Joint multi-branch adaptive equalization and denoising method based on deep learning

Abstract

The application relates to the technical field of underwater acoustic communication, in particular to a joint multi-branch adaptive equalization and noise reduction method based on deep learning which can effectively weaken noise items contained in the output of an equalizer, so that the overall bit error rate performance of a receiver is better, and the method is characterized in that a joint multi-branch adaptive equalization and intelligent noise reduction network DL-JAED based on deep learning is built, noise features in a signal sequence are learned by using deep learning, noise reduction of the signal sequence is realized, a cyclic iteration is formed between an equalizer and a noise reduction module, the outputs of the two are used as transmission information, and iteration gain is fully utilized; an error is calculated from the output after noise reduction, and is used as a feedback signal to update a forward filter and a reverse filter of the equalizer.

Description

Technical fields:

[0001] This invention relates to the field of underwater acoustic communication technology, specifically to a deep learning-based joint multi-branch adaptive equalization and noise reduction method that can effectively reduce the noise term contained in the output of the equalizer, thereby improving the overall bit error rate performance of the receiver. Background technology:

[0002] Underwater acoustic channels suffer from time-varying multipath propagation, severe fading, and strong noise, which can affect the reliable transmission of underwater acoustic signals. This is an issue that must be considered to improve the reliability of underwater acoustic communication links.

[0003] To address the severe fading problem, diversity is typically employed, where multiple hydrophones are used at the receiver to achieve diversity gain. However, for high-speed underwater acoustic communication, time-varying multipath propagation can also introduce significant inter-symbol interference, which must also be considered and addressed. Therefore, when processing signals received from multiple hydrophones, not only multi-branch merging but also equalization processing is necessary.

[0004] Traditional multi-branch merging and equalization are implemented independently. Research shows that jointly implementing multi-branch merging and equalization can significantly improve receiver performance. Existing technology proposes a multi-branch joint detector for frequency-selective channels, in which multi-branch merging and equalization are implemented jointly, adjusting the tap coefficients of each branch and merging the branches based on the total error. However, underwater acoustic channels are time-varying. To improve adaptability to time-varying underwater acoustic channels, existing technology also proposes a multi-branch merging and equalization joint implementation algorithm with an embedded phase-locked loop (PLL). This algorithm can jointly implement multi-branch merging, phase adjustment, and equalization of each branch. The introduction of the PLL enables better tracking of channel changes.

[0005] After the signals received by multiple hydrophones at the receiving end are processed by multi-branch merging and equalization, the effects of inter-symbol interference and channel attenuation can be eliminated to a certain extent; similarly, it will also have a certain effect on suppressing noise, but it cannot completely eliminate it.

[0006] Most current noise reduction research focuses on image processing. With the development of deep learning technology, more and more researchers are using it to solve problems in the traditional physical layer of communication. In the physical layer of communication, signal processing typically has specific mathematical models, meaning that problems can be modeled and described using mathematical models. While these models provide interpretability, they lack flexibility. Summary of the Invention:

[0007] This invention addresses the shortcomings and deficiencies of existing technologies by proposing a deep learning-based joint multi-branch adaptive equalization and noise reduction method that can effectively reduce the noise term in the equalizer output and improve the overall bit error rate performance of the receiver.

[0008] This invention achieves its purpose through the following measures:

[0009] A deep learning-based joint multi-branch adaptive equalization and denoising method is characterized by constructing a deep learning-based joint multi-branch adaptive equalization and intelligent denoising network DL-JAED, utilizing deep learning to learn noise features in the signal sequence to achieve denoising, forming a cyclic iteration between the equalizer and the denoising module, and using the outputs of both as information transmission to fully utilize the iteration gain; the error is calculated from the denoised output and used as a feedback signal to update the forward and reverse filters of the equalizer, specifically including the following steps:

[0010] Step 1: The multi-branch signal sequences received by the receiving end are [r k,1 ,r k,2 ,…,r k,n The received signal is processed by a feedforward equalizer and phase compensation, and then combined through multiple branches to obtain signal p. k , Step 2: With feedback signal q k The output y of the equalizer is obtained by subtraction. k :

[0011]

[0012] Step 3: Obtain the equalized sequence y with a length equal to the data packet length using a shift register:

[0013] y = [y1, y2, ..., y k (15)

[0014] Step 4: Input the sequence y into the denoising network to obtain the noise estimation sequence.

[0015] Step 5: Equalized sequence y and estimated noise sequence Subtraction:

[0016] Step 6: Use the denoised sequence Update the feedforward and feedback filters:

[0017]

[0018] in,

[0019] Step 7: Continue the process from Step 1 to Step 6 in a loop until the set number of iterations is reached.

[0020] The deep learning-based joint multi-branch adaptive equalization and intelligent noise reduction network DL-JAED described in this invention includes a multi-branch NLMS equalizer and a deep learning noise reduction network model. In the multi-branch NLMS equalizer, the equalizer receives multiple signals from n hydrophones at time k, denoted as r... k,1 ,r k,2 ,…,r k,n ,in:

[0021]

[0022] Where L f The length of the feedforward filter is given. After equalization and combining by the equalizer, the received signal sequence y is obtained. After passing through the intelligent noise reduction network, the denoised signal sequence is obtained as follows: The tap length of the feedback filter is L b The corresponding phase output vectors of the n phase-locked loops are The feedforward filter tap vectors are respectively

[0023] For ease of representation, the vectors are combined and represented as shown in equation (4):

[0024]

[0025] The output after merging multiple branches can be represented as shown in equation (5):

[0026]

[0027] The output of the equalizer is shown in equation (6):

[0028]

[0029] The output of the decision-maker is shown in equation (7):

[0030]

[0031] The deep learning noise reduction network model includes convolutional layers, pooling layers, and upsampling layers, which are used to extract features from the input signal, reduce the size of the feature map, and increase the size of the feature map, respectively.

[0032] The deep learning-based joint multi-branch adaptive equalization and intelligent noise reduction network DL-JAED described in this invention needs to be trained before it can be used. During the training process, based on a semi-steady channel, training is completed using a communication frame structure containing training sequences. The total length of the communication frame structure containing training sequences is 10 data packets, containing two parts of information: training sequences and information sequences. The first three data packets of each frame are the training sequences, and all subsequent parts are information sequences. Based on this communication frame structure, DL-JAED will alternately switch between two modes: training mode and transmission mode. Step A: When the first data packet of the training sequence is received, according to the NLMS algorithm mentioned above, the equalizer will initialize the parameters under the current channel state through the data packet, and achieve equalization of the channel response in a relatively coarse manner. At this time, DL-JAED is working in training mode.

[0033] Step B: When the second and third data packets of the training sequence are received, the channel changes. Based on the coarse synchronization, the equalizer will perform more refined tracking and parameter updates according to the training sequence, enter the convergence state, achieve synchronization, and then use the equalized training sequence as training samples to input into the network for training. At this time, the DL-JAED algorithm is working in training mode.

[0034] Step C: When the data packet of the information sequence is received, the channel changes. Due to the synchronization of the training sequence, the equalizer can keep track of the channel response well. The equalization is applied to the information sequence, and the resulting equalized sequence is input into the denoising network for denoising. Hard decision is made on the denoised sequence, and the decision result is used to update the tap parameters of the equalizer. It can also be used as a new training sample for the denoising network. At this time, the DL-JAED algorithm is working in transmission mode.

[0035] Step D: Maintain step C until the information sequence ends, and keep the equalizer and noise reduction network updated during transmission; Step E: When the next frame of the training sequence is received, maintain the working mode of steps AD.

[0036] Unlike existing methods, the proposed DL-JAED uses deep learning to denoise the equalized signal and constructs an iterative loop between the equalizer and the denoising module, thereby achieving iterative gain and further eliminating inter-symbol interference and noise. Simulation results show that the proposed algorithm achieves better performance than existing methods. Attached image description:

[0037] Figure 1 This is a schematic diagram of the underwater acoustic multi-branch communication system model in this invention.

[0038] Figure 2This is a schematic diagram of the receiver structure in this invention.

[0039] Figure 3 This is a structural diagram of the multi-branch NLMS equalizer in this invention.

[0040] Figure 4 This is a diagram of the intelligent noise reduction network structure based on deep learning in this invention.

[0041] Figure 5 This is a structural block diagram of DL-JAED in this invention.

[0042] Figure 6 This is a schematic diagram of the communication frame structure used by the DL-JAED algorithm in this invention.

[0043] Figure 7 This is a schematic diagram of the working mode of the DL-JAED algorithm in this invention.

[0044] Figure 8 Schematic diagram of underwater acoustic channel model.

[0045] Figure 9 Multipath delay and response diagram of underwater acoustic channel.

[0046] Figure 10 Bit error rate performance curves before and after the introduction of intelligent noise reduction network.

[0047] Figure 11 Bit error rate performance curves before and after signal denoising in scenarios with different numbers of branches.

[0048] Figure 12 The cost function curve of the intelligent noise reduction network.

[0049] Figure 13 Error rate performance curve of DL-JAED algorithm in single-branch scenario.

[0050] Figure 14 Error rate performance curve of DL-JAED algorithm in multi-branch scenarios.

[0051] Figure 15 Bit error rate performance curves of the DL-JAED algorithm with different iteration numbers in a single-branch scenario. Detailed implementation method:

[0052] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0053] This invention proposes a Deep Learning-based Joint Adaptive Equalization and Denoising Algorithm (DL-JAED). First, a deep learning-based denoising algorithm is proposed. Then, to further improve the performance of underwater acoustic communication systems, the DL-JAED algorithm is presented. The DL-JAED algorithm consists of two modules: a multi-branch adaptive equalization module and a deep learning-based intelligent denoising module. By forming an iterative loop between these two modules, receiver performance can be further improved through iterative processing. In the algorithm implementation, the merging of multi-branch signals, equalization of each branch, phase adjustment, and denoising are not independent but jointly implemented. Simulation results show that the proposed algorithm achieves better performance compared to existing methods.

[0054] Depend on Figure 1 It is known that in an underwater environment at a depth of h, there exists a transmitter at a distance h from the bottom of the water. t n hydrophones at different depths are deployed underwater, with their distances from the bottom of the water body being [h...]. d1 ,h d2 ,…,h dn The transmitter sends a signal sequence s(t). s(t) can be expressed as:

[0055]

[0056] Among them, b j For equally probable independent Quadrature Phase Shift Keying (QPSK) data, T b Let P(t) represent the duration of the bit symbol and the normalized cosine pulse waveform.

[0057] The signal sequence received by n hydrophones is r(t) = [r1(t), r2(t), ..., r n (t)]. The horizontal distance between the transmitter and the receiving hydrophone is d. The received signal can be represented by equation (2):

[0058]

[0059] Where h1(t), h2(t) and h n (t) represents the channel impulse response between the transmitter and different hydrophones.

[0060] z1(t), z2(t) and z n (t) represents the ambient noise of the channel from the transmitter to different hydrophones.

[0061] Since the transmitting end typically uses waveform adjustment, the filters used in the equalization process are fractional-interval equalizers. The received signal r k,i It is caused by signal r i (t) is obtained after discretization sampling, i∈{1,…,n}, and the tap length of the feedforward filter with n branches is L. f The received signals on branches 1 to n at time k are respectively [r k,1 ,r k,2 ,…,r k,n ].

[0062] The receiver mainly consists of two parts: a multi-branch adaptive equalizer and a deep learning-based intelligent noise reduction network. The receiver structure is as follows: Figure 2 As shown.

[0063] The equalizer receives multiple signals from n hydrophones at time k, denoted as r. k,1 ,r k,2 ,…,r k,n .in:

[0064]

[0065] Where L f The length of the feedforward filter is given. After equalization and combining by the equalizer, the received signal sequence y is obtained. After passing through the intelligent noise reduction network, the denoised signal sequence is obtained as follows: The adaptive multi-branch equalizer in this invention employs a multi-branch equalizer with an embedded phase-locked loop based on the NLMS algorithm, and its specific structure is as follows: Figure 3 As shown.

[0066] The tap length of the feedback filter is L b The corresponding phase output vectors of the n phase-locked loops are The feedforward filter tap vectors are respectively For ease of representation, the vectors are combined and represented as shown in equation (4):

[0067]

[0068]

[0069]

[0070] The output after merging multiple branches can be represented as shown in equation (5):

[0071]

[0072] The output of the equalizer is shown in equation (6):

[0073]

[0074] The output of the decision-maker is shown in equation (7):

[0075]

[0076] This invention further proposes a joint adaptive equalization and intelligent noise reduction algorithm. The innovations of this algorithm are as follows: (1) The algorithm builds an intelligent noise reduction network based on deep learning, and uses deep learning to learn the noise features in the signal sequence to achieve noise reduction of the signal sequence; (2) The algorithm introduces the deep learning intelligent noise reduction algorithm into the receiver, and forms a loop iteration between the equalizer and the noise reduction module, and uses the output of the two as the transmission information to make full use of the iteration gain; (3) The algorithm calculates the error through the output after noise reduction, and uses it as a feedback signal to update the forward filter and reverse filter of the equalizer, thereby improving the overall performance of the system.

[0077] Deep learning-based intelligent noise reduction network structure, such as Figure 4 As shown. The specific parameters of each layer in the network are also shown.

[0078] Table 1 Parameters of each layer in the noise reduction network

[0079]

[0080]

[0081] The first two dimensions of the input and output sizes depend on the length of the signal sequence in the actual system.

[0082] This noise reduction network mainly consists of three types of network layers: convolutional layers, max-pooling layers, and upsampling layers. Convolutional, max-pooling, and upsampling layers are three commonly used layer types in deep learning. They are used to extract features from the input signal, reduce the size of the feature map, and increase the size of the feature map, respectively. The signal processing procedures of these three layers are described below and expressed with formulas.

[0083] Convolutional layers are crucial tools for extracting features from data such as images, sound, and text. Their primary function is to extract spatial features from data through local connections and shared weights. The denoising algorithm proposed in this paper uses convolutional layers to extract local features (noise features) from the input data by filtering it, employing multiple filters to extract different features. In convolutional layers, the size and number of filters are user-defined hyperparameters, whose optimal values ​​need to be determined through experimentation and tuning. The relatively small number of parameters in convolutional layers helps avoid overfitting, reduces computational cost, and improves model speed.

[0084] For a one-dimensional convolutional layer, assuming the input signal is... Where L is the signal sequence length, C is the number of channels, the convolution kernel size is k, and the output feature map is... Where F is the number of convolution kernels. The convolution operation is expressed by the formula shown in equation (8).

[0085]

[0086] in, These are the convolution kernel parameters. is the bias parameter, and f is the activation function, usually the ReLU function.

[0087] The purpose of a pooling layer is to pool the data, reducing the size of the feature map and thus decreasing computational cost. Specifically, it reduces the dimensionality of the data by dividing the input data into a series of non-overlapping subsequences and selecting the maximum value from each subsequence. For a one-dimensional pooling layer, if the input feature map is... The output feature map is The pooling process can be expressed by the formula (9):

[0088] h' i,j =max{h iS,j ,h iS+1,j ,…,h iS+(S-1),j}(9)

[0089] Where S is the pooling factor, which is also the pooling window size.

[0090] Upsampling layers increase the dimensionality of the input data, i.e., increase the size of the feature map, by upsampling the input data. Specifically, this involves copying each element of the input data several times and placing the copies at intervals to increase the dimensionality. In the signal denoising task presented in this paper, upsampling layers can effectively restore the low-dimensional feature map to a high-dimensional representation of the original signal.

[0091] For a one-dimensional upsampling layer, assume the input feature map is... The output feature map is Where K is the upsampling factor, that is, the upsampling layer inserts a 0 between K adjacent elements, and then multiplies all elements by K. This process can be expressed by the formula (10):

[0092] h' Ki,j =h i,j

[0093] h' Ki+1,j =0

[0094] h' i,j =Kh′ Ki,j (10), where i = 0, 1, ..., L-1, j = 0, 1, ..., F-1.

[0095] In network design, pooling layers and upsampling layers are used sequentially because, in deep learning, pooling layers can reduce the size of feature maps while retaining the main features, thus reducing the computational cost of subsequent layers. Upsampling layers, on the other hand, enlarge the size of feature maps, adding more detailed information. This combination allows the network to retain important features while adding more detailed information, thereby improving the model's accuracy.

[0096] Meanwhile, the combination of pooling layers and upsampling layers can also play a role in regularization, preventing the network from overfitting. During training, pooling layers can force the network to learn more robust features, while upsampling layers can compensate for the shortcomings of pooling layers and retain more detailed information.

[0097] Both pooling layers and upsampling layers have their own parameters: the pooling factor S and the upsampling factor K. The values ​​of these parameters need to be adjusted based on the specific problem. Furthermore, it's important to note that excessive pooling can lead to excessive feature loss, reducing the model's expressive power. Therefore, when designing neural networks, it's necessary to comprehensively consider the number of pooling layers and the selection of the pooling factor to ensure a balance between the model's expressive power and computational efficiency.

[0098] Building upon previously proposed deep learning-based denoising networks, and utilizing the iterative approach of Turbo Equalization, a new deep learning-based Joint Adaptive Equalization and Denoising Algorithm (DL-JAED) is proposed (using the iterative concept in Turbo Equalization). The structure of the DL-JAED algorithm is as follows: Figure 5 As shown. By Figure 5 As can be seen, the DL-JAED algorithm structure mainly consists of the adaptive equalizer and noise reduction network proposed above. The multi-branch signal sequences received by the receiver are respectively [r k,1,r k,2 ,…,r k,n The received signal is processed by a feedforward equalizer and phase step, and then combined through multiple branches to obtain signal p. k , and feedback signal q k The output y of the equalizer is obtained by subtraction. k , denoted as equation (11):

[0099] y k =p k -q k (11)

[0100] Unlike the structure mentioned above that only has an equalizer, in DL-JAED, y k Instead of directly determining the output, the data is stored in registers until a total sequence y of length one data packet is obtained, at which point it is input into the denoising network. The denoising network uses deep learning to calculate the noise in each bit of the signal sequence, ultimately outputting a noise sequence of the same length as the input. This process is represented by equation (12):

[0101] Where F(·) represents the signal processing by the noise reduction network.

[0102] And for Then we have: Representation: By comparing the equalized output y with the estimated noise sequence By subtracting signals, noise can be eliminated, resulting in a denoised signal sequence. And will The result d is input into the feedback equalizer to adjust and optimize the equalizer.

[0103] The loss function of the DL-JAED denoising network is shown in equation (14):

[0104] in, d is the output of the noise reduction network, and d is the desired value.

[0105] After obtaining the noise-reduced signal sequence Next, it is necessary to The result is input into the feedback equalizer, which adjusts and optimizes the feedforward and feedback filters in the NLMS-PL-DFE. This step links the equalizer's adaptive update to the denoising network. In the original scheme where the equalization and denoising networks were separate, the equalizer could only update the tap coefficients based on a decision-guided method, which would lead to error propagation problems.

[0106] In contrast, using the denoised signal sequence as the feedback signal can eliminate errors caused by the decision to some extent. Therefore, the combined adaptive equalization and denoising network architecture can improve the overall bit error rate performance of the receiver to a certain degree.

[0107] Besides the differences in system architecture between DL-JAED and the equalization and noise reduction separation scheme, the tap coefficient update algorithm of the adaptive equalizer also changes. Combining the update formula of the adaptive filter, the DL-JAED algorithm can be summarized as shown in Table 1.

[0108] Table 1 Summary of DL-JAED Algorithm

[0109]

[0110]

[0111] As can be seen from the DL-JAED algorithm flow, both the equalizer and neural network training phases require training sequences to complete. When simulating the algorithm in an underwater acoustic channel environment, it is assumed that the underwater acoustic channel changes within the time of one data packet, remaining in a semi-steady state. A semi-steady channel (Quasi-Static Channel) is a common channel model. Under this model, the statistical characteristics of the channel change slowly over the communication time scale, thus the channel can be considered relatively stable during communication. Based on the semi-steady channel, this section proposes a communication frame structure that includes training sequences, the specific structure of which is as follows: Figure 6 As shown.

[0112] like Figure 6 As shown, in the DL-JAED algorithm, the total frame length received by the receiver is 10 data packets, containing two parts of information: a training sequence and an information sequence. The first three data packets of each frame constitute the training sequence, and all subsequent packets constitute the information sequence. Based on this communication frame structure, the DL-JAED algorithm alternates between two modes: training mode and transmission mode. The operating modes of DL-JAED are as follows: Figure 7 As shown.

[0113] The working modes of the DL-JAED algorithm are summarized as follows:

[0114] Step 1: When the first data packet of the training sequence is received, according to the NLMS algorithm mentioned above, the equalizer will initialize the parameters under the current channel state through the data packet, and achieve equalization of the channel response in a relatively coarse manner. At this time, the DL-JAED algorithm is working in training mode.

[0115] Step 2: When the second and third data packets of the training sequence are received, the channel changes. Based on the coarse synchronization, the equalizer will perform more refined tracking and parameter updates according to the training sequence, enter the convergence state, achieve synchronization, and then use the equalized training sequence as training samples to input into the network for training. At this time, the DL-JAED algorithm is working in training mode.

[0116] Step 3: When the data packets of the information sequence are received, the channel changes. Due to the synchronization of the training sequence, the equalizer can now maintain good tracking of the channel response. Equalization is applied to the information sequence, and the resulting equalized sequence is input into the denoising network for noise reduction. Hard decision is made on the denoised sequence, and the decision result is used to update the equalizer's tap parameters. This result can also be used as new training samples for the denoising network; at this point, the DL-JAED algorithm operates in transmission mode.

[0117] Step 4: Continue in step 3 until the end of the information sequence, with the equalizer and noise reduction network being updated during transmission;

[0118] Step 5: When the next frame of the training sequence is received, maintain the working mode of steps 1 to 4.

[0119] Example:

[0120] To verify the performance of the proposed joint multi-branch adaptive equalization and intelligent noise reduction algorithm, the algorithm is simulated and verified below.

[0121] The underwater acoustic channel used in the simulation was generated using BELLHOP software. The simulation parameters for the underwater acoustic channel are shown in Table 2. Based on the parameters shown in Table 2, channel simulation was performed, yielding a schematic diagram of the underwater acoustic channel model and multipath delay and response diagrams, as shown below. Figure 9 and Figure 10 As shown.

[0122] Table 2 Simulation parameters of underwater acoustic channel

[0123]

[0124] By introducing a deep learning-based intelligent noise reduction algorithm, the noise term in the equalizer output can be effectively reduced, resulting in better overall bit error rate performance of the receiver. Therefore, this section will simulate the deep learning-based intelligent noise reduction network and compare it with a single equalizer scheme without a noise reduction network.

[0125] Simulation parameter settings: The channel is the same as in the simulation above, using the communication frame structure designed above. The length of the equalizer feedforward filter is set to 60, and the length of the feedback filter is 40. The number of training iterations for the training data packets is 20. The number of Monte Carlo simulations is 1000. Simulations are performed in a single-branch scenario, and the simulation results are as follows. Figure 10 As shown.

[0126] from Figure 10 As can be seen, the addition of the intelligent noise reduction network significantly improves the overall bit error rate performance of the receiver, and the improvement increases with the increase of the signal-to-noise ratio (SNR). When the SNR is greater than 8 dB, the performance improvement brought by introducing the intelligent noise reduction network can reach more than 2 dB.

[0127] Using the same simulation parameters, simulations were performed with different branch scenarios to obtain receiver bit error rate curves for scenarios with different numbers of branches, as shown below. Figure 11 As shown.

[0128] from Figure 11 As can be seen, the introduction of intelligent noise reduction networks can improve the bit error rate performance of the receiver system under different branch count scenarios, and this improvement increases with the increase of the signal-to-noise ratio. However, when the signal-to-noise ratio is low, the improvement brought by the noise reduction network is not significant.

[0129] To optimize the cost function and improve the network's fitting ability, the denoising network needs to be repeatedly trained on the training samples. Simultaneously, analyzing the optimization curve of the cost function reveals the network's fitting and convergence degree. Therefore, in addition to analyzing the bit error rate performance, simulation experiments are also needed to analyze the network's cost function curve.

[0130] Based on the operating mode, only two data packets per frame are used for training the denoising network. Therefore, the denoising network will be trained twice for each received frame. The simulation parameters are consistent with the experiments described above. The Monte Carlo simulation was run 100 times. The cost function curve of the deep learning-based intelligent denoising network is shown below. Figure 12 As shown.

[0131] pass Figure 12 It can be seen that the noise reduction network can learn the noise in the equalizer output signal very well, and the network's fitting convergence speed is very fast. After the receiver receives about 10 data frames, the network's cost function has already converged to a low value, proving that the noise reduction network can be well applied to real-time signal noise reduction.

[0132] Next, we will conduct simulation experiments on the DL-JAED algorithm mentioned above, which is a joint multi-branch adaptive equalization and noise reduction algorithm. We will investigate whether the introduction of the joint algorithm can improve the overall performance of the receiver. The simulation parameters will remain consistent with the previous experiments, using a single-branch receiver, setting the joint iteration count to 5, and performing 100 Monte Carlo simulations. The bit error rate performance of the DL-JAED algorithm in the single-branch scenario is shown in the attached figure. Figure 13 As shown.

[0133] from Figure 13 As shown in the figure, the DL-JAED algorithm has significant advantages over using equalization algorithms and intelligent noise reduction networks alone. With 5 iterations, when the signal-to-noise ratio is 10... -3 At that time, DL-JAED provides a performance improvement of approximately 4dB. Furthermore, the magnitude of this improvement increases with the increase in signal-to-noise ratio.

[0134] Similarly, simulation experiments need to be conducted in a multi-branch scenario, with the number of branches set to 2, and all other simulation parameters remaining the same as above. The bit error rate performance of the DL-JAED algorithm in the multi-branch scenario is obtained as follows: Figure 14 As shown.

[0135] After demonstrating the superiority of the DL-JAED algorithm, we then conducted simulation experiments on the bit error rate performance of the joint algorithm with different iteration numbers under the same simulation conditions. Assuming the iteration numbers are 2, 5, and 10, the bit error rate performance of the DL-JAED algorithm with different iteration numbers is plotted as follows: Figure 15 The figure shows

[0136] from Figure 15 As can be seen, the performance improvement brought by the DL-JAED algorithm increases with the number of iterations compared to not using the joint algorithm. However, the performance improvement is not limitless. It can be observed that when the signal-to-noise ratio (SNR) is approximately 6dB, the performance of 10 iterations is equal to that of 5 iterations, and better than that of 2 iterations. Only when the SNR is greater than 6dB does the performance of 10 iterations significantly surpass that of 5 iterations. This indicates that the performance improvement gradually diminishes with increasing iteration count, especially under low SNR conditions.

Claims

1. A joint multi-branch adaptive equalization and denoising method based on deep learning, characterized in that, A deep learning-based joint multi-branch adaptive equalization and intelligent noise reduction network, DL-JAED, is constructed. Deep learning is used to learn the noise features in the signal sequence to achieve noise reduction. An iterative loop is established between the equalizer and the noise reduction module, using their outputs as information transmission to fully utilize the iteration gain. The error is calculated from the noise reduction output and used as a feedback signal to update the forward and reverse filters of the equalizer. The specific steps include: Step 1: The multi-branch signal sequences received by the receiving end are as follows: The received signal is processed by a feedforward equalizer and phase compensation, and then combined with multiple branches to obtain the final signal. , (5); Step 2: Subtract the feedback signal to obtain the output of the equalizer; Step 3: Obtain the balanced sequence with a length equal to the data packet length using a shift register. : （15） ， Step 4: Sequence Inputting the noise reduction network yields a noise estimation sequence. , (12), Step 5: Equalized Sequence With estimated noise sequence Subtraction: (13) Step 6: Use the denoised sequence Update the feedforward and feedback filters: （16） ， in, (17); Step 7: Continue the process from Step 1 to Step 6 in a loop until the set number of iterations is reached; The deep learning-based joint multi-branch adaptive equalization and intelligent noise reduction network DL-JAED includes a multi-branch NLMS equalizer and a deep learning noise reduction network model. In the multi-branch NLMS equalizer, the equalizer reception time... From The multiple signals from each hydrophone are denoted as follows: ,in: （3）， in The length of the feedforward filter, after equalization and combining, yields the received signal sequence. The denoised signal sequence obtained after passing through the intelligent noise reduction network is as follows: The tap length of the feedback filter is Corresponding The phase output vector of each phase-locked loop is The feedforward filter tap vectors are respectively , For ease of representation, the vectors are combined and represented as shown in equation (4): （4）， The output after merging multiple branches can be represented as shown in equation (5): （5）， The output of the equalizer is shown in equation (6): （6）， The output of the decision-maker is shown in equation (7): （7）； The deep learning noise reduction network model includes convolutional layers, pooling layers, and upsampling layers, which are used to extract features of the input signal, reduce the size of the feature map, and increase the size of the feature map, respectively.

2. The deep learning-based joint multi-branch adaptive equalization and denoising method according to claim 1, characterized in that... The deep learning-based joint multi-branch adaptive equalization and intelligent noise reduction network DL-JAED requires training before it can be used. During training, based on a semi-steady channel, a communication frame structure containing training sequences is used. This communication frame structure has a total length of 10 data packets and contains two parts: the training sequence and the information sequence. The first three data packets of each frame are the training sequence, and all subsequent packets are the information sequence. Based on this communication frame structure, DL-JAED alternately switches between two modes: training mode and transmission mode. Step A: When the first data packet of the training sequence is received, according to the NLMS algorithm mentioned above, the equalizer will initialize the parameters under the current channel state through the data packet, and achieve equalization of the channel response in a relatively coarse manner. At this time, DL-JAED is working in training mode. Step B: When the second and third data packets of the training sequence are received, the channel changes; based on the coarse synchronization, the equalizer will perform more refined tracking and parameter updates according to the training sequence, enter the convergence state, reach the synchronization state, and use the equalized training sequence as training samples to input into the network for training. At this time, the DL-JAED algorithm is working in training mode. Step C: When the data packet of the information sequence is received, the channel changes. Due to the synchronization of the training sequence, the equalizer can keep track of the channel response well. The equalization is applied to the information sequence, and the resulting equalized sequence is input into the denoising network for denoising. Hard decision is made on the denoised sequence, and the decision result is used to update the tap parameters of the equalizer. It can also be used as a new training sample for the denoising network. At this time, the DL-JAED algorithm is working in transmission mode. Step D: Continue with step C until the end of the information sequence, while the equalizer and noise reduction network are kept updated during transmission; Step E: When the next frame of the training sequence is received, maintain the working mode of steps AD.

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