Adaptive frequency domain equalization method for underwater acoustic OFDM communication using transformer

Abstract

The application discloses a kind of underwater acoustic OFDM communication adaptive frequency domain equalization methods using Transform, it is related to underwater acoustic communication technical field, to solve the problems that existing underwater acoustic OFDM equalization method relies on cyclic prefix, is not sensitive to channel dynamic change, hard decision is prone to error propagation, the Transform framework containing only encoder is used in the present application, the soft decision of received symbol is completed by multi-head self-attention mechanism, and adaptive filtering is realized in combination with feedforward network;In the training phase, the loss function is calculated based on the network output and the true value, and the network parameters and the feedforward equalization filter coefficients are updated synchronously;In the inference phase, the network output is fed back to update the filter coefficients, and the real-time changes of the channel are adapted;The present application significantly reduces the probability of error propagation, and improves the communication reliability under complex underwater acoustic channel.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic communication technology, specifically an adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer. Background Technology

[0002] Underwater acoustic communication is a core technology for underwater information transmission, widely used in marine resource exploration, environmental monitoring, collaborative operations of underwater vehicles, and national defense. However, marine acoustic channels inherently possess characteristics such as narrow bandwidth, significant multipath effects, and strong environmental noise, easily leading to severe inter-symbol interference and frequency-selective fading. OFDM technology, due to its high spectral efficiency and multipath resistance, is widely used in underwater acoustic communication. Traditional OFDM-based frequency domain equalization algorithms include zero-forcing equalization and decision feedback equalization. These algorithms suffer from high bit error rates in complex underwater acoustic channels and cannot obtain accurate and complete information. Zero-forcing equalization is insensitive to channel changes, amplifies additive noise, relies on cyclic prefixes, and its effectiveness is greatly reduced in complex multipath channels with high scattering attenuation. Decision feedback equalization algorithms have high computational complexity, poor real-time performance, and employ a hard decision mechanism, causing errors to amplify step by step during the iteration process, resulting in severe bit error rates in complex channels.

[0003] Therefore, to improve the problems of sluggish response to channel changes and high hard-decision error propagation rate in cyclic prefix-dependent communication, an adaptive equalization method for underwater acoustic OFDM communication using Transformer is proposed. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides an adaptive equalization method for underwater acoustic OFDM communication using Transformer, which can effectively enhance the adaptability to complex underwater acoustic channel changes and reduce the probability of error propagation.

[0005] To address the problems of existing underwater acoustic OFDM equalization methods, such as reliance on cyclic prefixes, insensitivity to dynamic channel changes, and the susceptibility of hard decision-making to error propagation, this invention proposes an adaptive equalization method for underwater acoustic OFDM communication based on Transformer.

[0006] The method includes the following steps: The transmitting end generates an original bit stream and encodes and modulates it to generate a complex symbol sequence; then, it performs an inverse Fast Fourier Transform (IFFT) to obtain time-domain OFDM symbols; a cyclic prefix is ​​added before transmission to the underwater acoustic channel; the receiving end receives the signal transmitted through the underwater acoustic channel, removes the cyclic prefix, and performs an IFFT to obtain OFDM frequency-domain symbols. The method further includes the following steps: S1: Perform data preprocessing on the OFDM frequency domain symbols to construct a dataset for the input of the Transformer neural network; S2: Input the dataset into the trained Transformer neural network. The Transformer neural network adopts an architecture containing only encoders. It performs contextual feature weighted fusion on the input frequency domain symbol sequence through a multi-head self-attention mechanism to complete the soft decision of the received symbols. Then, it performs nonlinear transformation and adaptive filtering on the features output by the soft decision through a feedforward network to output the equalized OFDM frequency domain symbols. S3: During the training phase, the loss function is calculated based on the output value of the Transformer neural network and the true frequency domain symbol value. The network parameters of the Transformer neural network are updated through error backpropagation, and the frequency domain coefficients of the feedforward equalization filter are updated based on the network output. S4: In the inference phase, the equalized OFDM frequency domain symbol output by the Transformer neural network is used as the final recovered frequency domain symbol for subsequent demodulation. At the same time, the output value is fed back to the feedforward equalization filter to update the filter coefficients in real time to adapt to changes in the underwater acoustic channel.

[0007] Preferably, the encoder unit of the Transformer neural network includes a multi-head self-attention layer, a feedforward network, a residual connection module, and a layer normalization module; the residual connection module is used to perform a skip-addition of the input and output of the encoder unit, preserving the original input features while learning the incremental mapping.

[0008] Preferably, the underwater acoustic channel is a shallow water acoustic channel, and the channel model expression is: ; In the formula, Let P be the amplitude of the transmission path. Let L be the time delay function of the Pth transmission path, and L be the total number of underwater acoustic channel paths; the mth OFDM frequency domain symbol expression obtained by the receiver through Fast Fourier Transform is: ; In the formula, T is the OFDM symbol period, and T′m is the time offset of the m-th OFDM symbol.

[0009] Preferably, the length of the cyclic prefix added to the time-domain OFDM symbol is Δ; in the total number of paths L of the underwater acoustic channel, The number of paths satisfying τp≤Δ is Q1, and the number of paths satisfying τp>Δ is L−Q1; the complete expression for the m-th OFDM frequency domain symbol is: ; In the formula, Xm(k) is the frequency domain value of the kth subcarrier of the m-th OFDM symbol at the transmitter, and Sa(⋅) is the sampling function.

[0010] Preferably, the data preprocessing in step S1 specifically includes: S11: Input the OFDM frequency domain symbols into the feedforward equalizer to obtain a row vector of dimension 1×m. , where m is the total number of subcarriers in the OFDM system, and i is the symbol number; S12: For row vectors The complex value corresponding to each subcarrier is decomposed into real and imaginary parts in subcarrier order to obtain an extended output vector with dimension 1×2m. ; S13: Expand the output vector Combined with the expanded output vectors of the preceding o historical symbols, we obtain the original input matrix with dimension o×2m. , where o is the buffer order of the feedforward equalizer; S14: Convert the original input matrix Dimensions expanded to o× Then, positional encoding is added to obtain the final input sequence. All input sequences constitute the input dataset.

[0011] Preferably, the loss function used in the training phase is the mean squared error function, expressed as: ; In the formula, n is the number of frequency domain symbols in the current batch. The true frequency domain symbol value, The current frequency domain symbol value is recovered for the Transformer; the network parameters of the Transformer neural network are updated using the Adam optimizer, with the learning rate update strategy as follows: ; In the formula, steps is the number of training iterations, and warmup_steps is the number of warmup steps for the learning rate.

[0012] Preferably, in one embodiment, in order to update the error OFDM frequency domain symbol values ​​output by the transformer neural network The frequency domain values ​​should be maintained as the true frequency domain values ​​of the known training sequence during the retraining phase, and as the frequency domain values ​​corresponding to the i-th symbol recovered by the Transformer-encoder during the inference phase. The frequency domain coefficients of the feedforward filter... The update must follow the minimum mean square error (MMSE) criterion and adopt the minimum mean square (LMS) algorithm, whose iterative update formula is as follows: ; In the formula, Let $\frac{i}{i}$ be the frequency domain coefficients of the filter corresponding to the $i$-th symbol, $j = 0, 1, ..., (o-1)$, and $o$ be the order of the filter buffer. The iteration step size is also updated using the minimum mean square error (MMSE). For error signals, The frequency domain sign value of the Transformer neural network output. This is the preprocessed frequency domain symbol vector. is the conjugate value of the ij-th frequency domain symbol.

[0013] Preferably, the update formula for the iteration step size μi is: ; In the formula, α is the step size adjustment coefficient. The frequency domain coefficients are derivatives with respect to the step size, and their update formula is: .

[0014] Compared with existing technologies, this invention provides an adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer, which has the following advantages: This invention provides an adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer. Compared with the prior art, the adaptive frequency domain equalization method for underwater acoustic OFDM communication based on Transformer proposed in this invention has significant technical advantages.

[0015] This invention combines OFDM modulation technology with traditional frequency domain equalization, utilizing the global feature modeling capabilities of Transformer neural networks. Through a soft information processing mechanism, it transforms the traditional "interference elimination" equalization approach into a "reasoning recovery" method based on historical symbol information, thereby achieving more efficient symbol reconstruction. This method significantly reduces the error propagation risk caused by symbol-by-symbol hard decision-making, enhances the system's adaptability to complex time-varying underwater acoustic channels, and exhibits stronger robustness when channel estimation is imperfect or nonlinear distortion exists. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating an adaptive frequency domain equalization method for underwater acoustic OFDM communication based on Transformer, as shown in the embodiment. Figure 2This is a schematic diagram of frequency domain symbol data processing; Figure 3 This diagram illustrates the comparison of bit error rates for different frequency domain equalization algorithms. Detailed Implementation

[0017] The present invention will now be described with reference to embodiments. It should be understood that the embodiments described herein are for the purpose of more clearly illustrating the invention, and not for limiting the scope of the invention.

[0018] The endpoints and any values ​​of the ranges disclosed herein are not limited to the precise ranges or values, and these ranges or values ​​should be understood to include values ​​close to these ranges or values. For numerical ranges, the endpoint values ​​of the various ranges, the endpoint values ​​of the various ranges and individual point values, and individual point values ​​can be combined with each other to obtain one or more new numerical ranges, which should be considered as specifically disclosed herein.

[0019] The basic principle of the Transformer-based adaptive frequency domain equalization algorithm for underwater acoustic OFDM communication is as follows: The signal, after processing by a feedforward filter and data preprocessing, is input into a Transformer neural network. The self-attention mechanism calculates the correlation strength between each token in the current symbol and its neighboring tokens, and weights and fuses this correlation to generate a new context vector representation. This process does not directly decide on the current symbol, but rather performs soft decision-making based on contextual information, thus more accurately characterizing the dependencies between symbols. Subsequently, a feedforward neural network (FFN) is used to upscale the features processed by the self-attention module, extracting higher-dimensional enhanced features, and adaptive filtering of contextual information is achieved through nonlinear mapping and dimensionality reduction operations. Then, during the training phase, the neural network output is used to construct the loss function and calculate error backpropagation, thereby simultaneously updating the Transformer network parameters and the feedforward filter to achieve closed-loop optimization. Finally, the frequency domain symbols to be equalized are input into the Transformer equalization system constructed based on the method of this invention to obtain the equalized output symbols.

[0020] Reference Figure 1-3 This invention provides an adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer. This method utilizes a Transformer neural network consisting of a multi-head self-attention layer, a feedforward network, residual connections, and a layer normalization structure. Through the Transformer's self-attention mechanism, it performs feature mapping and weighted calculation of the input signal (Query, Key, and Value) to achieve soft decision-making on the received symbols. The feedforward neural network employs multi-layer linear transformations and nonlinear activations to achieve nonlinear modeling and feature extraction of the feedback filter. Furthermore, by combining residual connections and the layer normalization structure, it performs skip-addition of input and output within the network, preserving original features and learning incremental mappings, thereby effectively mitigating the gradient vanishing and performance degradation problems of deep models. The specific implementation steps of this method are as follows: The transmitter first generates a raw random signal bit stream based on a random bit stream generator and encodes it. The encoded bit stream is then modulated to generate a complex symbol sequence. Finally, the inverse fast Fourier transform (IFFT) is used to obtain time-domain OFDM symbols.

[0021] Then, a cyclic prefix is ​​added to the corresponding time-domain OFDM symbol to generate the final transmitter output signal.

[0022] The output signal from the transmitter is input into the underwater acoustic channel. Since this invention focuses on communication in shallow water environments and the communication problems of low-speed cruising underwater robots, the extremely low relative motion speed allows for the approximate neglect of the Doppler effect. Therefore, the underwater acoustic channel model can be described as follows: .

[0023] in Let be the amplitude on the Pth path, and be the time delay function of the Pth path. At the receiving end, the OFDM time-domain symbol of the Mth symbol after transmission through the shallow sea acoustic channel can be obtained.

[0024] Right now: ; Next, the cyclic prefix is ​​removed, and then a Fast Fourier Transform (FFT) is performed to transform it from the time domain to the frequency domain, yielding the Mth OFDM frequency domain symbol affected by the shallow sea acoustic channel. That is: .

[0025] Next, this OFDM frequency domain symbol is processed into a dataset. Using this dataset as input, a Transformer neural network based on the adaptive equalization algorithm for underwater acoustic OFDM communication is trained to obtain the trained Transformer neural network. Then, the OFDM frequency domain symbol data to be tested is input into the trained Transformer neural network, and the output is the OFDM frequency domain symbol after frequency domain equalization.

[0026] As a further preferred embodiment of the present invention: to enable the trained transformer neural network to account for insufficient cyclic prefix length, the time-domain OFDM symbols in the dataset should have a cyclic prefix length of [length missing]. Furthermore, the total underwater acoustic path L must consist of two types of paths.

[0027] Right now: satisfy The number of paths ≤Δ satisfy The number of paths >Δ. Therefore, the Mth frequency domain OFDM symbol can be written as: ; Therefore, any frequency domain symbol will be subject to subcarrier interference, inter-symbol interference, and frequency-selective fading.

[0028] As a further preferred embodiment of the present invention: the specific operation of processing OFDM frequency domain symbols into a dataset includes: input frequency domain symbols The input is fed into a feedforward equalizer, whose frequency domain coefficients are derived from the sequence. definition.

[0029] The parameter 'o' represents the buffer order and also the number of past symbols utilized. This is achieved through the feedforward filter. It is a row vector with a dimension of 1×m, where m corresponds to the total number of subcarriers in the OFDM system.

[0030] Because frequency domain data consists of complex numbers, the complex values ​​corresponding to each subcarrier need to be decomposed into real and imaginary parts.

[0031] That is, the real part of each subcarrier is arranged in subcarrier order. With the imaginary part This yields the extended output vector. The dimensions are 1×2m. Then... Combined with past symbols The total length of its symbol sequence is 0, and its dimension is expanded to 0×2m. Then, to enhance the model's expressive power and nonlinear fitting ability, the input matrix... Extended to Dimensions are added, and positional encoding is used to provide sequence order information, resulting in the final input sequence. Construct a set from all the input sequences to form the final input dataset.

[0032] As a further preferred embodiment of the present invention: considering that the standard Transformer model adopts an encoder-decoder architecture, the length ratio of its input sequence to its output sequence is not constant, while the ratio of the received signal to the corresponding transmitted signal in underwater OFDM is often fixed. Therefore, the Transformer neural network based on the adaptive equalization algorithm for underwater acoustic OFDM communication adopts an encoder architecture as the decision maker and feedback filter part in the frequency domain equalization. Finally, a feedforward neural network (FFN) is added for information aggregation, and finally the symbol of this decision is output. .

[0033] Furthermore, to ensure stable training and system convergence, this output value... The specific meaning varies depending on the operational stage. During the algorithm training phase, the decision maker output... Corresponding to the true frequency domain value of the known training sequence, while when the input... When the symbol is a valid information symbol, it represents the frequency domain value corresponding to the i-th symbol recovered by the Transformer-encoder. Afterwards, this value... It will also be used to update the error signal. This updates the feedforward filter, thus establishing a closed loop. The transformer-encoder update uses Adam as the parameter optimizer, and the learning rate update strategy is as follows: .

[0034] The loss function used during training is the mean squared error (MSE), expressed as: ; Where n represents the number of frequency domain symbols that need to be checked in the current batch. and These represent the actual frequency domain data and the current frequency domain data recovered by the Transformer-encoder, respectively.

[0035] As a specific embodiment of the present invention: like Figure 1 As shown in the embodiment, the process of the Transformer-based adaptive frequency domain equalization method for underwater acoustic OFDM communication of the present invention includes: 1. Generate the corresponding dataset by preprocessing the OFDM frequency domain symbols received by the receiver through the underwater acoustic channel.

[0036] 2. Add position vectors to the dataset and then input it into the model.

[0037] 3. The transformer neural network receives a dataset consisting of actual OFDM frequency domain symbols, and the generator finally generates the estimated OFDM current frequency domain symbol values ​​after the decision.

[0038] 4. The loss function is used to estimate the difference between the actual OFDM frequency domain symbol value and the estimated OFDM frequency domain symbol value. This difference is then used to update the weight matrix of each layer of the transformer neural network.

[0039] 5. The OFDM frequency domain symbols estimated by the transformer neural network are used to update the current error function. Subsequently, the error function Used to update the frequency domain coefficients of the feedforward filter.

[0040] The underwater acoustic channel model involved in this embodiment is shown in Table 1-2 below: Table 1 parameter value water depth 15m underwater speed of sound 1400m / s Transmission distance 2km transmitter height 7.5m Receiver height 7.5m Number of paths 5 Transmission factors 1.5 Table 2 parameter AC·1 AC·2 AC·3 AC·4 AC·5 Relative delay (seconds) 0 1.0 1.0 2.8 3.3 normalization degree 1 -0.75 -0.75 0.1 -0.05 The research scenario is primarily limited to a shallow water underwater communication environment, focusing on the communication problems of low-speed cruising underwater robots in this environment. Due to the low operating speed of the underwater robot, the Doppler frequency shift and Doppler spread effects caused by relative motion are weak and can be approximately ignored in this embodiment. To highlight the main transmission characteristics of the shallow water acoustic channel, the channel modeling and algorithm analysis mainly consider the multipath propagation effect and the influence of underwater environmental noise. Therefore, the underwater acoustic channel model can be described as: .in Let P be the magnitude on the path P. It is the time delay function of the P-th path. Furthermore, to ensure the trained transformer neural network considers the case of insufficient cyclic prefix length, the cyclic prefix length added to the time-domain OFDM symbols in the dataset should be [length missing]. Furthermore, the total underwater acoustic path L must consist of two types of underwater acoustic paths. That is: satisfy The number of underwater paths, satisfy Number of underwater paths.

[0041] This embodiment provides a specific implementation of a frequency domain equalization algorithm based on a transformer neural network. The data preprocessing method includes passing the current OFDM frequency domain symbol value through a feedforward filter, the frequency domain coefficients of which are... The real part of each complex value of the OFDM frequency domain symbol passed through the feedforward filter is arranged in subcarrier order. virtual part Decomposition, such as Figure 2 As shown. Then, it is combined with previous symbols to form a matrix. Finally Expanding dimensions to .

[0042] In one embodiment, the loss function is the mean squared error (MSE), and its expression is: .

[0043] The transformer neural network uses only the encoder architecture as the decision maker and feedback filter in the frequency domain equalization, and then adds a feedforward neural network (FFN) layer for information aggregation. The weight matrices of each layer are updated using Adam as the parameter optimizer, and the learning rate update strategy is as follows: .

[0044] In another embodiment, in order to update the error OFDM frequency domain symbol values ​​output by the transformer neural network During the retraining phase, the frequency domain value should be maintained as the true frequency domain value of the known training sequence, and during the inference phase, it should be maintained as the frequency domain value corresponding to the i-th symbol recovered by the Transformer-encoder.

[0045] The frequency domain coefficients of the feedforward filter The update must follow the minimum mean square error (MMSE) criterion and adopt the minimum mean square (LMS) algorithm, whose iterative update formula is as follows: .

[0046] in Its step length It is also updated via minimum mean square error (MMSE). The formula is: .

[0047] in addition, At step size The derivative is given below, therefore, its update formula is: .

[0048] like Figure 3 As shown, the bit error rate curves under different signal-to-noise ratio conditions indicate that the DFE frequency domain equalization algorithm and the traditional frequency domain equalization algorithm have limited effect on suppressing bit errors and are difficult to meet the requirements of reliable communication. The frequency domain equalization algorithm based on Transformer has significantly improved the system bit error performance due to its ability to model the long-term dependence of historical symbols. In particular, it can stably maintain a low bit error rate in high signal-to-noise ratio environments, effectively ensuring communication reliability.

[0049] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. An adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer, comprising the following steps: The transmitting end generates a raw bit stream and encodes and modulates it to generate a complex symbol sequence. This sequence is then subjected to an inverse Fast Fourier Transform (IFFT) to obtain time-domain OFDM symbols. A cyclic prefix is ​​added before the sequence is transmitted to the underwater acoustic channel. The receiving end receives the signal transmitted through the underwater acoustic channel, removes the cyclic prefix, and then performs an IFFT to obtain OFDM frequency-domain symbols. The method is characterized by further including the following steps: S1: Perform data preprocessing on the OFDM frequency domain symbols to construct a dataset for the input of the Transformer neural network; S2: Input the dataset into the trained Transformer neural network. The Transformer neural network adopts an architecture containing only encoders. It performs contextual feature weighted fusion on the input frequency domain symbol sequence through a multi-head self-attention mechanism to complete the soft decision of the received symbols. Then, it performs nonlinear transformation and adaptive filtering on the features output by the soft decision through a feedforward network to output the equalized OFDM frequency domain symbols. S3: During the training phase, the loss function is calculated based on the output value of the Transformer neural network and the true frequency domain symbol value. The network parameters of the Transformer neural network are updated through error backpropagation, and the frequency domain coefficients of the feedforward equalization filter are updated based on the network output. S4: In the inference phase, the equalized OFDM frequency domain symbol output by the Transformer neural network is used as the final recovered frequency domain symbol for subsequent demodulation. At the same time, the output value is fed back to the feedforward equalization filter to update the filter coefficients in real time to adapt to changes in the underwater acoustic channel.

2. The adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer according to claim 1, characterized in that, The encoder unit of the Transformer neural network includes a multi-head self-attention layer, a feedforward network, a residual connection module, and a layer normalization module. The residual connection module is used to perform a skip-addition of the input and output of the encoder unit, preserving the original input features while learning the incremental mapping.

3. The adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer according to claim 1, characterized in that, The underwater acoustic channel is a shallow water acoustic channel, and the channel model expression is as follows: ； In the formula, Let P be the amplitude of the transmission path. Let L be the time delay function of the Pth transmission path, and L be the total number of underwater acoustic channel paths; the mth OFDM frequency domain symbol expression obtained by the receiver through Fast Fourier Transform is: ； In the formula, T is the OFDM symbol period, and T′m is the time offset of the m-th OFDM symbol.

4. The adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer according to claim 3, characterized in that, The length of the cyclic prefix added to the time-domain OFDM symbol is Δ; in the total number of paths L of the underwater acoustic channel, The number of paths satisfying τp≤Δ is Q1, and the number of paths satisfying τp>Δ is L−Q1; the complete expression for the m-th OFDM frequency domain symbol is: ； In the formula, Xm(k) is the frequency domain value of the kth subcarrier of the m-th OFDM symbol at the transmitter, and Sa(⋅) is the sampling function.

5. The adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer according to claim 1, characterized in that, The data preprocessing in step S1 specifically includes: S11: Input the OFDM frequency domain symbols into the feedforward equalizer to obtain a row vector of dimension 1×m. , where m is the total number of subcarriers in the OFDM system, and i is the symbol number; S12: For row vectors The complex value corresponding to each subcarrier is decomposed into real and imaginary parts in subcarrier order to obtain an extended output vector with dimension 1×2m. ; S13: Expand the output vector Combined with the expanded output vector of the preceding o historical symbols, we obtain the original input matrix with dimension o×2m. , where o is the buffer order of the feedforward equalizer; S14: Convert the original input matrix Dimensions expanded to o× Then, positional encoding is added to obtain the final input sequence. All input sequences constitute the input dataset.

6. The adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer according to claim 1, characterized in that, The loss function used in the training phase is the mean squared error function, expressed as: ； In the formula, n is the number of frequency domain symbols in the current batch. The true frequency domain symbol value, The current frequency domain symbol value is recovered for the Transformer; the network parameters of the Transformer neural network are updated using the Adam optimizer, with the learning rate update strategy as follows: ； In the formula, steps is the number of training iterations, and warmup_steps is the number of warmup steps for the learning rate.

7. The adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer according to claim 6, characterized in that, It also includes the frequency domain coefficients of the feedforward filter. The update must follow the minimum mean square error (MMSE) criterion and adopt the minimum mean square (LMS) algorithm, whose iterative update formula is as follows: ； In the formula, Let $\frac{i}{i}$ be the frequency domain coefficients of the filter corresponding to the $i$-th symbol, $j = 0, 1, ..., (o-1)$, and $o$ be the order of the filter buffer. The iteration step size is also updated using the minimum mean square error (MMSE). For error signals, The frequency domain sign value of the Transformer neural network output. This is the preprocessed frequency domain symbol vector. Let be the conjugate value of the ij-th frequency domain symbol.

8. The adaptive frequency domain equalization method for underwater acoustic OFDM communication using Transformer according to claim 7, characterized in that, The update formula for the iteration step size μi is: ； In the formula, α is the step size adjustment coefficient. The frequency domain coefficients are derivatives with respect to the step size, and their update formula is: 。

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