Passive Optical Networks (PONs) have attracted widespread attention due to their high bandwidth, low latency, and excellent scalability. They have been widely applied in various scenarios such as home access, enterprise networks, and data centers, becoming one of the key technologies for next-generation optical access systems. However, the nonlinear effects of optoelectronic devices and fiber optic channels in PON systems are gradually becoming a significant obstacle to performance improvement, especially at high bit rates, where signals are easily subject to severe distortion, affecting communication quality. Therefore, how to perform efficient signal equalization processing at the receiving end has become one of the key technical challenges for improving the performance of PON systems. Nonlinear effects refer to the complex interactions between the optical signal and the fiber medium itself when the optical power transmitted in the fiber reaches a certain level, leading to signal distortion, crosstalk, and performance degradation.

[0003] To address this, researchers have proposed various receiver signal equalization methods to compensate for signal distortion. Traditional methods, such as Decision Feedback Equalizer (DFE), Minimum Mean Square Error (MMSE) equalizers, Volterra filters, and clustering equalization methods, perform reasonably well in low- and medium-speed PON systems. However, because they are inherently offline and static, they cannot track channel changes in real time. Under dynamic and complex channels and scenarios with strong nonlinear distortion, their performance bottlenecks are gradually exposed, making it difficult to meet the increasing system demands. Therefore, adaptive equalization methods have emerged. Their greatest advantage lies in their ability to dynamically adjust model parameters based on the statistical characteristics of the input signal and the channel state, thereby achieving more accurate compensation for nonlinear distortion. During the automatic adjustment of the denoising threshold, the system can achieve more intelligent, locally sensitive, and robust signal processing effects.

[0004] In recent years, deep learning technology has gradually penetrated the field of optical networks, especially in signal recovery tasks at the receiver. Backward Propagation (BP) networks can automatically extract complex nonlinear mapping relationships through end-to-end training, but they suffer from weak local information extraction capabilities in the time and frequency domains. Wavelet Neural Networks (WNNs), combining the advantages of time-frequency analysis and neural networks, can simultaneously capture the local time features and frequency structure of signals. By establishing a nonlinear equalization model with an adaptive embedded wavelet neural network, not only can multi-resolution analysis of the signal be performed while iteratively optimizing parameters, but the distortion of high-order modulated signals after transmission in PON can also be effectively restored. By extending to a deeper structure or introducing a timing modeling mechanism, the stability of the model under long-distance transmission or dynamic interference can be further improved, providing a feasible solution for improving the transmission quality of PON systems.

[0005] Therefore, how to provide an adaptive equalization method in a PON system is a technical problem that urgently needs to be solved. Summary of the Invention

[0006] In view of this, embodiments of the present invention provide an adaptive equalization method for PON to eliminate or improve one or more defects existing in the prior art, and to improve the problem that the existing BP neural network has a weak ability to extract local features of time domain and frequency domain information.

[0007] One aspect of the present invention provides an adaptive equalization method for PON, the method comprising the following steps: decomposing the input unequalized signal into a preset number of layers using the Mallat decomposition algorithm to obtain high-frequency detail coefficients and low-frequency approximation coefficients for each layer; performing denoising processing on the high-frequency detail coefficients of each layer, including: calculating the GCV score of the high-frequency detail coefficients of the current layer using the generalized cross-validation thresholding method, determining the optimal denoising threshold for denoising processing based on the GCV score, and performing denoising processing on the high-frequency detail coefficients using a nonlinear shrinkage function based on the optimal denoising threshold; iteratively reconstructing the denoised data symbol sequence layer by layer using the Mallat reconstruction algorithm based on the high-frequency detail coefficients of each layer after denoising processing and the low-frequency approximation coefficients of the corresponding layer; using the denoised data symbol sequence as the input of a pre-trained embedded wavelet neural network and outputting an equalized signal; wherein, the embedded wavelet neural network is a backpropagation neural network in which wavelet functions are embedded in each neuron, and the neurons embedded with wavelet functions extract time-frequency local features from the input denoised data symbol sequence, and the output layer of the embedded wavelet neural network outputs the equalized signal based on all the extracted time-frequency local features.

[0008] In some embodiments of the present invention, the step of using the Mallat decomposition algorithm to decompose the input unequalized signal into a preset number of layers to obtain high-frequency detail coefficients and low-frequency approximation coefficients for each layer includes: performing multi-layer recursive filtering and downsampling operations on the input unequalized signal to obtain low-frequency decomposed components and high-frequency decomposed components of a preset number of layers; performing a 2x downsampling on the low-frequency decomposed components to obtain low-frequency approximation coefficients; and performing a 2x downsampling on the high-frequency decomposed components to obtain high-frequency detail coefficients; wherein, even-numbered index points are retained during the 2x downsampling process.

[0009] In some embodiments of the present invention, determining the optimal denoising threshold for denoising processing based on the GCV score includes: taking the threshold that minimizes the GCV score as the basic denoising threshold, performing inter-layer weighting on the obtained basic denoising threshold to obtain the optimal denoising threshold; wherein the weighting factor used for inter-layer weighting increases linearly with the layer level.

[0010] In some embodiments of the present invention, the nonlinear contraction function is expressed by the following formula: ; in, This represents the optimal denoising threshold. Indicates the first The first layer High-frequency detail coefficients, This represents the high-frequency detail coefficients after noise reduction processing.

[0011] In some embodiments of the present invention, the method further includes: initially constructing an embedded wavelet neural network model before the pre-training of the backpropagation neural network begins, and replacing the activation function in each neuron of the backpropagation neural network with the first derivative of the Gaussian wavelet function.

[0012] In some embodiments of the present invention, the embedded wavelet neural network includes an input layer, a wavelet function calculation layer, and an output layer; the step of using the denoised data symbol sequence as input to a pre-trained embedded wavelet neural network and outputting an equalized signal includes: inputting the denoised data symbol sequence into the input layer; extracting time-frequency local features from the input denoised data symbol sequence using neurons embedded with wavelet functions in the wavelet function calculation layer; and weighting and summing all the extracted time-frequency local features in the output layer, adding the bias term contained in the pre-trained embedded wavelet neural network model, and outputting an equalized signal.

[0013] Corresponding to the above method, the present invention also provides an adaptive equalization system for PON, comprising: an adaptive threshold preprocessing module, used to decompose the input unequalized signal into a preset number of layers using the Mallat decomposition algorithm to obtain high-frequency detail coefficients and low-frequency approximation coefficients of each layer; used to perform denoising processing on the high-frequency detail coefficients of each layer, including: calculating the GCV score of the high-frequency detail coefficients of the current layer using the generalized cross-validation thresholding method, determining the optimal denoising threshold for denoising processing based on the GCV score, and performing denoising processing on the high-frequency detail coefficients using a nonlinear shrinkage function based on the optimal denoising threshold; and further used to perform denoising processing on the high-frequency detail coefficients based on the denoising processing... The high-frequency detail coefficients of each layer after noise processing and the low-frequency approximation coefficients of the corresponding layer are reconstructed layer by layer using the Mallat reconstruction algorithm to obtain a denoised data symbol sequence; a pre-trained wavelet neural network module is used to output an equalized signal based on the input denoised data symbol sequence; wherein, the embedded wavelet neural network is a backpropagation neural network that embeds wavelet functions in each of its neurons, and uses the neurons with embedded wavelet functions to extract time-frequency local features from the input denoised data symbol sequence, and the output layer of the embedded wavelet neural network outputs an equalized signal based on all the extracted time-frequency local features.

[0014] In some embodiments of the present invention, the wavelet neural network module includes an input layer, a wavelet function calculation layer, and an output layer; wherein, the input layer is used to input the denoised data symbol sequence; the wavelet function calculation layer is used to extract time-frequency local features from the input denoised data symbol sequence using neurons embedded with wavelet functions; the output layer is used to perform a weighted summation of all extracted time-frequency local features, and add the bias term contained in the pre-trained embedded wavelet neural network model to output the equalized signal.

[0015] Corresponding to the above methods, the present invention also provides an electronic device, including a processor, a memory, and a computer program / instructions stored in the memory, wherein the processor is configured to execute the computer program / instructions, and when the computer program / instructions are executed, the electronic device implements the steps of any of the methods described in the above embodiments.

[0016] In accordance with the above methods, the present invention also provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the method as described in any of the above embodiments.

[0017] Corresponding to the above methods, the present invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the method as described in any of the above embodiments.

[0018] The adaptive signal equalization processing method in the PON system proposed in this invention employs the Mallat signal decomposition and reconstruction algorithm to achieve fast discrete wavelet transform. The Mallat decomposition algorithm overcomes the limitations of traditional Fourier transform in processing non-stationary signals, while the Mallat reconstruction algorithm helps to reconstruct the complete denoised data symbol sequence, effectively preserving key signal features and reducing information distortion and energy loss. Furthermore, by using the generalized cross-validation thresholding method to track the distribution of high-frequency detail coefficients at each layer and adaptively selecting the optimal denoising threshold, it facilitates nonlinear shrinkage denoising of high-frequency detail coefficients, preserving the complete amplitude of large coefficients to ensure signal fidelity. In addition, by constructing and pre-training an embedded wavelet neural network model, wavelet functions are embedded in the activation function, enabling the network to capture the frequency information of the signal and accurately locate the signal in the time dimension. This facilitates multi-scale time-frequency nonlinear modeling and avoids the blindness inherent in traditional BP neural network design. Additional advantages, objectives, and features of this invention will be set forth in part in the description which follows, and will in part become apparent to those skilled in the art upon studying the description, or may be learned by practice of the invention. The objectives and other advantages of the present invention can be achieved and obtained through the structures specifically pointed out in the specification and drawings.

[0019] Those skilled in the art will understand that the objectives and advantages achievable with the present invention are not limited to those specifically described above, and that the above and other objectives achievable with the present invention will become clearer from the following detailed description. Attached Figure Description

[0020] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, are not intended to limit the scope of the invention. The components in the drawings are not drawn to scale but are merely illustrative of the principles of the invention. For ease of illustration and description of certain parts of the invention, corresponding portions in the drawings may be enlarged, i.e., may appear larger relative to other components in an exemplary device actually manufactured according to the invention. In the drawings: Figure 1 This is a flowchart of an adaptive signal equalization processing method according to an embodiment of the present invention. An adaptive equalization method for PON. Figure 2 This is a structural diagram of an adaptive equalization system for PON in one embodiment of the present invention.

[0021] Figure 3 This is a flowchart of the Mallat decomposition algorithm in one embodiment of the present invention.

[0022] Figure 4 This is a flowchart illustrating the denoising process for high-frequency detail coefficients using the generalized cross-validation threshold method in one embodiment of the present invention.

[0023] Figure 5 This is a flowchart of the Mallat reconstruction algorithm in one embodiment of the present invention.

[0024] Figure 6 This is a schematic diagram of the embedded wavelet neural network module structure in one embodiment of the present invention.

[0025] Figure 7(a) is a time-frequency diagram of an unequalized signal under 10km-32G-PAM8 according to an embodiment of the present invention.

[0026] Figure 7(b) is a time-frequency diagram of the signal after equalization under 10km-32G-PAM8 according to an embodiment of the present invention.

[0027] Figure 8(a) is a comparison of bit error rates under different received optical powers in a 32G-PAM8 optical fiber link with a length of 5 km according to an embodiment of the present invention.

[0028] Figure 8(b) is a comparison of bit error rates under different received optical powers in a 32G-PAM8 optical fiber link with a length of 10 km according to an embodiment of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. Here, the illustrative embodiments and descriptions of this invention are used to explain the invention, but are not intended to limit the invention.

[0030] It should also be noted that, in order to avoid obscuring the invention with unnecessary details, only the structures and / or processing steps closely related to the solution according to the invention are shown in the accompanying drawings, while other details that are not closely related to the invention are omitted.

[0031] It should be emphasized that the term "including / comprises" as used herein refers to the presence of a feature, element, step, or component, but does not exclude the presence or addition of one or more other features, elements, steps, or components.

[0032] It should also be noted that, unless otherwise specified, the term "connection" in this article can refer not only to a direct connection, but also to an indirect connection involving an intermediary.

[0033] In the following description, embodiments of the invention will be illustrated with reference to the accompanying drawings. In the drawings, the same reference numerals represent the same or similar parts, or the same or similar steps.

[0034] In a typical PON architecture, multiple Optical Network Units (ONUs) are connected to Optical Line Terminals (OLTs) via passive optical splitters (ODNs), achieving a highly efficient network structure with bidirectional transmission and passive splitting. This structure boasts advantages such as high bandwidth, low power consumption, ease of deployment, and long-distance operation, making it widely used in multi-user access scenarios. However, this architecture also has some drawbacks. For example, fiber transmission and the devices themselves introduce nonlinear effects such as Self-Phase Modulation (SPM), Cross-Phase Modulation (XPM), and Four-Wave Mixing (FWM), affecting the accuracy of signal transmission. Therefore, to ensure the accuracy of uplink data transmission and system stability, an adaptive equalization algorithm module needs to be deployed at the receiver. This module learns the complex nonlinear mappings in the channel to accurately restore the received impaired signal, thereby fully leveraging the advantages of the PON system.

[0035] In PON networks, nonlinear effects can impact the quality of the received signal. To address this, an adaptive equalization algorithm module can be deployed at the receiver. This module performs signal processing based on a nonlinear adaptive equalization algorithm, accurately restoring the impaired signal by learning the complex nonlinear mappings in the channel. The receiver processing steps are: ① Converting the optical signal into an electrical signal using a photodetector; ② Sampling the signal using a receiver; ③ Performing offline digital signal processing using a digital signal processing module. This offline digital signal processing includes data normalization, resampling, low-pass filtering, clock recovery, and frame synchronization, as well as nonlinear adaptive equalization processing. The focus of this solution is on this nonlinear adaptive equalization process.

[0036] Figure 1 This is a flowchart of an adaptive signal equalization processing method according to an embodiment of the present invention. The method includes: Step S110: Use the Mallat decomposition algorithm to decompose the input unequalized signal into a preset number of layers to obtain the high-frequency detail coefficients and low-frequency approximation coefficients of each layer.

[0037] Step S120: Denoise the high-frequency detail coefficients of each layer, including: calculating the GCV score of the high-frequency detail coefficients of the current layer using the generalized cross-validation thresholding method, determining the optimal denoising threshold for denoising based on the GCV score, and denoising the high-frequency detail coefficients using a nonlinear shrinkage function based on the optimal denoising threshold.

[0038] Step S130: Based on the high-frequency detail coefficients of each layer after denoising and the low-frequency approximation coefficients of the corresponding layer, the Mallat reconstruction algorithm is used to iteratively reconstruct the denoised data symbol sequence layer by layer.

[0039] Step S140: The denoised data symbol sequence is used as the input to a pre-trained embedded wavelet neural network, and the output is an equalized signal; wherein, the embedded wavelet neural network is a backpropagation neural network that embeds wavelet functions in each of its neurons, and uses the neurons with embedded wavelet functions to extract time-frequency local features from the input denoised data symbol sequence, and the output layer of the embedded wavelet neural network outputs an equalized signal based on all the extracted time-frequency local features.

[0040] The adaptive signal equalization processing method in the PON system proposed in this invention employs the Mallat signal decomposition and reconstruction algorithm to achieve fast discrete wavelet transform. The Mallat decomposition algorithm helps overcome the insufficient ability of traditional Fourier transform to process non-stationary signals, while the Mallat reconstruction algorithm helps to restore the complete denoised data symbol sequence, effectively preserving key signal features and reducing information distortion and energy loss. Furthermore, by using the generalized cross-validation thresholding method, the distribution of high-frequency detail coefficients in each layer is tracked, and the optimal denoising threshold is adaptively selected. This facilitates nonlinear shrinkage denoising of high-frequency detail coefficients, preserving the complete amplitude of large coefficients to ensure signal fidelity. In addition, by constructing and pre-training an embedded wavelet neural network model, the wavelet function is embedded in the activation function, enabling the network to capture the frequency information of the signal and accurately locate the signal in the time dimension. This facilitates multi-scale time-frequency nonlinear modeling and avoids the blindness in the design of traditional BP neural networks.

[0041] In some embodiments of the present invention, the step of using the Mallat decomposition algorithm to decompose the input unequalized signal into a preset number of layers to obtain high-frequency detail coefficients and low-frequency approximation coefficients for each layer includes: performing multi-layer recursive filtering and downsampling operations on the input unequalized signal to obtain low-frequency decomposed components and high-frequency decomposed components of a preset number of layers; performing a 2x downsampling on the low-frequency decomposed components to obtain low-frequency approximation coefficients; and performing a 2x downsampling on the high-frequency decomposed components to obtain high-frequency detail coefficients; wherein, even-numbered index points are retained during the 2x downsampling process.

[0042] Using this embodiment of the invention, the Mallat decomposition algorithm extracts high and low frequency components of each layer through decomposition filtering, improves processing efficiency through downsampling, and separates high-frequency detail coefficients and low-frequency approximation coefficients containing damage features. This helps to reduce the scale of data processing and overcomes the problem that traditional Fourier transform is insufficient for processing non-stationary signals.

[0043] Furthermore, the subsequent Mallat reconstruction algorithm obtains high and low frequency reconstruction coefficients through layer-by-layer upsampling and reconstruction filtering, and finally restores the complete denoised data symbol sequence, effectively preserving key signal features and reducing information distortion and energy loss.

[0044] In some embodiments of the present invention, determining the optimal denoising threshold for denoising processing based on the GCV score includes: taking the threshold that minimizes the value of the GCV score as the basic denoising threshold, and performing inter-layer weighting on the obtained basic denoising threshold to obtain the optimal denoising threshold; wherein the weighting factor used for inter-layer weighting increases linearly with the layer level.

[0045] This invention employs a generalized cross-validation thresholding method to track the distribution of high-frequency detail coefficients in each layer and adaptively select the optimal denoising threshold. Nonlinear shrinkage denoising is performed on the high-frequency detail coefficients, suppressing noise while preserving key details of the original signal. It retains the full amplitude of large coefficients to ensure signal fidelity, and effectively suppresses noise and avoids introducing reconstruction artifacts by smoothly compressing small coefficients. This achieves more accurate compensation for nonlinear distortion, improves the accuracy of signal modeling and recognition, and facilitates subsequent network training.

[0046] In some embodiments of the present invention, the nonlinear contraction function is expressed by the following formula: ; in, This represents the optimal denoising threshold. Indicates the first The first layer High-frequency detail coefficients, This represents the high-frequency detail coefficients after noise reduction processing.

[0047] Using this embodiment of the invention, an example of denoising high-frequency detail coefficients based on an optimal denoising threshold is given.

[0048] In some embodiments of the present invention, the method further includes: before the pre-training of the backpropagation neural network begins, initially constructing an embedded wavelet neural network model, and using the first derivative of the Gaussian wavelet function to replace the activation function in each neuron of the backpropagation neural network.

[0049] In other embodiments of the present invention, the embedded wavelet neural network includes an input layer, a wavelet function calculation layer, and an output layer. Accordingly, the step of using the denoised data symbol sequence as input to a pre-trained embedded wavelet neural network and outputting an equalized signal includes: inputting the denoised data symbol sequence into the input layer; extracting time-frequency local features from the input denoised data symbol sequence using neurons embedded with wavelet functions in the wavelet function calculation layer; and weighting and summing all extracted time-frequency local features in the output layer, adding a bias term included in the pre-trained embedded wavelet neural network model, and outputting an equalized signal.

[0050] By constructing an embedded wavelet neural network model and embedding the wavelet function into the activation function, the network can capture the frequency information of the signal and accurately locate the signal in the time dimension. This is beneficial for realizing multi-scale time-frequency nonlinear modeling, avoiding the blindness in the design of traditional BP neural networks, improving the approximation ability of the neural network, overcoming the local minima problem, further enhancing the recovery ability of damaged signals after nonlinear equalization, and effectively reducing the bit error rate of signal transmission.

[0051] Corresponding to the above method, the present invention also provides an adaptive equalization system for PON, comprising: an adaptive threshold preprocessing module, used to decompose the input unequalized signal into a preset number of layers using the Mallat decomposition algorithm to obtain high-frequency detail coefficients and low-frequency approximation coefficients of each layer; used to perform denoising processing on the high-frequency detail coefficients of each layer, including: calculating the GCV score of the high-frequency detail coefficients of the current layer using the generalized cross-validation thresholding method, determining the optimal denoising threshold for denoising processing based on the GCV score, and performing denoising processing on the high-frequency detail coefficients using a nonlinear shrinkage function based on the optimal denoising threshold; and further used to perform denoising processing on the high-frequency detail coefficients based on the denoising processing... The high-frequency detail coefficients of each layer after noise processing and the low-frequency approximation coefficients of the corresponding layer are reconstructed layer by layer using the Mallat reconstruction algorithm to obtain a denoised data symbol sequence; a pre-trained wavelet neural network module is used to output an equalized signal based on the input denoised data symbol sequence; wherein, the embedded wavelet neural network is a backpropagation neural network that embeds wavelet functions in each of its neurons, and uses the neurons with embedded wavelet functions to extract time-frequency local features from the input denoised data symbol sequence, and the output layer of the embedded wavelet neural network outputs an equalized signal based on all the extracted time-frequency local features.

[0052] In some embodiments of the present invention, the wavelet neural network module includes an input layer, a wavelet function calculation layer, and an output layer; wherein, the input layer is used to input the denoised data symbol sequence; the wavelet function calculation layer is used to extract time-frequency local features from the input denoised data symbol sequence using neurons embedded with wavelet functions; the output layer is used to perform a weighted summation of all extracted time-frequency local features, and add the bias term contained in the pre-trained embedded wavelet neural network model to output the equalized signal.

[0053] Figure 2 This is a structural diagram of an adaptive equalization system for PON in one embodiment of the present invention.

[0054] First, a fiber optic communication system is built to collect the damaged signal after dynamic channel equalization.

[0055] In a PON system, the optical fiber communication system consists of a transmitter, a transmission link, and a receiver. The transmitter mainly comprises a signal modulation module, a laser, a driver circuit, and a modulator (e.g., an MZM modulator). The transmission link consists of optical fiber and an optical amplifier. The receiver mainly consists of a photodetector, a receiver, and a digital signal processing algorithm module. First, the transmitter modulates and maps the raw bitstream, performing pulse shaping and amplitude equalization to drive a Mach-Zehnder modulator (MZM modulator) to modulate the electrical signal into a corresponding optical intensity signal. Second, the transmission link uses single-mode optical fiber (SMF) to transmit the modulated optical signal. Nonlinear distortion and noise may be introduced into the transmission link; an optical amplifier is used to compensate for losses. Finally, the receiver converts the optical signal into an electrical signal via a photodetector. After sampling and processing by the receiver, the signal is sent to the digital signal processing module. The digital signal processing algorithm module includes operations such as data normalization, resampling, low-pass filtering, clock recovery, and frame synchronization. In high-speed, high-order transmission, the digital signal processing capabilities of the receiver are crucial for offsetting the linear and nonlinear effects of the link. The distorted signal output after fiber optic communication provides the processing target for subsequent nonlinear equalization modules.

[0056] Figure 2The processing procedure of the fiber optic communication system is illustrated below: Random data is mapped via PAM8, pulse-shaped, and fed into an AWG (Arrow-Augmented Grating) to enter the MZM modulator. It then passes through an erbium-doped grating amplifier (EDFA) and a single-mode fiber (SMF) to reach the tunable optical attenuator (VOA), followed by a photodetector (PD) to the receiver, and finally to the offline digital signal processing (DSP). The offline DSP module processes the received signal through data normalization, resampling, low-pass filtering, clock recovery, frame synchronization, adaptive nonlinear equalization, and demapping, ultimately producing the output signal indicating the end of offline processing. The main improvement of this scheme lies in the adaptive nonlinear equalization stage.

[0057] also, Figure 2 For a detailed introduction to the adaptive threshold preprocessing module and the wavelet neural network module below, please see [link to documentation / details]. Figures 3-6 In the introduction.

[0058] The workflow of the adaptive threshold preprocessing module includes the following steps: First, the Mallat decomposition algorithm is used to initially filter the signal output after data normalization, resampling, low-pass filtering, clock recovery, and frame synchronization by the offline digital signal processing module. The high and low frequency components of the obtained signal are downsampled to obtain high-frequency detail coefficients and low-frequency approximation coefficients. Only the low-frequency approximation coefficients are recursively filtered and downsampled in the next round until a preset number of decomposition layers is reached, obtaining the high-frequency detail coefficients of each layer and a set of low-frequency approximation coefficients for the deepest layer. Second, the optimal denoising threshold for each layer's high-frequency detail coefficients is calculated using the generalized cross-validation thresholding method to minimize the GCV score, followed by nonlinear shrinkage denoising. Finally, the Mallat reconstruction algorithm is used on the denoised high-frequency detail coefficients of each layer and the unprocessed low-frequency approximation coefficients of the deepest layer. Through upsampling and multi-layer filtering, high and low frequency reconstruction coefficients are obtained layer by layer, ultimately outputting a complete denoised data symbol sequence.

[0059] Figure 3 This is a flowchart of the Mallat decomposition algorithm in one embodiment of the present invention. The Mallat decomposition algorithm is a fast implementation of Discrete Wavelet Transformation (DWT). Through multiple recursive filtering and downsampling operations, it can directly calculate the decomposition coefficients of the signal without relying on the specific expression of the wavelet function, thus significantly reducing computational complexity. The Mallat decomposition algorithm includes two stages—filtering decomposition and downsampling—in each decomposition level, as shown in the diagram. Figure 3 As shown. First, the signal input to the adaptive threshold preprocessing module... Simultaneously, a pair of complementary wavelet low-pass and high-pass filters are used to extract the low-frequency and high-frequency components of the signal, respectively. The filter basis function adopts the Daubechies 4th order wavelet, which has good smoothness, tight support characteristics, and linear phase features, and is suitable for separating signal trends from details. Each filtering decomposition yields low-frequency and high-frequency components. Low-frequency decomposition components of the layer It can be represented as: (1) No. High-frequency decomposition components of the layer It can be represented as: (2) in, The length of the filter. This indicates the use of a low-pass filter with a db4 wavelet. This indicates the use of a high-pass filter with a db4 wavelet. Denotes the variables used for indexing filter taps, from formulas (1)-(2) arrive Ground traversal filter or All coefficients, and compare these coefficients with Multiply the shifted samples. For the first layer, That is, the original input signal . Represents a discrete-time index, for example, This represents the nth sample value of the low-frequency decomposition component at level j, where j indicates which level of wavelet decomposition is currently being processed.

[0060] Secondly, to effectively compress the number of coefficients while retaining the minimum coefficient set required for reconstructing the signal, the algorithm downsamples these two sets of decomposed components by a factor of 2. The downsampling process retains even-numbered index points, halving the length of each coefficient decomposition layer. After downsampling, the low-frequency approximation coefficients are output. and high frequency detail coefficient , No. Low-frequency approximation coefficient of the layer Represented as: (3) No. High-frequency detail factor of the layer Represented as: (4) Since most natural signal energy is concentrated in the low-frequency range, the low-frequency approximation coefficient... It contains the main structural information of the signal and is the basis for subsequent analysis, while the high-frequency detail coefficients The algorithm primarily includes mutations and noise. Further decomposition may lead to excessive dispersion of local information, making it difficult to extract effective features. Therefore, after each level of decomposition, the algorithm only approximates the low-frequency coefficients. The next round of filtering and downsampling is then performed, while the high-frequency detail coefficients are... This is retained as the final output of the layer. This recursive process continues until the preset number of decomposition layers is reached, ultimately obtaining the high-frequency detail coefficients of each layer and a set of low-frequency approximation coefficients for the deepest layer.

[0061] Figure 4 This is a flowchart illustrating the denoising process for high-frequency detail coefficients using the generalized cross-validation threshold method in one embodiment of the present invention.

[0062] In practical applications, since higher signal frequencies are generally more sensitive to structural damage, after completing multi-layer Mallat decomposition, the focus is on processing high-frequency detail coefficients that contain more noise and damage information. A generalized cross-validation (GCV) thresholding method is used to adaptively determine the optimal denoising threshold for each layer and perform denoising processing. This avoids prior estimation of noise variance and depends entirely on the input data, such as the structure... Figure 4 As shown. Figure 4 The process shown includes: [details of the process]. All high-frequency detail coefficients of the layer (common The absolute values ​​of the (number of thresholds) are sorted in ascending order to form the candidate threshold set. ,in Then, use each candidate threshold. For all Hard thresholding is performed sequentially, i.e. If the value is greater than the candidate threshold, retain it; otherwise, set it to 0 to obtain the processed result. During the calculation process The GCV score, which evaluates the quality of the threshold by balancing the sum of squared residuals and complexity of the model, is expressed as: (5) in, It refers to the effective degrees of freedom of the model, i.e., the degrees of freedom that are not set to zero after hard thresholding. The quantity. Determine the amount that... The optimal index with the smallest (i.e., GCV score) and the corresponding base denoising threshold : (6) (7) The obtained base denoising threshold Inter-layer weighting adjustment is performed to give higher frequency band components with greater noise levels stronger denoising processing. The optimal denoising threshold is reached after inter-layer weighting adjustment. (Abbreviated as optimal threshold): (8) Among them, the weighting factor used for inter-layer weighting With each level Linear growth is defined as: (9) Use a nonlinear shrinkage function for each high-frequency detail factor Processing, high-frequency detail coefficients after noise reduction Represented as: ; (10) when When, the high-frequency detail coefficients remain unchanged, when When performing compression processing, it can both preserve the full amplitude of large coefficients to ensure signal fidelity and effectively suppress noise by smoothing and compressing small coefficients, thus achieving more accurate compensation for nonlinear distortion.

[0063] Next, the high-frequency detail coefficients after denoising at layer j are summarized, and the results of all layers are summarized as follows: , Figure 4 The steps shown are now complete.

[0064] Figure 5 This is a flowchart of the Mallat reconstruction algorithm in one embodiment of the present invention.

[0065] Mallat reconstruction is the inverse process of Mallat decomposition, utilizing the high-frequency detail coefficients of each layer after thresholding. The deepest unprocessed low-frequency approximation coefficient The Mallat reconstruction algorithm recovers the original signal layer by layer. Each decomposition level includes two stages: upsampling and filtering reconstruction, as shown in the structure below. Figure 5 As shown. First, the high-frequency detail coefficients and low-frequency approximation coefficients of the current layer are upsampled, that is, a zero value is inserted between every two sample points in the sequence, thereby doubling the signal length and restoring it to the level of the previous layer. After upsampling, the... Low-frequency synthesis components of the layer Represented as: ; (11) High-frequency synthesized components after upsampling Represented as: ;(12) Secondly, the two upsampled components are passed through their respective low-pass reconstruction filters. With high-pass reconstruction filter This yields the low-frequency and high-frequency reconstruction coefficients. These two reconstruction filters are time-reverse versions of the decomposition filter (i.e., ...). , ). No. Low-frequency reconstruction coefficient of the layer Represented as: (13) No. High-frequency reconstruction coefficient of the layer It can be represented as: (14) Finally, by adding the low-frequency and high-frequency reconstruction coefficients point by point, the low-frequency approximation coefficients of the previous layer can be reconstructed. , represented as: (15) This process iterates upwards layer by layer until the approximation coefficients of layer 0 are reconstructed. That is, the complete denoised data symbol sequence. It should be noted that here... and the above The difference lies in whether or not noise reduction processing has been performed.

[0066] Figure 6 This is a schematic diagram of the embedded wavelet neural network module structure in one embodiment of the present invention.

[0067] The complete denoised data symbol sequence obtained from the above steps An embedded wavelet neural network model is constructed as input for training and testing. The first derivative of the Gaussian wavelet function is used instead of the activation function. By constructing a wavelet function computation layer and introducing adjustable frequency and translation factors, multi-scale time-frequency nonlinear equalization of the signal is performed, and the final output is an equalization result that is close to the ideal symbol sequence.

[0068] While traditional backpropagation (BP) neural networks possess powerful nonlinear mapping and self-learning capabilities, they suffer from problems such as blind structural design and susceptibility to local optima. Therefore, to overcome these shortcomings, wavelet analysis is combined with BP neural networks to construct an embedded wavelet neural network. By replacing the activation function in traditional neurons with a wavelet function, the network can not only learn weights but also adaptively adjust the frequency and translation factors of the wavelet during training. This allows it to quickly capture time-frequency local features in the input data, significantly improving the model's nonlinear modeling ability and convergence efficiency.

[0069] In some embodiments of the present invention, the embedded wavelet neural network consists of three parts: an input layer, a wavelet function calculation layer, and an output layer, as shown in the following structure. Figure 3 As shown. The complete denoised data symbol sequence from the Mallat reconstruction steps described above is input into the input layer. The wavelet function computation layer embeds a wavelet function into each neuron to calculate the correlation between the input signal and the wavelet, i.e., to extract local time-frequency features. The first derivative of the Gaussian wavelet, suitable for optical communication systems, is chosen as the wavelet function. , represented as: (16) input denoised data symbol sequence After processing by neurons embedded with wavelet functions, the time-frequency local features of the signal can be extracted. The output of each neuron Represented as: (17) in, To obtain the first layer of the neural network input layer The first neuron to the hidden layer The weights between neurons This represents the number of hidden layer units. Indicates the first The frequency factor of the wavelet function on each neuron determines the frequency resolution of the neuron. Indicates the first The translation factor of the wavelet function on each neuron controls and determines the neuron's temporal localization ability. This is achieved by setting multiple wavelet functions with different translation factors. and The neurons in the network can capture the frequency information of the signal and accurately locate the signal in the time dimension, effectively processing nonlinear distortion signals using time-frequency analysis.

[0070] The output layer performs a weighted summation of the time-frequency local features extracted by the wavelet function computation layer, adds a bias term, and finally outputs the equalized signal, as follows: (18) The bias term in the backpropagation neural network refers to the term that is randomly initialized at the beginning of training and is continuously adjusted and optimized during training. In this scheme, during the backpropagation phase, the weight coefficients of each connection layer, the frequency factor of each neuron, the translation factor, and the bias term of the output layer are adjusted by gradient descent.

[0071] in, To calculate the layer from the wavelet function The weighting coefficients between individual neurons and single neurons in the output layer This represents the bias generated during network training. The network uses the backpropagation algorithm to update its parameters, minimizing the mean squared error (MSE) between the network output and the ideal symbol sequence. The loss function is defined as: (19) During the backpropagation phase, gradient descent is used to adjust the weights of each connection layer, the frequency factor of each neuron, the translation factor, and the bias term of the output layer. Through iterative updates, the network can gradually correct erroneous responses to signal frequency components and temporal localization, achieving more accurate training. After training, the output signal is... By performing demapping, a near-ideal balanced symbol sequence can be recovered, thus completing the nonlinear equalization of the damaged signal.

[0072] Figure 7(a) shows the time-frequency diagram of the unequalized signal under 10km-32G-PAM8 according to an embodiment of the present invention. Figure 7(b) shows the time-frequency diagram of the equalized signal under 10km-32G-PAM8 according to an embodiment of the present invention. The time-frequency diagrams of the unequalized signal with a received optical power of 2dBm and the signal processed by the algorithm of this model are compared when the parameters are set as follows: fiber link length of 10 km, number of neurons of 300, learning rate of 0.01, number of iterations of 2000, training data of 30%, and test data of 60%.

[0073] As shown in Figure 7, the equalization process reduces the peak amplitude of the signal to a certain extent, making the energy distribution of the signal flatter and suppressing large noise peaks in the signal. Experimental results show that the adaptive equalization method for PON disclosed in this invention effectively removes signal impairments under 32Gbaud-PAM8 single-mode fiber conditions by processing the high-frequency detail coefficients in the wavelet transform of the signal.

[0074] Figure 8(a) shows a comparison of the bit error rate (BER) of a 32G-PAM8 optical fiber link with a length of 5 km-ROP (dBm) under different received optical powers, according to an embodiment of the present invention. Figure 8(b) shows a comparison of the BER of a 32G-PAM8 optical fiber link with a length of 10 km under different received optical powers, according to an embodiment of the present invention. The experimental parameters were set as follows: optical fiber link lengths of 5 km and 10 km, 300 neurons, learning rate of 0.01, number of iterations of 2000, training data of 30%, and test data of 60%. The performance curves of the BER as a function of received optical power were compared with those of the algorithm without equalization, the algorithm with Volterra equalization, the algorithm with WNN equalization, and the adaptive equalization method (AdaptiveWNN) proposed in this invention.

[0075] As shown in Figure 8, the adaptive equalization method (AdaptiveWNN) proposed in this invention performs better in the low-received optical power region model, exhibiting stronger nonlinear modeling capabilities. However, in the high-received optical power region model, it struggles to finely fit subtle distortions, leading to a gradual plateau in performance improvement. Considering that modeling and data acquisition inevitably introduce certain errors, this adaptive equalization method can be considered reasonable and relatively accurate. Experimental results demonstrate that the PON adaptive equalization method disclosed in this invention achieves rapid discrete wavelet transform by using a tower-shaped algorithm based on Mallat signal decomposition and reconstruction, avoids the influence of noise variance estimation errors by employing a generalized cross-thresholding method, and balances effective denoising with signal structure preservation. The use of wavelet neural networks for multi-scale time-frequency analysis avoids the blind spots in BP neural network design and improves the approximation capability of the neural network. Under the condition of 32Gbaud-PAM8 single-mode fiber, the damaged signal is effectively recovered after nonlinear equalization.

[0076] Corresponding to the above method, the present invention also provides an electronic device, which includes a computer device, the computer device including a processor and a memory, the memory storing computer instructions, the processor executing the computer instructions stored in the memory, and when the computer instructions are executed by the processor, the electronic device performs the steps of the method as described above.

[0077] Corresponding to the methods described above, the present invention also provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the method as described in any of the above embodiments. The computer-readable storage medium may be a tangible storage medium, such as random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, register, floppy disk, hard disk, removable storage disk, CD-ROM, or any other form of storage medium known in the art.

[0078] Corresponding to the above methods, the present invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the method as described in any of the above embodiments.

[0079] Those skilled in the art will understand that the exemplary components, systems, and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software, or a combination of both. Whether implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention. When implemented in hardware, it can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this invention are programs or code segments used to perform the desired tasks. The programs or code segments can be stored in a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried in a carrier wave.

[0080] It should be clarified that the present invention is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present invention is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of the present invention.

[0081] In this invention, features described and / or illustrated for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or in place of features of other embodiments.

[0082] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, various modifications and variations of the embodiments of the present invention are possible. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An adaptive equalization method for PON, characterized in that, include: The Mallat decomposition algorithm is used to decompose the input unequalized signal into a preset number of layers to obtain the high-frequency detail coefficients and low-frequency approximation coefficients of each layer. Denoising is performed on the high-frequency detail coefficients of each layer, including: calculating the GCV score of the high-frequency detail coefficients of the current layer using the generalized cross-validation thresholding method, determining the optimal denoising threshold for denoising based on the GCV score, and denoising the high-frequency detail coefficients using a nonlinear shrinkage function based on the optimal denoising threshold. Based on the high-frequency detail coefficients of each layer after denoising and the low-frequency approximation coefficients of the corresponding layers, the Mallat reconstruction algorithm is used to iteratively reconstruct the denoised data symbol sequence layer by layer. The denoised data symbol sequence is used as the input to a pre-trained embedded wavelet neural network, which outputs an equalized signal. The embedded wavelet neural network is a backpropagation neural network that embeds wavelet functions in each of its neurons. The neurons with embedded wavelet functions extract time-frequency local features from the input denoised data symbol sequence. The output layer of the embedded wavelet neural network outputs an equalized signal based on all the extracted time-frequency local features.

2. The method according to claim 1, characterized in that, The Mallat decomposition algorithm is used to decompose the input unequalized signal into a preset number of layers to obtain the high-frequency detail coefficients and low-frequency approximation coefficients of each layer, including: The input unbalanced signal is subjected to multi-layer recursive filtering and downsampling operations to obtain low-frequency decomposition components and high-frequency decomposition components of a preset number of layers. The low-frequency decomposed components are downsampled by a factor of 2 to obtain low-frequency approximation coefficients, and the high-frequency decomposed components are downsampled by a factor of 2 to obtain high-frequency detail coefficients; wherein, even-numbered index points are retained during the downsampling process.

3. The method according to claim 1, characterized in that, The step of determining the optimal denoising threshold for denoising processing based on the GCV score includes: The threshold that minimizes the GCV score is used as the basic denoising threshold. The obtained basic denoising threshold is then weighted between layers to obtain the optimal denoising threshold. The weighting factor used for inter-layer weighting increases linearly with the layer level.

4. The method according to claim 3, characterized in that, The nonlinear contraction function is expressed by the following formula: ； in, This represents the optimal denoising threshold. Indicates the first The first layer High-frequency detail coefficients, This represents the high-frequency detail coefficients after noise reduction processing.

5. The method according to claim 1, characterized in that, The method further includes: before the pre-training of the backpropagation neural network begins, initially constructing an embedded wavelet neural network model, and using the first derivative of the Gaussian wavelet function to replace the activation function in each neuron of the backpropagation neural network.

6. The method according to claim 1, characterized in that, The embedded wavelet neural network comprises an input layer, a wavelet function calculation layer, and an output layer; the step of using the denoised data symbol sequence as input to the pre-trained embedded wavelet neural network and outputting an equalized signal includes: The denoised data symbol sequence is input into the input layer; In the wavelet function computation layer, neurons embedded with wavelet functions are used to extract time-frequency local features from the input denoised data symbol sequence; In the output layer, all extracted time-frequency local features are weighted and summed, and the bias term contained in the pre-trained embedded wavelet neural network model is added to output the equalized signal.

7. An adaptive equalization system for PON, characterized in that, include: The adaptive threshold preprocessing module is used to decompose the input unequalized signal into a preset number of layers using the Mallat decomposition algorithm, and obtain the high-frequency detail coefficients and low-frequency approximation coefficients of each layer. The method for denoising the high-frequency detail coefficients of each layer includes: calculating the GCV score of the high-frequency detail coefficients of the current layer using the generalized cross-validation thresholding method; determining the optimal denoising threshold for denoising based on the GCV score; and denoising the high-frequency detail coefficients using a nonlinear shrinkage function based on the optimal denoising threshold. It also includes iteratively reconstructing the denoised data symbol sequence layer by layer using the Mallat reconstruction algorithm based on the denoised high-frequency detail coefficients of each layer and the corresponding low-frequency approximation coefficients. A pre-trained wavelet neural network module is used to output an equalized signal based on the input denoised data symbol sequence; wherein, the embedded wavelet neural network is a backpropagation neural network that embeds wavelet functions in each of its neurons, and uses the neurons with embedded wavelet functions to extract time-frequency local features from the input denoised data symbol sequence, and the output layer of the embedded wavelet neural network outputs the equalized signal based on all the extracted time-frequency local features.

8. The system according to claim 1, characterized in that, The wavelet neural network module comprises an input layer, a wavelet function calculation layer, and an output layer; wherein... The input layer is used to input the denoised data symbol sequence; The wavelet function computation layer is used to extract time-frequency local features from the input denoised data symbol sequence using neurons embedded with wavelet functions; The output layer is used to perform a weighted summation of all extracted time-frequency local features, and add the bias term contained in the pre-trained embedded wavelet neural network model to output the equalized signal.

9. An electronic device comprising a processor, a memory, and a computer program / instructions stored in the memory, characterized in that, The processor is used to execute the computer program / instructions, and when the computer program / instructions are executed, the electronic device implements the steps of the method as described in any one of claims 1 to 6.

10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method as described in any one of claims 1 to 6.

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