Underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraint

Abstract

The application relates to the field of underwater acoustic channel response prediction and discloses a method for predicting an underwater acoustic channel response based on complex deep learning and frequency domain structure constraint. In order to solve the problems that the existing method cannot make full use of the real-imaginary coupling relationship in the complex channel and cannot guarantee the consistency of the overall structure of the frequency domain channel only by relying on point value error, the underwater acoustic channel time domain response at continuous sampling time is transformed into complex frequency domain channel responses at each sampling time; each frequency point in the complex frequency domain channel is divided into a frequency point subgroup according to the correlation between the frequency points, the complex frequency domain channel responses in the same frequency point subgroup are arranged in time sequence, and historical time sequence samples of each frequency point subgroup are constructed; the historical time sequence samples of each frequency point subgroup are taken as the input of a complex deep learning prediction model with frequency domain structure constraint, and the complex frequency domain channel responses at future time are predicted under the condition of frequency domain structure constraint; and the prediction results of each frequency point subgroup are spliced in the original frequency point order to obtain complete underwater acoustic frequency domain channel response prediction results.

Description

Technical Field

[0001] This application belongs to the field of underwater acoustic channel response prediction. Background Technology

[0002] Underwater acoustic channel response prediction is a crucial foundation for channel equalization, adaptive modulation, power control, and spectrum resource management in underwater acoustic communication systems. Accurate channel prediction provides real-time channel state information, effectively compensating for signal distortion caused by the underwater acoustic channel and ensuring the reliability of the communication link and the quality of data transmission. However, due to the combined influence of various factors such as sea surface undulations, seabed reflections, ocean current disturbances, platform motion, and multipath propagation, underwater acoustic channels typically exhibit complex characteristics such as strong time-varying properties, long delay spread, and frequency-selective fading. In practical underwater acoustic communication, rapid changes in channel state directly affect the amplitude, phase, and spectral characteristics of the received signal, potentially leading to a significant degrade in communication system performance. Therefore, accurately predicting the underwater acoustic channel response in future moments based on historical channel state information has become one of the key issues for improving the overall performance of underwater acoustic communication systems.

[0003] In recent years, deep learning methods have been widely applied to underwater acoustic channel response prediction tasks due to their powerful nonlinear feature extraction capabilities and data-driven modeling advantages. Long Short-Term Memory (LSTM) networks, with their unique gating mechanism and memory unit structure, can effectively capture the dependencies and temporal evolution patterns in underwater acoustic channel sequences; Convolutional Neural Networks (CNNs) can extract local correlation features of the channel response in the frequency or time domain; and attention mechanisms enhance the utilization of key historical information by dynamically evaluating the importance of different positions in the input sequence. All of these methods have achieved certain performance improvements in underwater acoustic channel response prediction, providing valuable channel state references for subsequent signal processing.

[0004] However, existing deep learning-based underwater acoustic channel response prediction methods still have two key shortcomings in practical applications, which restrict further improvement in prediction accuracy.

[0005] On the one hand, most existing prediction models employ real-valued network structures, which do not fully utilize the complex nature of the underwater acoustic frequency domain channel response itself, making it difficult to accurately model the inherent coupling relationship between the real and imaginary parts of the complex channel. The underwater acoustic frequency domain channel response is essentially a complex signal, and its physical significance lies in the fact that the real and imaginary parts jointly determine the amplitude and phase characteristics of the channel, with phase information having a significant impact on coherent demodulation, channel equalization, and signal recovery. The real and imaginary parts are not independent but tightly coupled through an amplitude-phase relationship; any change in the value of either the real or imaginary part will simultaneously affect both the amplitude and phase responses of the channel. However, existing methods typically employ two strategies when processing complex channel data: one approach treats the real and imaginary parts as two independent real-valued features for prediction. This fragmented approach ignores the inherent numerical coupling and physical correlation between the real and imaginary parts, leading to accumulated prediction biases in phase information. The other approach, while concatenating the real and imaginary parts and inputting them into the network, still uses ordinary real-valued networks. Their internal convolutions or linear transformations follow real-valued operation rules, lacking physical adaptation to complex domain multiplication and addition operations, making it difficult to maintain phase consistency between the real and imaginary parts during feature extraction. The fundamental reason for these approaches is that existing models do not design network structures from the perspective of complex signal processing, nor do they fully consider the signal representation characteristics of underwater acoustic channels in the complex domain, thus limiting the model's ability to characterize phase change patterns and the dynamic features of complex channels.

[0006] On the other hand, existing deep learning prediction models mostly use mean square error (MSE) as the main loss function, focusing on constraining the point-by-point numerical error between the predicted and true values. However, they lack effective constraints on the structural consistency of the predicted channel across the entire frequency band, making it difficult to ensure that the predicted frequency domain channel closely approximates the true channel in its overall form. For underwater acoustic frequency domain channel prediction, the ultimate goal is not only to make the predicted value at each frequency point close to the true value, but more importantly, to ensure that the predicted channel response across the entire frequency domain maintains a high degree of consistency with the true channel in terms of amplitude distribution, frequency fluctuation trends, and energy distribution along the frequency points. This is because subsequent channel equalization and adaptive modulation rely on the comprehensive characteristics of the channel across the entire frequency band. However, as a point-by-point numerical metric, the optimization focus of mean square error is on reducing the numerical deviation at each frequency point, without constraining the prediction results from the perspective of the overall frequency domain structure. In practical applications, the absolute value of the error in the prediction result may be small at each frequency point, but the overall frequency domain response curve may exhibit problems such as overall morphological shift, amplitude distribution distortion, or reversed frequency domain fluctuation trends, resulting in significant differences in the frequency domain structure between the predicted channel and the true channel. The underlying reason for this deviation is that the mean square error is essentially a point-to-point numerical loss. Its gradient information only reflects the degree of deviation of the independent values ​​at each frequency point, and cannot characterize the relative relationship between frequency points, the overall trend of amplitude changes, or the concentration and dispersion characteristics of energy in the frequency domain. Due to the lack of a constraint mechanism on the overall frequency domain structure, the model tends to prioritize reducing the deviation at frequency points where the numerical error is easy to converge during training, while lacking a clear driving force for optimizing the consistency of the overall frequency domain channel shape. Ultimately, this makes it difficult for the prediction result to achieve satisfactory results in both point-by-point accuracy and frequency domain shape consistency.

[0007] In summary, existing underwater acoustic channel response prediction methods still have significant shortcomings in terms of complex information modeling and frequency domain structure constraints. Most methods fail to fully capture the coupling relationship and phase change characteristics of the channel's real and imaginary parts from the perspective of complex signal processing. At the same time, they lack effective constraints on the overall structure of the predicted frequency domain channel, making it difficult to achieve a good balance between pointwise numerical accuracy and frequency domain morphological consistency in the prediction results. Summary of the Invention

[0008] This application aims to address the problems of existing underwater acoustic channel response prediction methods that fail to fully utilize the real-virtual coupling relationship in complex channels and cannot guarantee the overall consistency of the frequency domain channel structure by relying solely on point value errors. It provides an underwater acoustic channel response prediction method that can fully utilize the characteristics of complex channels and frequency domain structure information, and can better adapt to the inherent characteristics of complex underwater acoustic channels such as strong time variation, complex coupling, and frequency selective fading.

[0009] The first aspect of this application provides a method for predicting the response of an underwater acoustic channel, characterized in that it includes:

[0010] The time-domain response of the underwater acoustic channel at consecutive sampling times is transformed into the complex frequency-domain channel response at each sampling time.

[0011] Based on the correlation between frequency points in the complex frequency domain channel, all frequency points are divided into multiple frequency point subgroups. The complex frequency domain channel responses at multiple historical sampling times in the same frequency point subgroup are arranged in time sequence to construct the historical time sequence samples of each frequency point subgroup.

[0012] The historical time series samples of each frequency point subgroup are used as input to the complex deep learning prediction model with frequency domain structure constraints. Under the condition of frequency domain structure constraints, the complex frequency domain channel response of each frequency point subgroup at future time is predicted. The frequency domain structure constraints are used to constrain the error between the prediction result of each frequency point subgroup and the corresponding true value. The error includes point-by-point numerical deviation at each frequency point and structural deviation over the entire frequency band.

[0013] The prediction results of each frequency subgroup are spliced ​​together in the original frequency order to obtain the complete underwater acoustic frequency domain channel response prediction results.

[0014] In one possible design, the frequency domain structural constraints include: basic point value error constraints and structural error constraints;

[0015] The basic point value error constraint is used to constrain the numerical deviation between the prediction results of each frequency subgroup and the corresponding true values ​​at each frequency point in terms of the real and imaginary parts.

[0016] The structural error constraint is used to constrain the structural consistency between the prediction results of each frequency subgroup and the corresponding true values ​​across the entire frequency band.

[0017] In one possible design, the structural error constraints include:

[0018] Frequency domain amplitude constraint is used to ensure consistency between the amplitude variation trend of the predicted amplitude vector and the true amplitude vector at frequency points;

[0019] Frequency domain energy constraints are used to constrain the consistency of the overlap between the predicted energy distribution vector and the true energy distribution vector at each frequency point.

[0020] The frequency domain global offset constraint is used to constrain the overall offset between the predicted result and the true result in the complex plane.

[0021] In one possible design, the frequency domain structure-constrained complex deep learning prediction model includes: an input layer, a temporal soft attention layer, a complex long short-term memory network layer, and an output layer;

[0022] The input layer is used to receive historical time-series samples of each frequency point subgroup;

[0023] The time-based soft attention layer is used to assign different weights to the channel state at different times in the input sample and perform weighted operations to obtain the historical complex frequency domain channel feature sequence.

[0024] The complex long short-term memory network layer is used to extract time-series features from the historical complex frequency domain channel feature sequence and output complex domain channel features that integrate the coupling relationship between the real and imaginary parts.

[0025] The output layer is used to perform a complex linear transformation on the complex domain channel features to obtain a complex frequency domain channel response prediction result.

[0026] In one possible design, the frequency domain structure constraint is introduced into the training process of the complex deep learning prediction model in the form of a loss function, which includes: a basic point value error term and a structure error term;

[0027] The basic point value error term is the mean square error at each frequency point;

[0028] The structural error terms include: frequency domain amplitude correlation structural error, frequency domain energy distribution structural error, and frequency domain mean offset error.

[0029] In one possible design, the loss function is expressed as:

[0030] ,

[0031] in, Represents the loss function. The error term is the base point value. For structural error terms, This refers to the overall weighting coefficient for the structural error term;

[0032] The expression for the structural error term is:

[0033] ,

[0034] in, For frequency domain amplitude-related structural errors, For frequency domain energy distribution structure error, This represents the frequency domain mean shift error. , and Decomposed into , and The coefficient.

[0035] In one possible design, the frequency domain amplitude-related structural error The expression is:

[0036] ,

[0037] in, and The first At the sampling time, the first The first frequency point subgroup The true and predicted values ​​of the channel amplitude at each frequency point and The first At the sampling time, the first The mean of the true amplitude vector and the predicted amplitude vector of each frequency subgroup in the frequency dimension. For the first The number of frequency points in each frequency point subgroup;

[0038] The frequency domain energy distribution structure error The expression is:

[0039] ,

[0040] in, and The first At the sampling time, the first The first frequency point subgroup True frequency domain energy distribution and predicted frequency domain energy distribution at each frequency point;

[0041] The frequency domain mean offset error The expression is:

[0042] ,

[0043] in, and The first At the sampling time, the first The first frequency point subgroup The real and imaginary parts of the actual channel at each frequency point and The first At the sampling time, the first The first frequency point subgroup Predict the real and imaginary parts of the channel at each frequency point.

[0044] The historical time series samples of each frequency point subgroup are constructed using a sliding window method, where the window length is the preset historical observation duration and the prediction step size is a single future sampling moment.

[0045] The beneficial effects of this application are:

[0046] (1) Underwater acoustic channels exhibit strong time-varying characteristics, and the influence of channel states at different historical moments on future channel changes varies significantly. This application employs a time-based soft attention layer, which learns the attention weights of features at each moment in the input sequence and weights the complex frequency domain channel features at each moment during the model's forward computation. This enables the network to dynamically filter out historical information that is more relevant to the prediction target and suppress the influence of redundant or interfering historical moments. This application does not rely on a fixed time window decay assumption but learns the attention distribution through data-driven learning. Therefore, it can adaptively adapt to the channel change rhythm under different underwater acoustic environments, providing a feature-purified input sequence for the subsequent time-series modeling of complex long short-term memory network layers, effectively enhancing the model's ability to capture the time-varying patterns of the channel.

[0047] (2) The frequency domain channel response of underwater acoustic signals is essentially a complex signal, the amplitude and phase of which are determined by the real and imaginary parts. These two parts are physically tightly coupled through Euler's formula, and any change in either the real or imaginary part will simultaneously affect the amplitude and phase response of the channel. When processing complex data, traditional real-valued long short-term memory networks, whether treating the real and imaginary parts as independent features or splicing them together as input, follow the real-valued operation rules for gating and state updates. Essentially, they treat the real and imaginary parts as two unrelated numerical channels, failing to maintain the complex domain coupling relationship between them. This application adopts a complex long short-term memory network layer. Through the complex domain operation mechanism, the network can simultaneously capture the evolution law of the frequency domain channel amplitude and the continuous change trend of the phase when extracting time-series features. This fundamentally avoids the phase information fragmentation problem caused by separate modeling of the real and imaginary parts, making the prediction results more consistent with the real physical channel characteristics in the complex domain.

[0048] (3) As a pointwise numerical loss function, the gradient information of the mean square error only reflects the degree of deviation of the independent values ​​of each frequency point, and cannot characterize the relative relationship between frequency points, the overall trend of amplitude change, and the concentration and dispersion characteristics of energy in the frequency domain. If the mean square error is used as the optimization objective, the model may converge to a local optimum with small pointwise numerical deviations but distorted shape of the entire frequency domain response curve during training. For example, problems such as overall offset, amplitude distribution distortion, or reversed frequency domain fluctuation trend may occur. These problems will cause structural misguidance to subsequent channel equalization and adaptive modulation. This application introduces three structural error constraints on the basis of the mean square error. The four error terms form a comprehensive constraint on the predicted channel from four dimensions: numerical accuracy, shape trend, energy distribution, and overall offset. This makes the model not only pursue pointwise approximation during training, but also pursue the structural consistency of the entire frequency domain channel, thereby ensuring that the prediction results have higher practical value at both the physical and system application levels.

[0049] (4) The three structural error terms in the frequency domain structural constraint loss have significant differences in numerical scale, physical meaning, and gradient propagation characteristics. In the early stage of training, the mean offset error converges slowly due to its relatively gentle gradient, while the energy distribution structural error quickly dominates due to its steep gradient. If fixed weights are used, the direction of model parameter update will be dominated by the error terms with larger gradients, causing other structural constraints to be marginalized during training. This application adopts a gradient-based dynamic weight adjustment method, which calculates the gradient norm of each structural error term relative to the model output layer parameters in each training iteration, and adaptively adjusts the weights of each error term based on the average gradient norm. At the same time, for the mean offset error, this application further introduces the correlation adjustment coefficient and the energy distribution concentration consistency coefficient as weight correction factors. When the correlation between the predicted amplitude and the true amplitude is low or the energy distribution concentration consistency is poor, the weight of the mean offset error is appropriately increased to prevent the negative impact of the overall offset from being amplified. Through the gradient balancing mechanism described above, the three structural error terms maintain a roughly equal optimization pace throughout the training process, avoiding optimization imbalances caused by differences in numerical scales or gradient characteristics. This ensures that each component of the frequency domain structural constraint loss can effectively guide model parameter updates, ultimately improving the convergence stability and prediction generalization performance of the model training.

[0050] In summary, this application achieves dual adaptive modeling of the time-varying characteristics and complex coupling characteristics of underwater acoustic frequency domain channels through the collaborative design of a time-soft attention layer and a complex long short-term memory network layer. Furthermore, through the synergistic optimization of frequency domain structure constraint loss and a gradient-based dynamic weight adjustment method, it jointly ensures both the point-by-point numerical accuracy and frequency domain structure consistency of the predicted channel. These methods work together in a progressive manner, resulting in predictions that not only outperform traditional real-valued models in terms of point-value errors but also exhibit better physical consistency in frequency domain morphology, energy distribution, and overall trend. This provides more accurate channel state prediction results for channel equalization, adaptive modulation, and communication performance optimization in underwater acoustic communication systems, effectively improving the reliability and communication quality of the system in complex underwater acoustic environments. Attached Figure Description

[0051] Figure 1 The flowchart illustrates the underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints, as described in a specific implementation.

[0052] Figure 2 This is a schematic diagram of the FDSC-CDL prediction model structure described in a specific implementation.

[0053] Figure 3 This is a schematic diagram of the structural error term and GDW dynamic weighting method described in the specific implementation method;

[0054] Figure 4The diagram shows a comparison of the cumulative distribution function of the channel relative squared error on the public dataset BCH1 for the methods described in the specific implementation, the real number long short-term memory network prediction method that predicts the real and imaginary parts separately, and the real number long short-term memory network prediction method that predicts the real and imaginary parts together. Detailed Implementation

[0055] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0056] Specific implementation method one: Refer to Figure 1 This embodiment specifically describes the underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints, which includes:

[0057] Step 1: Obtain the time-domain response of the underwater acoustic channel at continuous sampling times, and obtain the corresponding complex frequency-domain channel response through Fourier transform.

[0058] The underwater acoustic channel time-domain response at continuous sampling times is obtained from the Watermark dataset. In this embodiment, the BCH1 channel measured in the port of Brest, France, is selected from the dataset, and the complex frequency domain channel response corresponding to the channel is obtained through Fourier transform.

[0059] The first The complex frequency domain channel response at each sampling time is denoted as:

[0060] .

[0061] No. The sampling time, the first Complex frequency domain channel response at each frequency point Represented as:

[0062] ,

[0063] in, The frequency sampling interval, , This represents the total number of frequency points.

[0064] Step 2: Based on the correlation between frequency points in the BCH1 complex frequency domain channel, Grouping frequency points, adjacent frequency points with strong correlations are assigned to the same frequency subgroup (grouping can be determined based on the correlation coefficient between frequency points or existing frequency domain grouping rules), resulting in... A frequency point subgroup. Among them, the first... The frequency subgroup at the first The complex frequency domain channel response at each sampling time is expressed as:

[0065] ,

[0066] in, , For the first The number of frequency points in a frequency point subgroup, and satisfying: .

[0067] Using a sliding window technique, time-series prediction samples are constructed based on the historical complex frequency domain responses of each subgroup, with the historical observation window length set as... If the prediction step size is 1, then the th The historical complex frequency domain channel input sequence corresponding to each frequency point subgroup is represented as follows:

[0068] .

[0069] The prediction target is expressed as:

[0070] .

[0071] The input sequence and the prediction target are matched one-to-one as sample pairs, and divided into training set, validation set and test set according to a preset ratio to provide standard data input for subsequent model training.

[0072] Step 3: Establish frequency-domain structure-constrained complex deep learning (FDSC-CDL) prediction models for each frequency subgroup, such as... Figure 2 As shown, the model includes an input layer, a temporal soft attention layer, a complex long short-term memory network layer, and an output layer.

[0073] 1. The input layer is used to receive historical complex frequency domain channel input sequences. Then the input is passed to the next layer of temporal soft attention.

[0074] 2. The temporal soft attention layer is used to assign different weights to the channel states at different times in the historical input sequence, so as to highlight the historical channel states that contribute more to the channel prediction at the next sampling time.

[0075] Input sequence After processing by the time-based soft attention layer, the weighted historical complex frequency domain channel feature sequence is represented as follows:

[0076] ,

[0077] in, This is a time-based soft attention mapping.

[0078] 3. The complex long short-term memory network layer is used to extract time-series features from the weighted historical complex frequency domain channel feature sequence and learn the coupling relationship between the real and imaginary parts of the complex frequency domain channel.

[0079] Let the real and imaginary parts of the weighted input sequence be respectively and The real part of the output features of complex long short-term memory network layers and the virtual part They are represented as follows:

[0080] ,

[0081] ,

[0082] in, and These represent the real and imaginary part mappings in complex long short-term memory network layers, respectively.

[0083] 4. The output layer is a complex linear mapping layer, used to perform a complex linear transformation on the output of the complex long short-term memory network layer, obtaining the real and imaginary parts of the predicted channel, which are represented as follows:

[0084] ,

[0085] ,

[0086] in, and These are the real and imaginary parts of the weights of the complex linear mapping layer, respectively. and These are the real and imaginary parts of the bias term in the complex linear mapping layer, respectively.

[0087] Combining the prediction results of the real and imaginary parts, we obtain the first... The complex frequency domain channel prediction results for each frequency point subgroup are expressed as follows:

[0088] .

[0089] Step 4: Train the FDSC-CDL prediction model corresponding to each frequency subgroup using the constructed training set, and introduce frequency domain structure constraint loss during the model training process. Furthermore, a gradient-based dynamic weight adjustment method (GDW) is employed to jointly constrain the mean square error, amplitude correlation, energy distribution, and overall offset between the predicted and actual channels, such as... Figure 3As shown. Finally, the optimal prediction model is found using the validation set. The details are as follows:

[0090] 1. Frequency domain structural constraint loss It consists of a fundamental point error term and a structural error term. The fundamental point error term is the mean square error at each frequency point. The structural error term includes frequency domain amplitude-dependent structural errors. Frequency domain energy distribution structure error and frequency domain mean offset error Frequency domain structural constraint loss The specific calculation methods for each error term are as follows:

[0091] (1) Calculate the mean square error between the predicted channel and the actual channel based on the prediction results. The mean square error is used to constrain the numerical prediction difference between the real and imaginary parts at each frequency point. Represented as:

[0092] ,

[0093] in, and The first At the sampling time, the first The first frequency point subgroup The real and imaginary parts of the actual channel at each frequency point and The first At the sampling time, the first The first frequency point subgroup Predict the real and imaginary parts of the channel at each frequency point.

[0094] (2) Based on the real complex frequency domain channel and predicting complex frequency domain channels Calculate the true magnitude vector respectively and predicted magnitude vector :

[0095] ,

[0096] ,

[0097] in, and These are the actual and predicted values ​​of the channel amplitude at the first frequency point, and so on.

[0098] Calculating frequency domain amplitude correlation structure error using amplitude vectors This is used to constrain the consistency of the amplitude variation trend between the predicted channel and the real channel in the frequency dimension, and is a frequency domain amplitude correlation structure error. Represented as:

[0099] ,

[0100] Among them, intermediate variables ,

[0101] and The first The mean of the true amplitude vector and the predicted amplitude vector of each frequency point subgroup in the frequency dimension.

[0102] (3) The squares of the true amplitude and the predicted amplitude are normalized exponentially to obtain the true frequency domain energy distribution. and predict frequency domain energy distribution :

[0103] ,

[0104] ,

[0105] The frequency domain energy distribution structure error was calculated using the Bhattacharyya coefficients. This is used to constrain the degree of overlap between the energy distribution of the predicted channel and the real channel at different frequency points, and to measure the frequency domain energy distribution structure error. Represented as:

[0106] .

[0107] (4) Calculate the frequency domain mean offset error by the mean offset between the real channel and the predicted channel in the real and imaginary parts. Used to constrain the overall offset between the predicted channel and the true channel in the real and imaginary parts, frequency domain mean offset error. Represented as:

[0108] .

[0109] GDW is used to dynamically weight the individual errors in the structural error term, but not the basic point value error term. Because... , and The numerical scales of error terms and their gradient influence on model parameter updates differ. If fixed weights are used, one error term may dominate during training, while the role of other error terms is weakened. Therefore, a gradient-based dynamic weight adjustment method is adopted, which adaptively adjusts the weights of each error term according to the gradient norm of each error term relative to the model output layer parameters, so that multiple structural error terms maintain a relatively balanced optimization contribution during training.

[0110] GDW dynamically weights the various errors in the structural error term as follows:

[0111] Let the three structural error terms be:

[0112] , , .

[0113] Let the output layer parameters of the model be In the During the training iteration, the first... The gradient norm corresponding to each structural error term is:

[0114] , .

[0115] The average gradient norm of the three structural error terms is:

[0116] .

[0117] Based on the true amplitude vector and predicted magnitude vector Calculate the relevant adjustment coefficient :

[0118]

[0119] in, and These are the standard deviations of the true magnitude vector and the predicted magnitude vector, respectively.

[0120] Based on the true frequency domain energy distribution vector and predicted frequency domain energy distribution vector Calculate the uniformity coefficient of energy distribution concentration :

[0121] ,

[0122] in, and These are the standard deviations of the true frequency domain energy distribution vector and the predicted frequency domain energy distribution vector, respectively.

[0123] The dynamic weights of frequency domain amplitude-dependent structure error and frequency domain energy distribution structure error are obtained based on the gradient norm and the average gradient norm:

[0124] ,

[0125] ,

[0126] For the frequency domain mean offset error, its dynamic weight further incorporates a relevant adjustment coefficient and an energy distribution concentration consistency coefficient, expressed as:

[0127] .

[0128] Frequency domain structure error term Represented as:

[0129] ,

[0130] The frequency domain structure constraint loss can be expressed as:

[0131] ,

[0132] in, This represents the overall weighting coefficient for the structural error term.

[0133] The optimal prediction model is found using a validation set. In each training round, the validation set is input into the model, and the MSE loss is calculated on the predicted output of the validation set. The model with the minimum MSE loss across all training rounds is the optimal prediction model.

[0134] Step 5: Input the test set data of each frequency subgroup into the corresponding trained FDSC-CDL prediction model to obtain the complex frequency domain channel prediction results for each frequency subgroup. Since the complete frequency domain channel was divided into multiple frequency subgroups in Step 2, after each frequency subgroup obtains its corresponding prediction results, it needs to be restored and stitched together according to the original frequency point arrangement order in the complete frequency domain channel before the frequency point grouping. Through the above stitching process, the complete underwater acoustic frequency domain channel prediction results covering all frequency points are obtained.

[0135] The prediction errors of the FDSC-CDL prediction method proposed in this embodiment are compared with those of the real-number long short-term memory network prediction method (Sep-LSTM) which predicts the real and imaginary parts separately, and the real-number long short-term memory network prediction method (Cat-LSTM) which predicts the real and imaginary parts together. The mean squared errors of the three methods are calculated, as shown in the table below. The calculation shows that the method proposed in this embodiment has a lower prediction error.

[0136]

[0137] To characterize the error distribution of different methods across the entire test set, the relative squared error for each test sample is calculated, expressed as:

[0138] ,

[0139] in, This is real channel data. For predicting channel data.

[0140] Obtain the calculation results and convert them to dB form, then plot their cumulative distribution function (CDF) curve, as follows. Figure 4 As shown, the CDF curve of FDSC-CDL is generally located to the left of the curves of Sep-LSTM, Cat-LSTM, and the outdated channel, indicating that under the same cumulative probability, the proposed model has a smaller relative squared error, meaning it has a lower prediction error on most test samples. Compared with the ordinary LSTM method, the error distribution of FDSC-CDL is more concentrated in the low-error region, indicating that complex-valued structure modeling and frequency domain structure constraints can improve the overall stability of underwater acoustic frequency domain channel prediction.

[0141] Specific Implementation Method Two: An underwater acoustic channel response prediction device based on complex deep learning and frequency domain structure constraints, comprising:

[0142] Sampling unit: used to transform the frequency domain response of the underwater acoustic channel at consecutive sampling times into the complex frequency domain channel response at each sampling time;

[0143] Sample construction unit: Based on the correlation between each frequency point in the complex frequency domain channel, it divides all frequency points into multiple frequency point subgroups, arranges the complex frequency domain channel responses of multiple historical sampling times in the same frequency point subgroup in time sequence, and constructs the historical time sequence samples of each frequency point subgroup;

[0144] Prediction Unit: Used to take the historical time series samples of each frequency point subgroup as input to the complex deep learning prediction model with frequency domain structure constraints, and predict the complex frequency domain channel response of each frequency point subgroup at future time under the condition of frequency domain structure constraints. The frequency domain structure constraints are used to constrain the error between the prediction result of each frequency point subgroup and the corresponding true value. The error includes point-by-point numerical deviation at each frequency point and structural deviation over the entire frequency band.

[0145] The splicing unit is used to splice the prediction results of each frequency point subgroup according to the original frequency point order to obtain the complete underwater acoustic frequency domain channel response prediction results.

[0146] Specific Implementation Method 3: The underwater acoustic channel response prediction device based on complex deep learning and frequency domain structure constraints described in this implementation method includes a processor and a memory. The memory stores at least one instruction, which is loaded and executed by the processor to implement the underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints as described in Specific Implementation Method 1.

[0147] Specific Implementation Method Four: A computer storage medium as described in this implementation method stores at least one instruction, which is loaded and executed by a processor to implement the underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints as described in Specific Implementation Method One.

[0148] While specific embodiments of this application have been described herein with reference to them, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for predicting the underwater acoustic channel response based on complex deep learning and frequency domain structure constraints, characterized in that, include: The time-domain response of the underwater acoustic channel at consecutive sampling times is transformed into the complex frequency-domain channel response at each sampling time. Based on the correlation between frequency points in the complex frequency domain channel, all frequency points are divided into multiple frequency point subgroups. The complex frequency domain channel responses at multiple historical sampling times in the same frequency point subgroup are arranged in time sequence to construct the historical time sequence samples of each frequency point subgroup. The historical time series samples of each frequency point subgroup are used as input to the complex deep learning prediction model with frequency domain structure constraints. Under the condition of frequency domain structure constraints, the complex frequency domain channel response of each frequency point subgroup at future time is predicted. The frequency domain structure constraints are used to constrain the error between the prediction result of each frequency point subgroup and the corresponding true value. The error includes point-by-point numerical deviation at each frequency point and structural deviation over the entire frequency band. The prediction results of each frequency subgroup are spliced ​​together in the original frequency order to obtain the complete underwater acoustic frequency domain channel response prediction results.

2. The underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints according to claim 1, characterized in that, The frequency domain structural constraints include: basic point value error constraints and structural error constraints; The basic point value error constraint is used to constrain the numerical deviation between the prediction results of each frequency subgroup and the corresponding true values ​​at each frequency point in terms of the real and imaginary parts. The structural error constraint is used to constrain the structural consistency between the prediction results of each frequency subgroup and the corresponding true values ​​across the entire frequency band.

3. The underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints according to claim 2, characterized in that, The structural error constraints include: Frequency domain amplitude constraint is used to ensure consistency between the amplitude variation trend of the predicted amplitude vector and the true amplitude vector at frequency points; Frequency domain energy constraints are used to constrain the consistency of the overlap between the predicted energy distribution vector and the true energy distribution vector at each frequency point. The frequency domain global offset constraint is used to constrain the overall offset between the predicted result and the true result in the complex plane.

4. The underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints according to claim 1, characterized in that, The frequency domain structure-constrained complex deep learning prediction model includes: an input layer, a temporal soft attention layer, a complex long short-term memory network layer, and an output layer; The input layer is used to receive historical time-series samples of each frequency point subgroup; The time-based soft attention layer is used to assign different weights to the channel state at different times in the input sample and perform weighted operations to obtain the historical complex frequency domain channel feature sequence. The complex long short-term memory network layer is used to extract time-series features from the historical complex frequency domain channel feature sequence and output complex domain channel features that integrate the coupling relationship between the real and imaginary parts. The output layer is used to perform a complex linear transformation on the complex domain channel features to obtain a complex frequency domain channel response prediction result.

5. The underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints according to claim 4, characterized in that, The frequency domain structure constraint is introduced into the training process of the complex deep learning prediction model in the form of a loss function, which includes: a basic point value error term and a structure error term; The basic point value error term is the mean square error at each frequency point; The structural error terms include: frequency domain amplitude correlation structural error, frequency domain energy distribution structural error, and frequency domain mean offset error.

6. The underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints according to claim 5, characterized in that, The loss function expression is as follows: ， in, Represents the loss function. The error term is the base point value. For structural error terms, This refers to the overall weighting coefficient for the structural error term; The expression for the structural error term is: ， in, For frequency domain amplitude-related structural errors, For frequency domain energy distribution structure error, This represents the frequency domain mean shift error. , and Decomposed into , and The coefficient.

7. The underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints according to claim 6, characterized in that, The frequency domain amplitude-related structural error The expression is: ， in, and The first At the sampling time, the first The first frequency point subgroup The true and predicted values ​​of the channel amplitude at each frequency point and The first At the sampling time, the first The mean of the true amplitude vector and the predicted amplitude vector of each frequency subgroup in the frequency dimension. For the first The number of frequency points in a frequency point subgroup.

8. The underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints according to claim 6, characterized in that, The frequency domain energy distribution structure error The expression is: ， in, For the first Number of frequency points in a frequency point subgroup and The first At the sampling time, the first The first frequency point subgroup The actual frequency domain energy distribution and the predicted frequency domain energy distribution at each frequency point.

9. The underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints according to claim 6, characterized in that, The frequency domain mean offset error The expression is: ， in, For the first Number of frequency points in a frequency point subgroup and The first At the sampling time, the first The first frequency point subgroup The real and imaginary parts of the actual channel at each frequency point and The first At the sampling time, the first The first frequency point subgroup Predict the real and imaginary parts of the channel at each frequency point.

10. The underwater acoustic channel response prediction method based on complex deep learning and frequency domain structure constraints according to claim 1, characterized in that, The historical time series samples of each frequency point subgroup are constructed using a sliding window method, where the window length is the preset historical observation duration and the prediction step size is a single future sampling moment.

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