Signal processing method based on deep learning and adaptive filtering fusion

Abstract

The application discloses a signal processing method based on deep learning and adaptive filtering fusion, comprising the following steps: S1, original signal acquisition and pretreatment; S2, adaptive filtering; S3, constructing a deep neural network model to extract deep features of the filtered signal; S4, signal fusion to eliminate interference; S5, establishing a real-time closed-loop feedback mechanism for dynamic parameter adjustment; S6, end-to-end dynamic optimization process; S7, iterative update and high confidence sample judgment; S8, using the trained adaptive filtering module and deep neural network model to process newly collected signals, and generating reconstructed signals through signal fusion. The application effectively fuses adaptive filtering and deep neural network, realizes accurate suppression of multipath effect, nonlinear noise and transient interference in complex wireless signals, and high-dimensional feature extraction, thereby significantly improving the precision, robustness and real-time performance of signal processing.

Description

Technical Field

[0001] This invention relates to the fields of signal processing and artificial intelligence, specifically to a signal processing method based on the fusion of deep learning and adaptive filtering algorithms. Background Technology

[0002] With the widespread deployment of wireless communication devices, IoT terminals, and radar systems, the wireless signal environment is becoming increasingly complex. Multipath effects, nonlinear interference, and transient noise are becoming more prominent, severely impacting the reliability and accuracy of signal transmission. While traditional adaptive filtering techniques can dynamically adjust filtering parameters according to real-time environmental changes and effectively suppress some noise and interference, their processing capabilities are limited when facing complex nonlinear interference, often failing to meet the requirements of high-precision signal reconstruction. Deep learning-based signal processing methods demonstrate powerful capabilities in extracting deep-level signal features, but they typically require high-quality input data and are highly dependent on large amounts of labeled data. Their robustness and real-time performance in noisy environments are still insufficient to cope with the ever-changing real-world communication scenarios.

[0003] Furthermore, existing signal processing techniques often suffer from a lack of effective coordination between filtering preprocessing and deep feature extraction when achieving end-to-end optimization. Traditional methods, when using adaptive filtering or deep learning models alone, are prone to getting trapped in local optima, making it difficult to dynamically balance real-time performance and processing accuracy. They also lack mechanisms for real-time feedback and adjustment between processing results and preset performance indicators, leading to poor system stability in high-interference environments. To address this challenge, there is an urgent need for a novel signal processing method that fully integrates the advantages of deep learning in complex signal feature extraction with the real-time noise interference suppression capabilities of adaptive filtering. This would enable efficient and accurate processing of complex wireless signals, thereby meeting the stringent requirements of modern communication systems in variable and high-interference environments. Summary of the Invention

[0004] The purpose of this invention is to provide a signal processing method based on the fusion of deep learning and adaptive filtering. This method effectively integrates adaptive filtering technology with a deep neural network model to achieve precise suppression of multipath effects, nonlinear noise and transient interference in complex wireless signals and high-dimensional feature extraction, thereby significantly improving the accuracy, robustness and real-time performance of signal processing.

[0005] The objective of this invention is achieved through the following technical solution: a signal processing method based on the fusion of deep learning and adaptive filtering, comprising the following steps:

[0006] S1. Raw signal acquisition and preprocessing: Acquire continuous time-varying electromagnetic wave data as raw data, perform noise reduction and normalization on the raw data, and then use time-domain segmentation technology to divide the continuous signal into slices of fixed length.

[0007] S2. Input the preprocessed signal into the adaptive filtering module for adaptive filtering;

[0008] S3. Construct a deep neural network model to extract deep features from the filtered signal; the deep neural network model includes the following structure:

[0009] The first convolutional layer uses 64 convolutional kernels with a kernel size of 3 and the activation function ReLU.

[0010] First pooling layer: A max pooling layer is added after the first convolutional layer as the first pooling layer;

[0011] Multi-layer convolution stacked module: a stacked structure that connects the second convolutional layer, the second pooling layer, the third convolutional layer, the third pooling layer, the fourth convolutional layer, and the fourth pooling layer in sequence after the first pooling layer;

[0012] LSTM: The output features of multi-layer convolutional stacked modules are input into LSTM, and the hidden state of the last time step of LSTM is extracted as the global feature representation of the entire signal slice.

[0013] S4. Perform signal fusion and eliminate interference: fuse the output obtained by adaptive filtering with the features extracted by the deep neural network model;

[0014] S5. Establish a real-time closed-loop feedback mechanism for dynamic parameter adjustment: Measure the signal-to-noise ratio and bit error rate of the output signal, compare them with the preset standard, thereby generating a feedback signal, and adjust the relevant parameters in the adaptive filtering module and deep neural network model according to the feedback signal.

[0015] S6. Perform end-to-end dynamic optimization process: organically integrate the modules of adaptive filtering, deep feature extraction, deep interference elimination fusion and real-time feedback closed loop into an end-to-end dynamic optimization process.

[0016] S7. Iterative Update and High-Confidence Sample Judgment: Determine whether new high-confidence training samples are generated based on the current system processing status. If they exist, merge the newly acquired signals with the feedback data and continue to execute steps S1 to S6 for iterative update. If no new samples are generated within several consecutive cycles, it is determined that the system performance has stabilized, the iterative training process is terminated, and the model parameters are retained.

[0017] S8. The newly acquired signal is processed using the finally trained adaptive filtering module and deep neural network model, and a reconstructed signal is generated through signal fusion.

[0018] The beneficial effects of this invention are as follows:

[0019] 1. In complex wireless environments, traditional signal processing methods often struggle to simultaneously achieve real-time performance, accuracy, and robustness. This invention, by integrating deep neural networks and adaptive filtering techniques, aims to achieve precise suppression and signal restoration of multipath effects, nonlinear noise, and transient interference, thereby significantly improving system processing performance under high-interference conditions. This method is applicable to wireless communication, radar signal processing, satellite communication, and other applications requiring high-quality real-time signal processing.

[0020] 2. This invention combines adaptive filtering with deep neural networks to achieve accurate suppression and efficient feature extraction of multipath effects, nonlinear interference, and noise in complex wireless signals. The invention introduces a real-time feedback closed-loop mechanism into the processing flow, dynamically adjusting filter parameters and network weights to progressively optimize signal quality. It employs offline pre-training and online incremental update strategies for iterative training, continuously improving the robustness of signal processing. The system effectively addresses signal degradation caused by environmental interference, channel fading, and dynamic changes, maintaining excellent real-time performance and processing accuracy even under high interference conditions. Through adaptive fusion and dynamic optimization strategies, this invention continuously enhances generalization ability during model updates, achieving efficient analysis of all original signals and providing stable and accurate data support for subsequent modulation identification and channel decoding. Attached Figure Description

[0021] Figure 1 This is an overall flowchart of a signal processing method based on the fusion of deep learning and adaptive filtering according to the present invention. Detailed Implementation

[0022] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0023] like Figure 1 As shown, a signal processing method based on the fusion of deep learning and adaptive filtering according to the present invention includes the following steps:

[0024] S1. Raw signal acquisition and preprocessing: Acquire continuous time-varying electromagnetic wave data as raw data, perform noise reduction and normalization on the raw data, and then use time-domain segmentation technology to divide the continuous signal into slices of fixed length.

[0025] In this embodiment, six high-performance signal acquisition stations are deployed in the city center area. Each station uses a 14-bit analog-to-digital converter (ADC) with a sampling frequency of 20 MS / s. The acquired raw signal is time-varying electromagnetic wave data, denoted as x(t). First, Gaussian filtering is used to denoise the raw signal, with a filter window size of 5 ms and a standard deviation σ = 0.8 ms. Then, gain correction is used to adjust the signal amplitude, normalizing the signal amplitude. The normalization uses the minimum-maximum normalization formula:

[0026]

[0027] Where, x min and x max These are the minimum and maximum values ​​within the sampling window, respectively.

[0028] After denoising and gain correction, the continuous signal is divided into segments of uniform length, each 10ms long, forming a data sample set with a unified format. This step ensures data consistency and high-quality input in subsequent processing.

[0029] S2. Input the preprocessed signal into the adaptive filtering module for adaptive filtering; the specific implementation method is as follows: denot the preprocessed single slice signal as x. pre (t), which is discretized into a sequence x(n), where n represents the discrete-time index; each signal slice is used as a vector input to the adaptive filter;

[0030] To meet signal processing requirements, the filter length is set to L = 32, then the input vector is:

[0031]

[0032] The goal of an adaptive filter is to output y(n) from an input signal x(n) through a linear combination of a set of weights w(n), and to make the output y(n) as close as possible to a preset reference signal d(n); where the reference signal d(n) can be an injected training signal or a known pilot signal. The filter output calculation formula is:

[0033] y(n)=w(n) T x(n)

[0034] in, This is the current filter weight vector, which is usually set to zero vector initially, i.e., w(0) = 0.

[0035] To update the weights and gradually reduce the output error, the NLMS algorithm is used to update the weights:

[0036]

[0037] Where μ is the step size factor, controlling the magnitude of weight updates, and is set to 0.001 in this embodiment; ||x(n)|| 2 The squared L2 norm of x(n) is used to normalize the input energy, and is calculated as follows:

[0038]

[0039] ∈ is a small positive number used to prevent division by zero; e(n) is the error signal, defined as the difference between the reference signal and the actual output of the filter, i.e., e(n) = d(n) - y(n); it comes from the preset training signal or pilot signal to ensure that the filter can accurately track channel changes.

[0040] In practical implementation, with each update, the filter continuously adjusts the weights w(n) to minimize the error e(n), thereby achieving adaptive suppression of noise and interference. For example, when the sampling frequency is 20 MS / s, each filtering cycle processes 32 consecutive sampling points. After thousands of iterations, the weight vector w(n) gradually converges, and the signal-to-noise ratio of the output signal y(n) is significantly improved.

[0041] Furthermore, to ensure real-time performance, the adaptive filtering module in this embodiment is hardware-accelerated on an embedded system. Combined with a real-time feedback mechanism, after each filtering cycle, the current error signal is fed back to the algorithm controller, dynamically adjusting the step size factor μ to adapt to rapid changes in the channel environment. After the above processing, the output filtered signal y(n) becomes a high-quality input for subsequent deep neural network feature extraction, effectively improving the robustness and processing accuracy of the entire system in complex communication environments.

[0042] S3. Construct a deep neural network model to extract deep features from the filtered signal; slice the output signal y(n) from step S2 into time-domain segments of a fixed length N = 32, and construct the signal slice vector:

[0043]

[0044] Where y(n) represents the filtered discrete signal value, and n is the time sampling index.

[0045] The deep neural network model includes a convolutional neural network (CNN) module and an LSTM module. The convolutional neural network module includes:

[0046] First convolutional layer: The signal slice vector first enters the first convolutional layer for convolution processing. The first convolutional layer uses 64 convolutional kernels with a kernel size of 3 and the activation function is ReLU; used to extract local temporal features.

[0047] First pooling layer: After the first convolutional layer, a max pooling layer is added as the first pooling layer with a pooling window size of 2, which is used for dimensionality reduction and to achieve feature invariance.

[0048] Multi-layer convolution stacked module: To further enrich feature representation, a stacked structure of second convolutional layer, second pooling layer, third convolutional layer, third pooling layer, fourth convolutional layer and fourth pooling layer is connected in sequence after the first pooling layer to extract higher-level local features;

[0049] The feature maps output by the convolutional neural network module are shaped to form a time step sequence, with the feature vector dimension of each time step being 64.

[0050] LSTM (Long Short-Term Memory Network): The output features of multiple stacked convolutional modules are input into an LSTM. The hidden layer dimension of the LSTM is set to 128 to capture the global temporal dependencies of the signal. Finally, the hidden state of the last time step of the LSTM is extracted as the global feature representation of the entire signal slice, denoted as a vector.

[0051] S4. Perform signal fusion to eliminate interference: Fuse the output obtained from adaptive filtering with the features extracted by the deep neural network model; fuse the output y(n) obtained from adaptive filtering in step S2 with the high-dimensional feature vector f extracted by CNN+LSTM in step 3 to further eliminate multipath effects, nonlinear noise and other interference factors, and improve the accuracy of signal reconstruction. This step specifically includes:

[0052] S4.1 Feature fusion is performed using an attention-based fusion strategy; firstly, the output feature y(n) after adaptive filtering is transformed using a low-order transformation to obtain the feature vector f. af , will f af The features are concatenated or spliced ​​with the f extracted by deep learning to form a joint feature vector. The spliced ​​features are then input into a multilayer perceptron (MLP) module for processing. This module includes a hidden layer (64 pixels in size, using ReLU activation function) and an output layer. The vector output by the MLP module is normalized using Softmax to obtain attention weights. These weights are then used to weight the joint features to obtain fused features.

[0053] S4.2 Further optimization of fused features: The fused feature vector, which is weighted by the attention mechanism, is input into a fully connected layer (the output dimension remains 128), and further feature optimization and signal reconstruction are performed by combining batch normalization and Dropout;

[0054] S4.3 To ensure that the fused features accurately reflect the structural information of the original signal and effectively suppress multipath effects and other interferences, the mean square error (MSE) reconstruction loss function is used for training, and its loss is defined as:

[0055]

[0056] Where s i This means that before the actual signal is transmitted, the original sample, which has undergone advanced noise reduction processing, is preserved through system calibration. This represents the reconstructed signal output by the fusion module; N is the number of samples.

[0057] This loss function optimizes the parameters of the deep neural network model and the multilayer perceptron (MLP) module through backpropagation, ensuring that the overall network achieves high-precision signal restoration and anti-interference performance.

[0058] S5. Establish a real-time closed-loop feedback mechanism for dynamic parameter adjustment: Measure the signal-to-noise ratio (SNR) and bit error rate (BER) of the output signal, compare them with the preset standard, thereby generating a feedback signal, and adjust the relevant parameters in the adaptive filtering module and deep neural network model according to the feedback signal.

[0059] The specific implementation method is as follows: after the end of each training or processing cycle (a training cycle includes adaptive filtering, feature extraction by the deep neural network, feature fusion, and signal reconstruction), the reconstructed signal y of the current output is calculated. fusion The SNR of (n) is calculated using the following formula:

[0060]

[0061] Where P signal For signal power, P noise Noise power; preset target signal-to-noise ratio is SNR. target =35dB, then the signal-to-noise ratio error is:

[0062] ΔSNR=SNR target -SNR current

[0063] If ΔSNR exceeds the set threshold by 2dB, the system performance is considered substandard and requires dynamic adjustment.

[0064] Simultaneously, monitor the BER and compare it with the target BER (typically set to 10). -5 If the error ΔBER between the two values ​​is higher than the target value, the system performance is considered substandard and dynamic adjustment is required. Dynamic adjustment is needed if ΔSNR exceeds a set threshold or BER exceeds the target value, until both values ​​do not exceed the threshold / target value.

[0065] The signal-to-noise ratio (SNR) error or BER error is used as the feedback signal. After the feedback signal is generated, the weights w(n) of the adaptive filtering module and the parameters of the deep neural network model are adjusted according to the feedback error. The adjustment process adopts a dynamic step size, where the step size factor μ is initially set to 0.001, and when the feedback error is large, the step size will increase to 0.0015 to accelerate parameter updates; conversely, if the system output is close to the target, the step size is gradually reduced to achieve stable convergence. The entire closed-loop control process is implemented through a real-time monitoring module. After each processing cycle, the system automatically calculates the current SNR and BER, outputs adjustment commands through the feedback controller, updates the network parameters and filter weights, thereby ensuring that the subsequent output signal continuously approaches the preset performance target, and finally achieves stable convergence.

[0066] S6. Perform an end-to-end dynamic optimization process: organically integrate the modules of adaptive filtering, deep feature extraction, deep interference cancellation and fusion, and real-time feedback closed loop into an end-to-end dynamic optimization process; specifically including:

[0067] S6.1 System Integration and Real-time Monitoring: Through hardware and software integration, the preprocessing, adaptive filtering, feature extraction, and fusion modules are cascaded to achieve seamless data transmission and time synchronization. Simultaneously, a built-in real-time monitoring module is responsible for collecting performance indicators (signal-to-noise ratio SNR, bit error rate BER) for each processing stage, comparing these indicators with preset targets, and generating feedback signals. These feedback signals are then transmitted to the central controller in real time, which controls the dynamic adjustment of parameters in each module.

[0068] S6.2 Offline Pre-training and Online Incremental Update: First, offline pre-training is performed using historical large-scale signal data (data collected several times in the past) to construct initial model parameters. During pre-training, the Adam optimizer is used with an initial learning rate set to 0.005, and a cosine annealing strategy is used to achieve dynamic learning rate adjustment. After pre-training, newly collected data (data collected during incremental updates, i.e., data collected after deployment to the actual scene) are used to incrementally update the model parameters online in small batches. The performance metrics provided by the real-time feedback module are used to guide online training to adaptively adjust network layer weights and adaptive filter parameters.

[0069] S7. Iterative Update and High-Confidence Sample Judgment: After completing the online training of the newly collected data in step S6.2, the system immediately evaluates the confidence of the output results of the current cycle: the signal features processed by adaptive filtering and deep fusion network are compared with the thresholds for signal-to-noise ratio improvement and bit error rate reduction; if all threshold conditions are met, it is considered that a new high-confidence sample has been generated, and training continues; if no high-confidence sample is detected in this cycle, a "no new sample" event is recorded, and when there are no new samples for three consecutive training cycles, it is determined that the model performance has stabilized, the iterative training is terminated, and the current adaptive filter weights and deep neural network parameters are retained as the final deployment model of the system.

[0070] S8. The newly acquired signal is processed using the finally trained adaptive filtering module and deep neural network model, and a reconstructed signal is generated through signal fusion. At this point, the new signal, after being processed by the aforementioned modules, outputs a high-quality signal y. out (n), whose signal-to-noise ratio is ≥30dB and bit error rate is less than 10. -5 The system meets the requirements of providing stable and accurate input data for subsequent modulation identification or channel decoding. Simultaneously, the system utilizes a built-in intelligent monitoring interface to remotely monitor the overall operational status and perform self-diagnosis of faults. The monitoring module records key indicators during processing in real time and triggers an alarm mechanism in abnormal situations, automatically saving relevant logs and data for subsequent analysis. This ensures the entire signal processing flow maintains extremely high stability and robustness during long-term operation.

[0071] In summary, this invention achieves real-time adaptive processing of noise, interference, multipath effects, and nonlinear distortion in complex wireless signals by introducing a fusion architecture of deep neural networks and adaptive filtering technology. The method first uses a normalized least mean square algorithm to dynamically filter the original signal, thereby improving signal purity. Then, it combines a multi-layer deep feature extraction module based on convolutional neural networks and long short-term memory networks to effectively capture local and global temporal features in the signal. By introducing a deep interference cancellation fusion strategy based on an attention mechanism, this invention further optimizes the weighted fusion of features from different sources, significantly reducing signal reconstruction errors caused by complex channel environments.

[0072] During training, this invention dynamically adjusts key parameters in the filter and deep network through a real-time feedback closed-loop mechanism. It employs a strategy combining offline pre-training and online incremental updates to enable the model to continuously approach preset performance metrics (such as signal-to-noise ratio and bit error rate) across multiple iterative updates. This method utilizes feedback signals to guide adaptive parameter correction and, combined with the introduction of periodic high-confidence samples, enhances the model's robustness and generalization ability in the face of unknown or changing channel conditions. Furthermore, the comparative learning strategy using positive and negative sample pairs further optimizes the aggregation of similar samples and the separation of dissimilar samples in the feature space, thereby significantly improving the overall recognition accuracy of the model.

[0073] This invention provides a highly efficient, adaptive, and iteratively optimizable signal processing method, particularly suitable for practical applications such as wireless communication, spectrum management, and intelligent wireless monitoring. It exhibits significant advantages, especially in environments with severe noise interference, complex channel conditions, and high real-time requirements. This method not only provides high-quality input data for subsequent modulation identification and channel decoding but also possesses the ability to accurately suppress unknown interference and dynamically changing channels, providing solid technical support for building intelligent communication and monitoring systems.

[0074] 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 signal processing method based on the fusion of deep learning and adaptive filtering, characterized in that, Includes the following steps: S1. Raw signal acquisition and preprocessing: Acquire continuous time-varying electromagnetic wave data as raw data, perform noise reduction and normalization on the raw data, and then use time-domain segmentation technology to divide the continuous signal into slices of fixed length. S2. Input the preprocessed signal into the adaptive filtering module for adaptive filtering; S3. Construct a deep neural network model to extract deep features from the filtered signal; the deep neural network model includes the following structure: The first convolutional layer uses 64 convolutional kernels with a kernel size of 3 and the activation function ReLU. First pooling layer: A max pooling layer is added after the first convolutional layer as the first pooling layer; Multi-layer convolution stacked module: a stacked structure that connects the second convolutional layer, the second pooling layer, the third convolutional layer, the third pooling layer, the fourth convolutional layer, and the fourth pooling layer in sequence after the first pooling layer; LSTM: The output features of multi-layer convolutional stacked modules are input into LSTM, and the hidden state of the last time step of LSTM is extracted as the global feature representation of the entire signal slice. S4. Perform signal fusion and eliminate interference: fuse the output obtained by adaptive filtering with the features extracted by the deep neural network model; S5. Establish a real-time closed-loop feedback mechanism for dynamic parameter adjustment: Measure the signal-to-noise ratio and bit error rate of the output signal, compare them with the preset standard, generate a feedback signal, and adjust the relevant parameters in the adaptive filtering module and deep neural network model according to the feedback signal. S6. Perform end-to-end dynamic optimization process: organically integrate the modules of adaptive filtering, deep feature extraction, deep interference elimination fusion and real-time feedback closed loop into an end-to-end dynamic optimization process. S7. Iterative Update and High-Confidence Sample Judgment: Determine whether new high-confidence training samples are generated based on the current system processing status. If they exist, merge the newly acquired signals with the feedback data and continue to execute steps S1 to S6 for iterative update. If no new samples are generated within several consecutive cycles, it is determined that the system performance has stabilized, the iterative training process is terminated, and the model parameters are retained. S8. The newly acquired signal is processed using the finally trained adaptive filtering module and deep neural network model, and a reconstructed signal is generated through signal fusion.

2. The signal processing method based on the fusion of deep learning and adaptive filtering according to claim 1, characterized in that, The specific implementation method of step S2 is as follows: The preprocessed single slice signal is denoted as x. pre (t), which is discretized into a sequence x(n), where n represents the discrete-time index; each signal slice is used as a vector input to the adaptive filter; To meet the requirements of signal processing, the filter length is set to L, then the input vector is: The goal of an adaptive filter is to output y(n) from an input signal x(n) through a linear combination of a set of weights w(n), and to make the output y(n) as close as possible to a preset reference signal d(n); the filter output is calculated using the following formula: y(n)=w(n) T x(n) The weights are updated using the NLMS algorithm: Where μ is the step size factor, ||x(n)|| 2 Let represent the square of the L2 norm of x(n); ∈ is a small positive number used to prevent division by zero; e(n) is the error signal, defined as the difference between the reference signal and the actual output of the filter; The filter minimizes e(n) by continuously adjusting the weight w(n), thereby achieving adaptive suppression of noise and interference.

3. The signal processing method based on the fusion of deep learning and adaptive filtering according to claim 1, characterized in that, Step S4 specifically includes: S4.1 Feature fusion is performed using an attention-based fusion strategy; firstly, the output feature y(n) after adaptive filtering is transformed using a low-order transformation to obtain the feature vector f. af , will f af The features are concatenated or spliced ​​with the f extracted by deep learning to form a joint feature vector; then the spliced ​​features are input into the multilayer perceptron module for processing to obtain the fused features. S4.2 Further optimization of fused features: Input the fused feature vector into a fully connected layer, and combine batch normalization and Dropout for further feature optimization and signal reconstruction; S4.

3. The mean squared error (MSE) loss function is used for training, and its loss is defined as: Where s i Represents the original sample; This represents the reconstructed signal output by the fusion module; N is the number of samples. This loss function optimizes the parameters of the deep neural network model and the multilayer perceptron module through backpropagation.

4. The signal processing method based on the fusion of deep learning and adaptive filtering according to claim 1, characterized in that, The specific implementation method of step S5 is as follows: after each training or processing cycle, calculate the reconstructed signal y of the current output. fusion The SNR of (n) is calculated using the following formula: Where P signal For signal power, P noise Noise power; preset target signal-to-noise ratio is SNR. target Then the signal-to-noise ratio error is: ΔSNR=SNR target -SNR current If ΔSNR exceeds the set threshold by 2dB, the system performance is considered substandard and requires dynamic adjustment. At the same time, monitor the BER and compare it with the target BER. If the error ΔBER is higher than the target value, the system performance is considered to be substandard and dynamic adjustment is required. The signal-to-noise ratio error or BER error is used as the feedback signal. After the feedback signal is generated, the weight w(n) of the adaptive filtering module and the parameters of the deep neural network model are adjusted according to the feedback error. The adjustment process adopts a dynamic step size, where the step size factor μ is initially set to 0.001.

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