A hydroacoustic OTFS communication transmission system and method based on generative neural networks

Abstract

A generative neural network-based underwater acoustic OTFS communication transmission system and method are disclosed, relating to underwater communication transmission. Addressing the fractional spread problem caused by long delay spread and Doppler spread in broadband underwater acoustic channels, the system includes sequentially cooperating transmitter, receiver, channel estimation, and channel equalization units. The transmitter performs OTFS modulation, carrier modulation, and transmission; the receiver performs signal reception, preprocessing, and OTFS demodulation; the channel estimation unit combines a fractional-order dictionary matrix with a generative neural network, constructing a delay-Doppler domain refined grid and designing an unsupervised training model with double KL divergence constraints; and the channel equalization unit performs equalization processing and signal recovery. The method includes OTFS modulation transmission at the transmitter, underwater acoustic channel transmission, signal processing and demodulation at the receiver, generative neural network channel estimation, and equalization decoding. It requires no large number of labeled samples, has low computational complexity, short running time, and improves the transmission accuracy of underwater acoustic channels.

Description

Technical Field

[0001] This invention relates to the field of underwater communication transmission technology, specifically to an underwater acoustic OTFS communication transmission system and method based on generative neural networks designed for underwater acoustic channels, applicable to the communication transmission of the physical layer channel of underwater acoustic transmission systems in scenarios such as underwater exploration, seabed resource extraction, and underwater rescue. Background Technology

[0002] Underwater acoustic communication plays a crucial role in various marine applications, including underwater exploration, seabed resource extraction, and underwater rescue. However, underwater acoustic channels possess inherent characteristics that significantly distinguish them from other channels: long delay spread and significant Doppler spread, resulting in channel selectivity in both the time and frequency domains, posing a major challenge to reliable communication.

[0003] Orthogonal Time Frequency Space (OTFS), as a novel modulation technique, offers significant advantages in addressing the dual-selectivity channel problem. OTFS defines pulse transmission information symbols in the delay-Doppler (DD) domain. Benefiting from the stability, complete diversity, and separability of the channel in the DD domain, DD domain modulation and detection are particularly well-suited for such challenging dual-selectivity channels.

[0004] Currently, underwater acoustic transmission technology based on OTFS still suffers from the following core technical defects, making it difficult to meet patent licensing requirements and limiting its engineering applications:

[0005] 1. Traditional general compressed sensing channel estimation schemes have weak adaptability to fractional diffusion, resulting in low channel estimation accuracy and affecting transmission performance.

[0006] 2. To improve the adaptability of fractional diffusion, some technologies use high-order fractional dictionaries. However, as the dictionary size increases, the computational complexity increases sharply, which cannot meet the response speed requirements of underwater real-time communication.

[0007] 3. Existing deep neural network-based systems and methods require a large number of labeled channel samples for training, while underwater acoustic channel sample collection needs to be completed through sea trials. Sample labeling consumes a lot of manpower and is difficult to adapt to actual engineering deployment.

[0008] 4. In traditional underwater acoustic channel transmission, the channel estimation performance is greatly affected by human experience parameters. In scenarios where the underwater acoustic channel is rapidly time-varying and the fractional diffusion effect is variable, the stability is poor and the anti-interference ability is insufficient.

[0009] To address the technical challenges of underwater acoustic transmission technologies, there is an urgent need to design an underwater acoustic OTFS communication transmission technology that is highly targeted, accurate, low-complexity, and engineering-feasible, while simultaneously protecting the system and method. This technology should be adapted to the inherent characteristics of underwater acoustic channels to ensure the reliability and real-time performance of underwater communication. Summary of the Invention

[0010] The purpose of this invention is to address the technical problems of existing underwater acoustic OTFS transmission technology, such as low estimation accuracy, high computational complexity, reliance on a large number of labeled samples, and poor anti-interference stability in fractional diffusion scenarios. This invention provides an underwater acoustic OTFS communication transmission system and method based on a generative neural network. By introducing a channel estimation mechanism that matches the delay-Doppler domain structure into the OTFS modulation, transmission, and demodulation processes, it can efficiently estimate fractional diffusion channels without requiring a large number of labeled samples, reducing reliance on artificial parameters and controlling computational complexity. This adapts to underwater acoustic channels with long delay spread, Doppler spread, and fractional diffusion effects, ensuring the stability of physical layer signal transmission in the underwater acoustic transmission system.

[0011] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0012] An underwater acoustic OTFS communication transmission system based on generative neural networks includes a transmitting device, a receiving device, a channel estimation device, and a channel equalization device, which work together to form an end-to-end underwater acoustic OTFS communication transmission.

[0013] The transmitting device is used to perform OTFS modulation, carrier modulation, and transmission on the signal to be transmitted by the underwater platform based on Zak transform. The receiving device is used to receive the signal transmitted through the underwater acoustic channel, resample and downconvert the received signal to obtain the baseband signal, and perform discrete Zak transform and OTFS demodulation on the baseband signal. The channel estimation device is used to estimate the time delay, channel gain, and Doppler factor of each path in the underwater acoustic channel based on the signal after discrete Zak transform, using a generative neural network combined with a fractional dictionary matrix. The channel equalization device is used to perform channel equalization processing on the OTFS demodulated signal based on the channel estimation information, decode and recover the original data, and complete the underwater acoustic OTFS communication transmission.

[0014] The transmitting device includes an inverse discrete Zak transform unit, a cyclic prefix addition unit, a transmit pulse shaping unit, an up-conversion module, and a transducer, with each module connected in series.

[0015] The receiving device includes a hydrophone, a resampling module, a downconversion module, a receiving matched filter unit, a cyclic sequence prefix removal unit, and a discrete Zak transform unit, with each module connected in series.

[0016] The channel estimation device includes a fractional dictionary construction module, a neural network processing module, and an optimization calculation module, which are connected in series. The neural network processing module includes a pre-trained generative neural network. The fractional dictionary construction module constructs a refined grid and a fractional dictionary matrix for the fractional diffusion effect of the underwater acoustic channel.

[0017] The channel equalization device includes a channel equalization module and a signal recovery module connected in series.

[0018] Furthermore, the inverse discrete Zak transform unit is used to perform an inverse discrete Zak transform on the signal to be transmitted; the cyclic prefix addition unit is used to copy the last sample of the sequence and prepend it to form a cyclic prefix CP; the transmission pulse shaping unit is used to perform pulse amplitude modulation on the inverse discrete Zak transform result after adding the cyclic prefix; the up-conversion unit is used to modulate the OTFS modulated signal to the underwater acoustic transmission adaptation frequency band via carrier modulation; and the transducer is used to convert the electrical signal into an acoustic signal and transmit it.

[0019] Furthermore, the transmitting pulse shaping unit may employ a raised cosine roll-off filter; the transducer may employ a broadband underwater acoustic transducer.

[0020] Furthermore, the hydrophone is used to convert the acoustic signal into an electrical signal; the resampling module is used to perform resampling compensation processing on the received signal; the downconversion unit is used to perform downconversion processing on the resampled signal to obtain the baseband signal; the receiving matched filtering unit is used to perform matched filtering processing on the received signal; the cyclic sequence prefix removal unit is used to remove the leading cyclic prefix; and the discrete Zak transform unit is used to perform discrete Zak transform on the signal after removing the cyclic prefix.

[0021] Furthermore, the hydrophone of the receiving device is a vector hydrophone.

[0022] Furthermore, the fractional dictionary construction module is used to construct a refined grid and a corresponding fractional dictionary matrix for the fractional diffusion effect of the underwater acoustic channel; the neural network processing module includes a pre-trained generative neural network to extract features from the underwater acoustic pilot observation samples and output latent variable distribution parameters characterizing the prior structure of the underwater acoustic sparse channel; the optimization calculation module is used to optimize the model through observation consistency constraints and divergence constraints and output the channel estimation results.

[0023] Furthermore, the refined grid constructed by the fractional-order dictionary construction module has a time delay dimension step size of [missing information]. The step size of the Doppler dimension is Among them, the time delay dimension refinement coefficient , It is a symbol period. Indicates frequency interval, ; and Let represent the number of grids in the time delay dimension and the Doppler dimension, respectively; based on the refined time delay and Doppler grids, construct a time delay dictionary set and a Doppler dictionary set; the time delay dictionary set... Doppler dictionary set ;in, This indicates the step size for refining the grid in the delay dimension. This represents the maximum index value in the latency dimension. The number of grids represents the latency dimension. Indicates frequency interval; Represents a set of Doppler dictionaries. This indicates the step size for refining the Doppler dimension mesh. This represents the maximum index value of the Doppler dimension. The grid number represents the Doppler dimension. It is a symbol periodicity; the overall dictionary size is ,in, Indicates the size of the latency dimension dictionary. The scale of the Doppler dimension dictionary is indicated; the fractional dictionary building module is used to solve the problems of coarse dictionary modeling and poor fractional diffusion adaptability in traditional systems, and to achieve a fine characterization of sparse underwater acoustic channels.

[0024] Furthermore, the generative neural network adopts an "encoder-decoder" architecture. The encoder includes three linear layers and two convolutional layers, and the decoder includes three linear layers. The encoder is used to receive underwater acoustic pilot observation samples, extract signal features, and output the mean and variance of the posterior distribution of latent variables. The posterior samples of latent variables are obtained through reparameterized sampling. The decoder is used to receive the posterior samples of latent variables and output the parameters of the generation side, realizing unsupervised learning of the prior structure of the sparse underwater acoustic channel. This eliminates the need for a large number of labeled samples and improves engineering feasibility.

[0025] Furthermore, the optimization calculation module is used to collaboratively optimize model parameters through multiple constraints to achieve high-precision channel estimation. The core is to construct observation consistency constraints, KL divergence constraints between latent variable posterior and standard prior, and KL divergence constraints between conditional posterior and generated prior. These three are combined to form the training objective function, and the network parameters are updated through the Adam optimizer. In the inference stage, the conditional posterior mean is calculated by combining the fractional dictionary matrix, the generated prior parameters output by the decoder, and the compressed sensing observation model to obtain the sparse channel representation. Then, through the mapping relationship from dictionary to channel, the final channel estimation result is output. No iteration is required, which reduces the computational complexity and adapts to the real-time transmission requirements of the system.

[0026] The training objective function of the optimization calculation module is:

[0027]

[0028] in, and The first The network parameters of the decoder and encoder at the next iteration For the expected log-likelihood term, Indicates the first The conditional posterior distribution of the sparse channel representation at the next iteration; Representation of the sparse channel in a fractional dictionary matrix; Represents the posterior sample of the latent variable; This represents the underwater acoustic pilot frequency observation sample; Indicates underwater acoustic pilot observation samples about Log-likelihood, No. The posterior distribution of the latent variables at the nth iteration Representing latent variables The prior distribution, Indicates the first The prior distribution generated in the next iteration is determined solely by the latent variables. It is the KL divergence.

[0029] A method for underwater acoustic OTFS communication transmission based on generative neural networks, based on the aforementioned underwater acoustic OTFS communication transmission system, includes an OTFS modulation transmission at the transmitting end, underwater acoustic channel transmission, and signal processing and demodulation at the receiving end. The core is to achieve channel estimation and transmission link optimization through generative neural networks to complete stable communication transmission in the underwater acoustic channel. The method specifically includes the following steps:

[0030] Step 1: At the transmitting end, prepare the signal to be transmitted from the underwater platform. Perform OTFS modulation based on Zak transform to obtain an interference-resistant OTFS modulated signal for transmission. The OTFS modulation includes a signal to be transmitted consisting of an inverse discrete Zak transform unit. The inverse discrete Zak transform is performed, and a cyclic prefix is ​​added through a cyclic prefix addition module to suppress inter-frame interference. The signal is then pulse-modulated to obtain the OTFS modulated signal. ;

[0031] Step 2: Use an underwater acoustic communication transmitter to transmit the OTFS modulated signal obtained in Step 1. After carrier modulation, the signal is transmitted to the underwater acoustic channel via a transducer. The transmitted signal is represented as follows: ;

[0032] Step 3: At the receiving end, the signal After passing through the underwater acoustic channel, the signal reaches the receiving end, where the receiving end resamples and downconverts the received signal to obtain the baseband signal.

[0033] Step 4: The received matched filter module performs matched filtering on the baseband signal and removes the cyclic prefix. Then, it performs OTFS demodulation based on discrete Zak transform to obtain the OTFS demodulated signal. ;

[0034] Step 5: Demodulated signal based on OTFS Mapped to the time-delay-Doppler domain, the time delay, channel gain, and Doppler factor of each path in the channel are estimated by a generative neural network combined with a fractional dictionary matrix. The estimation process includes: constructing a refined grid and a corresponding fractional dictionary matrix for the fractional diffusion effect of the underwater acoustic channel; extracting underwater acoustic pilot observation samples and inputting them into the generative neural network to extract latent variables and generate constraint parameters; optimizing the model through observation consistency constraints and divergence constraints; and outputting channel estimation results based on the optimized model to adapt to the fast time-varying characteristics of the underwater acoustic channel.

[0035] Step 6: Based on the channel estimation results obtained in Step 5, perform channel equalization processing on the OTFS demodulated signal obtained in Step 4 to eliminate two-dimensional interference and transmission distortion in the time delay-Doppler domain, decode and recover the original data, and complete the underwater acoustic OTFS communication transmission.

[0036] In step 1, the OTFS modulated signal is obtained. The specific steps can be as follows:

[0037] Step 1.1: At the transmitting end, data symbols from the modulation set are mapped to a discrete-time delay-Doppler grid, and each symbol is denoted as... ;in, Indicates a delay index. , The number of grid cells in the time delay dimension; Indicates Doppler index, , The number of grid cells in the Doppler dimension;

[0038] Step 1.2, Data Symbols Perform inverse discrete Zak transform; to suppress inter-frame interference, remove the last element from the sequence. Each sample is copied and prepended to form a cyclic prefix (CP). This represents the number of samples corresponding to the cyclic prefix;

[0039] Step 1.3: Perform pulse amplitude modulation on the result of the inverse discrete Zak transform after adding the cyclic prefix to obtain the OTFS modulated signal. .

[0040] In step 2, the carrier-modulated signal for:

[0041]

[0042] in, This indicates upconversion processing. It is time. It is the base of the natural logarithm. It is the imaginary unit. For carrier frequency; Pi; It is an OTFS modulated signal.

[0043] In step 3, the channel response of the underwater acoustic channel for:

[0044]

[0045] in, It is the total number of paths in the channel. Represents the Dirac function, Represents the time delay variable. It is time. , and They represent the first Channel gain, delay, and Doppler factor for each path. For path index, .

[0046] In step 5, the signal based on the discrete Zak transform... The specific steps for estimating the time delay, channel gain, and Doppler factor of each path in the channel using a generative neural network combined with a fractional dictionary matrix are as follows:

[0047] Step 5.1: To accommodate the fractional diffusion effect, a refined mesh is introduced in both the time delay and Doppler dimensions, with the step size set to the same as the step size of the refined mesh in the time delay dimension. Step size for refining the mesh with Doppler dimensions Where the time delay dimension refinement coefficient is set , It is a symbol period. Indicates frequency interval, ; and These represent the number of grids in the time delay dimension and the Doppler dimension, respectively;

[0048] Step 5.2: Construct a time delay and Doppler dictionary set based on the refined time delay and Doppler grid.

[0049]

[0050]

[0051] in, Represents the set of delay dictionaries. This indicates the step size for refining the grid in the delay dimension. This represents the maximum index value in the latency dimension. The number of grids represents the latency dimension. Indicates frequency interval; Represents a set of Doppler dictionaries. This indicates the step size for refining the Doppler dimension mesh. This represents the maximum index value of the Doppler dimension. The grid number represents the Doppler dimension. It is the symbol period;

[0052] Furthermore, the overall dictionary size can be obtained as follows: ,in, Indicates the size of the latency dimension dictionary. Indicates the size of the Doppler dimension dictionary;

[0053] Step 5.3: Based on the time delay and Doppler dictionary set, and the signal to be transmitted by the underwater platform... Construct a fractional dictionary matrix from the pilot component. The signal after discrete Zak transform Extracting the pilot component yields underwater acoustic pilot observation samples. And set the initial number of iterations. ;

[0054] Step 5.4: Sample underwater acoustic pilot observations Input the encoder network to obtain the first The mean of the posterior distribution of the latent variables at the next iteration and variance ;in, For encoder network parameters;

[0055] Step 5.5, based on the first The mean of the posterior distribution of the latent variables at the next iteration and variance Construct the first The posterior distribution of latent variables at the next iteration Furthermore, a reparameterization method was used for sampling to obtain the posterior samples of the latent variables. This is used for subsequent differentiable optimization updates; among which, Representing latent variables, This represents the underwater acoustic pilot observation sample. Indicates encoder network parameters;

[0056] Step 5.6: The posterior sample of the latent variables... Input decoder network, output the first In the next iteration, the decoder outputs the parameters from the generation side. , used to constrain the distribution structure of sparse channels; where, These are the decoder network parameters;

[0057] Step 5.7: Based on the underwater acoustic pilot observation samples Fractional dictionary matrix and the In the next iteration, the decoder outputs the parameters from the generation side. Construct and calculate the first The conditional posterior distribution of the sparse channel representation at the next iteration Key statistics, including the conditional posterior mean With conditional posterior covariance The aforementioned statistics are used to couple the prior generated by the neural network with the compressed sensing linear observation model, thereby enabling computationally posterior inference for sparse channels.

[0058] in, The representation of a sparse channel in a fractional-order dictionary matrix;

[0059] Step 5.8: Based on the conditional posterior mean With conditional posterior covariance Construct observation consistency constraints and calculate the expected log-likelihood term. ;in, It is the first Sparse Channel Representation in Sub-iteration The conditional posterior distribution, It is an underwater acoustic pilot observation sample. about Log-likelihood, From the measurement equation and noise statistics Definition: Ω represents a fractional dictionary matrix;

[0060] Step 5.9: Calculate the posterior and prior distributions of the latent variables. KL divergence constraint latent variable distribution between:

[0061]

[0062] in, It is the KL divergence. It is the first The posterior distribution of the latent variables at the nth iteration For encoder parameters, Indicates the number of iterations; Representing latent variables, This represents the underwater acoustic pilot frequency observation sample; Representing latent variables The prior distribution is set as a standard Gaussian distribution. Indicates the summation index; Represents the hidden dimension of a generative neural network; Indicates the first The variance of the posterior distribution of the latent variable during the nth iteration is... The logarithm of each element; and The first The mean of the posterior distribution of the latent variables at the next iteration and variance The One element;

[0063] Step 5.10: Construct and compute the conditional posterior distribution of the sparse channel representation. Compared to the generative prior distribution determined solely by latent variables KL divergence between:

[0064]

[0065] in, Denotes KL divergence, Indicates the first The conditional posterior distribution of the sparse channel representation at the next iteration; Indicates the decoder network parameters; Indicates the number of iterations; Representation of the sparse channel in a fractional dictionary matrix; Represents the posterior sample of the latent variable; This represents the underwater acoustic pilot frequency observation sample; Indicates the first The prior distribution generated in the next iteration is determined only by the latent variables; The logarithm of a determinant; Indicates the first The decoder generates parameters during the next iteration; Indicates the first The covariance of the conditional posterior distribution at the next iteration; Indicates the overall size of the dictionary; This represents the computation of the trace of a matrix; This indicates the construction of a diagonal matrix; Indicates the first The decoder generates the inverse of the parameters in the next iteration; Indicates the first The mean of the conditional posterior distribution at the next iteration; Indicates the first Transpose of the mean of the conditional posterior distribution at the next iteration;

[0066] The conditional posterior distribution With prior distribution The KL divergence between them is used to align the sparse posterior inferred by compressed sensing with the prior structure characterized by the generative network, so that the network learns more effective generative constraints for sparse channels.

[0067] Step 5.11: Combine the three parts from steps 5.8-5.10 to form the training objective function. :

[0068]

[0069] in, and The first The network parameters of the decoder and encoder at the next iteration For the expected log-likelihood term, Indicates the first The conditional posterior distribution of the sparse channel representation at the next iteration; Representation of the sparse channel in a fractional dictionary matrix; Represents the posterior sample of the latent variable; This represents the underwater acoustic pilot frequency observation sample; Indicates underwater acoustic pilot observation samples about Log-likelihood, No. The posterior distribution of the latent variables at the nth iteration Representing latent variables The prior distribution, Indicates the first The prior distribution generated in the next iteration is determined solely by the latent variables. It is the KL divergence;

[0070] Furthermore, after averaging the batch of samples, the Adam optimizer is used to update the parameters according to the learning rate to obtain the parameters for the next iteration. ; Indicates the first The network parameters of the decoder at the next iteration; Indicates the first The encoder's network parameters at the next iteration;

[0071] Furthermore, after training, for any underwater acoustic pilot observation sample... To obtain a sparse channel estimate, perform the following steps:

[0072] Will The input encoder yields the mean of the posterior distribution of the latent variables. and variance Reparameterized sampling yields the posterior samples of latent variables. ;

[0073] The posterior sample of the latent variable Input the decoder to obtain the parameters from the decoder's generation side. And combined with fractional dictionary matrix Noise variance With underwater acoustic pilot observation samples Computational conditions posterior mean , As an estimation result of the sparse channel represented under a fractional dictionary matrix;

[0074] Based on the mapping relationship from dictionary to channel, the estimation results of sparse channel represented by fractional-order dictionary matrix are obtained. Corresponding delay dictionary set With Doppler dictionary set Perform the transformation to output the final channel estimate. .

[0075] In step 6, the receiver performs equalization processing on the OTFS demodulated signal obtained in step 4 based on the channel estimation results output in step 5. This process compensates for delay spread, Doppler spread, and fractional spread interference generated during underwater acoustic channel transmission, eliminates transmission distortion, and then decodes the equalized signal to recover the original data to be transmitted by the underwater platform, thus completing the entire underwater acoustic OTFS communication transmission process.

[0076] This invention provides a dedicated communication signal processing technology for overcoming obstacles in underwater acoustic media transmission. Compared with existing technologies, the beneficial effects and outstanding advantages of this invention are as follows:

[0077] 1. Excellent Transmission Performance: This invention addresses fractional diffusion caused by broadband Doppler spread in underwater acoustic systems. It introduces a refined grid to construct a dictionary set in the time delay and Doppler domains, and employs a generative neural network to learn the prior structure of the sparse channel representation, solving the problem of coarse modeling in traditional integer grid dictionaries. Simultaneously, it utilizes GVAE to learn the prior distribution of the sparse channel and achieves collaborative optimization of generated priors and observed data through double KL divergence constraints. Simulation results show that, at a signal-to-noise ratio (SNR) of approximately 15 dB, the normalized mean square error of this invention is reduced by about 3 dB compared to traditional OMP and SBL methods; at an SNR of approximately 10 dB, the original bit error rate of this invention is reduced by about 40%–50% compared to traditional SBL and OMP methods, demonstrating high transmission accuracy and adapting to the reliability requirements of underwater acoustic transmission systems.

[0078] 2. High real-time performance and low complexity: This invention directly outputs the conditional posterior mean as the sparse representation estimation result during the inference stage, avoiding high-complexity global search or multiple rounds of reconstruction iteration on a large-scale dictionary; Experimental data show that the running time of the method of this invention is at least 73% less than that of the SBL method and at least 60% less than that of the OMP method, significantly reducing the computational burden and computational complexity, which can meet the needs of underwater real-time communication and transmission.

[0079] 3. High engineering feasibility: This invention achieves unsupervised statistical learning by using observation consistency terms and posterior-prior KL alignment terms. It can complete the training of generative neural networks without providing explicit real channel labels for each sample, thereby significantly reducing offline labeling and maintenance costs and improving the engineering feasibility of underwater acoustic communication.

[0080] 4. Strong adaptability: This invention reduces the influence of human experience parameters on the estimation results by using posterior-prior aligned KL divergence constraints, thereby improving the consistency and repeatability of the estimation process and adapting to the complex and variable transmission characteristics of underwater acoustic channels. Attached Figure Description

[0081] Figure 1 This is a schematic diagram of the overall architecture of the underwater acoustic OTFS communication transmission system of the present invention;

[0082] Figure 2 This is a schematic diagram of the structure of the generative neural network (GVAE) used in this invention;

[0083] Figure 3 This is a schematic diagram of the transmission pilot symbols in the time-delay-Doppler domain of the present invention;

[0084] Figure 4 This is a schematic diagram of the receiving pilot symbols in the time-delay-Doppler domain of the present invention;

[0085] Figure 5 This is a pseudo-color image of the sparse channel coefficient distribution estimated by the method of this invention, OMP, and SBL methods;

[0086] Figure 6 The normalized mean square error comparison curves of the method of this invention with those of OMP, SBL, and LS methods when the Doppler dimension refinement factor is 0.5;

[0087] Figure 7 Comparison curves of the original transmission bit error rate of the method of this invention with OMP, SBL, and LS methods when the Doppler dimension refinement factor is 0.5. Detailed Implementation

[0088] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention. Unless otherwise specified, conventional techniques in the art can be employed.

[0089] This embodiment selects a typical shallow sea near-range underwater acoustic communication scenario, with a communication distance of 800m, a sound speed of 1500m / s, a water depth of 20m, a sound source depth of 2m, and a receiving hydrophone depth of 3~6m. The implementation process of the method of this invention is described in detail, and the system parameters are set as follows: symbol period... Frequency interval Overall dictionary size Hidden Dimensions of Generative Neural Networks (GVAE) .

[0090] I. Transmission System Deployment

[0091] like Figure 1 As shown, the underwater acoustic OTFS communication transmission system of the present invention includes a transmitting device, a receiving device, a channel estimation device, and a channel equalization device, forming an end-to-end underwater acoustic communication physical layer transmission architecture.

[0092] The transmitting device includes an OTFS modulation module, an up-conversion module, and a transducer. The OTFS modulation module performs OTFS modulation processing based on the Zak transform on the signal to be transmitted. Specifically, it includes an inverse discrete Zak transform unit, a cyclic sequence prefix addition unit, and a transmit pulse shaping unit. This unit maps the time-delay-Doppler domain signal to the time domain, converting data symbols on the discrete time-delay-Doppler grid into a transmittable time-domain signal. After processing by the OTFS modulation module, the signal is transmitted to the up-conversion module, which modulates the OTFS modulated signal to the carrier frequency band, ensuring effective transmission of the signal in the underwater acoustic channel. The signal modulated by the up-conversion module is further transmitted to the transducer, which converts the electrical signal into an acoustic signal and transmits it, achieving the conversion from electrical signal to underwater acoustic signal and completing the output of the transmitting signal.

[0093] The receiving device includes a hydrophone, a resampling module, a down-conversion module, and an OTFS demodulation module. The hydrophone receives acoustic signals transmitted in the underwater acoustic channel and converts them into electrical signals. The converted electrical signal is transmitted to the resampling module, which performs resampling compensation processing on the received signal to alleviate the Doppler effect. The resampled signal is then transmitted to the down-conversion module, which converts the received signal to baseband. The down-converted baseband signal is transmitted to the OTFS demodulation module, which performs matched filtering, cyclic prefix removal, and discrete Zak transform processing.

[0094] The channel estimation device sequentially comprises a fractional-order dictionary construction module, a neural network processing module, and an optimization calculation module. The channel estimation device is used to estimate the underwater acoustic channel based on a generative neural network and a fractional-order dictionary model. Specifically, the fractional-order dictionary construction module constructs a time-delay-Doppler domain refined grid and a fractional-order dictionary matrix to address the fractional diffusion effect of the underwater acoustic channel; the neural network processing module integrates a pre-trained generative neural network (including encoder and decoder modules) to extract features, compress dimensions, and generate parameters from underwater acoustic pilot observation samples, achieving unsupervised sparse channel prior learning; the optimization calculation module constructs observation consistency constraints and double KL divergence constraints, optimizes model parameters, calculates key statistics for channel estimation, outputs the channel estimation results, and transmits them to the channel equalization device.

[0095] The channel equalization device includes a channel equalization module and a signal recovery module. The channel equalization module receives the channel estimation result transmitted by the channel estimation device and the demodulated signal transmitted by the OTFS demodulation module. Based on the channel information output by the channel estimation device, it performs equalization processing on the OTFS demodulated signal to compensate for the time delay spread, Doppler spread, and fractional spread interference generated during underwater acoustic channel transmission and eliminate signal transmission distortion. The equalized signal processed by the channel equalization module is transmitted to the signal recovery module. The signal recovery module decodes and recovers the equalized signal to restore the original signal to be transmitted at the transmitter, thus completing the closed loop of the entire underwater acoustic OTFS communication transmission.

[0096] II. Transmission Method Flow

[0097] Step 1: The OTFS modulation module modulates the signal to be transmitted by the underwater platform. Perform OTFS modulation based on Zak transform to obtain the OTFS modulated signal. .

[0098] Step 1.1: At the transmitting end, the data symbols from the modulation set are first mapped to a discrete-time delay-Doppler grid, and each symbol is denoted as... ;in, Indicates a delay index. , The number of grid cells in the time delay dimension; Indicates Doppler index, , The number of grid cells in the Doppler dimension; in this embodiment, the number of grid cells in the Doppler dimension... Latency dimension grid number .

[0099] Step 1.2: Process the data symbols using the inverse discrete Zak transform unit. Inverse discrete Zak transform is performed. To suppress inter-frame interference, a cyclic sequence prefix addition unit is added to the end of the sequence. Each sample is copied and prepended to form a cyclic prefix (CP). This represents the number of samples corresponding to the cyclic prefix; in this embodiment, .

[0100] Step 1.3: The pulse shaping unit performs pulse amplitude modulation on the result of the inverse discrete Zak transform after adding the cyclic prefix to obtain the OTFS modulated signal. .

[0101] Step 2: Use an underwater acoustic communication transmitter to transmit the OTFS modulated signal obtained in Step 1. After carrier modulation by the up-conversion module, the signal is transmitted through the transducer, and the transmitted signal is represented as follows: :

[0102]

[0103] in, This indicates upconversion processing. It is time. It is the base of the natural logarithm. It is the imaginary unit. For carrier frequency; Pi; OTFS modulated signal; transmitted signal carrier frequency The transmitter sampling rate is 100kHz.

[0104] Step 3, Signal After passing through the underwater acoustic channel, the signal reaches the receiving end. The hydrophone of the receiving device converts the acoustic signal into an electrical signal. The resampling module then resamples the received signal, and the downconversion module converts the received signal to baseband to obtain the baseband signal.

[0105] The channel response of the underwater acoustic channel for:

[0106]

[0107] in, It is the total number of paths in the channel. Represents the Dirac function, Represents the time delay variable. It is time. , and They represent the first Channel gain, delay, and Doppler factor for each path. For path index, .

[0108] Step 4: The OTFS demodulation module performs matched filtering on the baseband signal, removes the cyclic prefix, and then performs OTFS demodulation based on the discrete Zak transform to obtain the OTFS demodulated signal. .

[0109] Step 5: Demodulated signal based on OTFS The channel estimation device, combined with a generative neural network and a fractional dictionary matrix, estimates the time delay, channel gain, and Doppler factor of each path in the channel; a schematic diagram of the generative neural network is shown below. Figure 2 As shown, the end-to-end architecture for sparse channel estimation in underwater acoustic OTFS communication is illustrated, including an encoder module and a decoder module, and underwater acoustic pilot observation samples. The data is transmitted to the encoder module, which consists of three linear encoder layers (with 256, 256, and 16 neurons respectively) and two convolutional encoder layers (with a kernel size of 3 and an output channel of 1). The activation function used is ReLU. This module is responsible for processing the underwater acoustic pilot observation samples. Perform feature extraction and dimensionality compression, and output the mean of the posterior distribution of the latent variables. and variance The extracted features are passed to a three-layer linear decoder layer (with 256 neurons each, and an overall dictionary size of 256). The decoder module consists of a ReLU activation function and a Sigmoid output layer. After receiving the data, the decoder performs feature reconstruction and parameter generation, and outputs the generated side parameters. Combined with a fractional dictionary matrix constructed based on a time-delay-Doppler dictionary Generate sparse channel representation And finally reconstruct the underwater acoustic pilot observation samples. The entire structure organically couples the generative prior of the neural network with the linear observation model of compressed sensing through an "input-encoding-sampling-decoding" process, achieving unsupervised sparse channel prior learning without requiring a large number of labeled channel samples for training. Specifically:

[0110] Step 5.1: To accommodate the fractional diffusion effect, a refined mesh is introduced in both the time delay and Doppler dimensions, with the step size set to the same as the step size of the refined mesh in the time delay dimension. Step size for refining the mesh with Doppler dimensions Where the time delay dimension refinement coefficient is set , It is a symbol period. Indicates frequency interval, ; and These represent the number of grids in the time delay dimension and the Doppler dimension, respectively.

[0111] Step 5.2: The fractional-order dictionary construction module obtains the time delay and Doppler dictionary set based on the refined time delay and Doppler grid.

[0112]

[0113]

[0114] in, Represents the set of delay dictionaries. This indicates the step size for refining the grid in the delay dimension. This represents the maximum index value in the latency dimension. The number of grids represents the latency dimension. Indicates frequency interval; Represents a set of Doppler dictionaries. This indicates the step size for refining the Doppler dimension mesh. This represents the maximum index value of the Doppler dimension. The grid number represents the Doppler dimension. It is the symbol period; in this embodiment, the maximum index value of the delay dimension is set. Maximum index value of Doppler dimension .

[0115] Furthermore, the overall dictionary size can be obtained as follows: ,in and These represent the size of the time delay and the Doppler dimension dictionary, respectively.

[0116] Step 5.3: The fractional dictionary construction module constructs the signal to be transmitted by the underwater platform based on the time delay and the Doppler dictionary set. Construct a fractional dictionary matrix from the pilot component. A schematic diagram of the transmitted pilot symbols is shown below. Figure 3 As shown, the pilot occupies one grid point, surrounded by a protection interval, and the number of protection grids in the time delay dimension is [number missing]. The number of Doppler-dimensional protected grids is From the signal Extracting the pilot component yields underwater acoustic pilot observation samples. The schematic diagram of the receiving pilot symbol is as follows: Figure 4 As shown, the extracted pilot portion is the grid where the guard interval is located, and the dimension of the underwater acoustic pilot observation sample is [dimension missing]. And set the initial number of iterations. .

[0117] Step 5.4: Based on the underwater acoustic pilot observation samples and the fractional dictionary matrix, use the encoder of the generative neural network GVAE to estimate the posterior distribution of the latent variables; [The text abruptly ends here, likely due to an incomplete sentence or missing information.] Input the encoder network to obtain the mean of the posterior distribution of the latent variables. and variance .

[0118] Step 5.5: The optimization calculation module is based on the mean. and variance Constructing the posterior distribution of latent variables Furthermore, a reparameterization method was used for sampling to obtain the posterior samples of the latent variables. This is for subsequent minor optimization updates.

[0119] Step 5.6: The posterior sample of the latent variables... The decoder of the input generative neural network GVAE outputs the parameters of the generator side. It is used to constrain the distribution structure of sparse channels.

[0120] Step 5.7: Based on the underwater acoustic pilot observation samples Fractional dictionary matrix and decoder output Construct and calculate the first The conditional posterior distribution of the sparse channel representation at the next iteration Key statistics, including the conditional posterior mean With conditional posterior covariance The aforementioned statistics are used to couple the prior information generated by the neural network with the compressed sensing linear observation model, thereby enabling computationally achievable posterior inference for sparse channels; whereby... This represents the sparse channel in a fractional-order dictionary matrix.

[0121] Step 5.8: Based on the conditional posterior mean With conditional posterior covariance Construct observation consistency constraints and calculate the expected log-likelihood term. ;in, It is the first Sparse Channel Representation in Sub-iteration The conditional posterior distribution, It is an underwater acoustic pilot observation sample. about Log-likelihood, From the measurement equation and noise statistics definition; This represents a fractional dictionary matrix.

[0122] Step 5.9: Calculate the posterior and prior distributions of the latent variables. KL divergence constraint latent variable distribution between:

[0123]

[0124] in, It is the KL divergence. It is the first The posterior distribution of the latent variables at the nth iteration For encoder parameters, Indicates the number of iterations; Representing latent variables, This represents the underwater acoustic pilot frequency observation sample; Representing latent variables The prior distribution is set as a standard Gaussian distribution. Indicates the summation index; Represents the hidden dimension of a generative neural network; Indicates the first The variance of the posterior distribution of the latent variable during the nth iteration is... The logarithm of each element; and The first The mean of the posterior distribution of the latent variables at the next iteration and variance The Each element.

[0125] Step 5.10: Construct and compute the conditional posterior distribution of the sparse channel representation. Compared to the generative prior distribution determined solely by latent variables KL divergence between:

[0126]

[0127] in, Denotes KL divergence, Indicates the first The conditional posterior distribution of the sparse channel representation at the next iteration; Indicates the decoder network parameters; Indicates the number of iterations; Representation of the sparse channel in a fractional dictionary matrix; Represents the posterior sample of the latent variable; This represents the underwater acoustic pilot frequency observation sample; Indicates the first The prior distribution generated in the next iteration is determined only by the latent variables; The logarithm of a determinant; Indicates the first The decoder generates parameters during the next iteration; Indicates the first The covariance of the conditional posterior distribution at the next iteration; Indicates the overall size of the dictionary; This represents the computation of the trace of a matrix; This indicates the construction of a diagonal matrix; Indicates the first The decoder generates the inverse of the parameters in the next iteration; Indicates the first The mean of the conditional posterior distribution at the next iteration; Indicates the first The transpose of the conditional posterior distribution mean at the next iteration.

[0128] The conditional posterior distribution With prior distribution The KL divergence between them is used to align the sparse posterior obtained by compressed sensing with the prior structure characterized by the generative network, enabling the network to learn more effective generative constraints for sparse channels.

[0129] Step 5.11: Combine the three parts from steps 5.8-5.10 to form the training objective function:

[0130]

[0131] in, and For the first The network parameters of the encoder and decoder at the next iteration For the expected log-likelihood term, Indicates underwater acoustic pilot observation samples about Log-likelihood, No. The posterior distribution of the latent variables at the nth iteration Representing latent variables The prior distribution, )and For the conditional posterior distribution and the generated prior distribution. It is the KL divergence.

[0132] Furthermore, after averaging the batches of samples (each batch containing 64 underwater acoustic pilot observation samples), the Adam optimizer is used with a learning rate of = Update the parameters to obtain the parameters for the next iteration. .

[0133] Furthermore, after training, for any underwater acoustic pilot observation sample... The sparse channel estimate is obtained by the channel estimation device performing the following steps:

[0134] underwater acoustic pilot observation samples The input encoder yields the mean of the posterior distribution of the latent variables. and variance Reparameterized sampling yields the posterior samples of latent variables. .

[0135] The posterior sample of the latent variable Input decoder And combined with fractional dictionary matrix Noise variance With underwater acoustic pilot observation samples Computational conditions posterior mean , This serves as an estimation result of the sparse channel representation under a fractional-order dictionary matrix.

[0136] Based on the mapping relationship from dictionary to channel, the estimation results of sparse channel represented by fractional-order dictionary matrix are obtained. Corresponding delay dictionary set With Doppler dictionary set Perform the conversion and output channel estimate. .

[0137] Step 6: Use the channel estimate obtained in Step 5 The channel equalization module demodulates the OTFS signal obtained in step 4. After equalization processing, the signal recovery module performs decoding and recovery processing to restore the original data from the transmitting end. Complete underwater acoustic OTFS communication transmission.

[0138] The performance of the transmission system of this invention is verified through numerical simulation. Compared with existing underwater acoustic OTFS transmission systems based on OMP, SBL, and LS methods, the simulation considers sparse channels with 8 multipaths, an average path delay interval of 1ms, independent channel gains for each path following a Gaussian distribution, and an exponential decrease in average power with time delay from 0ms to 20ms, with a power attenuation of approximately 15dB. The average relative movement speed between the transmitter and receiver is 1.2m / s. 5000 UWA channel samples are generated. The specific results are as follows:

[0139] Figure 5 This paper presents pseudo-color images of the sparse channel coefficient distribution obtained from the underwater acoustic OTFS communication transmission method based on generative neural networks (GVAE) and underwater acoustic transmission systems based on traditional OMP and SBL. The horizontal axis represents the time delay dimension grid, and the vertical axis represents the Doppler dimension grid. Figure 5As can be seen, compared with the transmission methods based on OMP and SBL, the channel coefficient distribution based on GVAE in this invention is highly consistent with the real channel. In contrast, the OMP and SBL methods have deviations in the estimation of some positions and amplitudes in the results, and their estimation accuracy is significantly lower than that of this invention. This indicates that the transmission method of this invention can more accurately capture the real distribution characteristics of sparse channels. In complex scenarios where underwater acoustic channels have fractional diffusion effects, large differences in multipath delay, and variable Doppler frequency shift, the transmission method of this invention can achieve fine modeling and high-precision estimation of underwater acoustic sparse channels, providing accurate support for signal decoding and recovery, and effectively ensuring the transmission reliability of the entire underwater acoustic OTFS transmission method.

[0140] Figure 6 Doppler dimension refinement coefficients are given. When the value is 0.5, the underwater acoustic OTFS communication transmission method based on generative neural networks (GVAE) of this invention is compared with the underwater acoustic transmission system based on OMP, SBL, and LS in terms of channel estimation normalized mean square error. The Doppler dimension refinement coefficient is set in the simulation. The value is chosen to match the fractional Doppler parameters of the channel to determine the fractional diffusion level; in the figure, the horizontal axis represents the signal-to-noise ratio (in dB), and the vertical axis represents the normalized mean square error (in dB); from Figure 6 As can be seen, throughout the entire signal-to-noise ratio range (0~15dB), the normalized mean square error (MSE) of the transmission method of this invention is consistently lower than that of the SBL, OMP, and LS methods, demonstrating the best estimation accuracy. With increasing signal-to-noise ratio, the MSE of all four methods shows a decreasing trend, but the GVAE method decreases at a faster rate. Around a signal-to-noise ratio of 15dB, the MSE of the method of this invention decreases by approximately 3dB compared to OMP and SBL, and is significantly lower than that of the LS method, indicating that the refinement coefficients in the Doppler dimension are optimized. In scenarios where λ = 0.5, the transmission method of this invention demonstrates outstanding channel estimation performance and provides more reliable channel information support for subsequent equalization and decoding, thereby improving the overall performance of the entire underwater acoustic OTFS transmission.

[0141] Figure 7 Doppler dimension refinement coefficients are given. When the value is 0.5, the original bit error rate (BER) comparison curves of the proposed method (GVAE) with OMP, SBL, and LS methods are shown. In the simulation, ξ is set to a value consistent with the channel fractional Doppler parameter to match the fractional diffusion degree. In the figure, the horizontal axis represents the signal-to-noise ratio (SNR) (unit: dB), and the vertical axis represents the original BER. Figure 7As can be seen, within the examined signal-to-noise ratio range (0–15 dB), the original bit error rate of the transmission method of this invention is generally lower than that of SBL, OMP, and LS methods, demonstrating better transmission reliability. Under a signal-to-noise ratio of 10 dB, the original bit error rate of the transmission method of this invention is reduced by approximately 40%–50% compared to SBL and OMP, and the improvement is more significant than that of the LS method. These results are consistent with the findings of this invention. Figure 6 The consistent performance of the channel estimation normalized mean square error indicates that the transmission method of the present invention can more effectively suppress bit errors and maintain stable performance in fractional diffusion scenarios, solving the problem of transmission instability in traditional methods when fractional diffusion intensifies, and meeting the transmission reliability requirements of practical underwater engineering communication.

[0142] Table 1 compares the complexity and runtime of the method of this invention with those of OMP and SBL. Indicates the overall size of the dictionary; Indicates the number of iterations; The number of grids representing the latency dimension; The number of grid cells represents the Doppler dimension; This represents the Doppler dimension refinement coefficient.

[0143] Table 1

[0144]

[0145] As can be seen from Table 1, the refinement coefficients in the Doppler dimension... 8 and In both scenarios, the runtime of the transmission method of this invention is significantly lower than that of the SBL and OMP methods: Doppler dimension refinement coefficient At that time, the transmission method of the present invention had a running time of only 11.18 ms, which is significantly lower than SBL's 41.96 ms and OMP's 36.218 ms; Doppler dimension refinement coefficient The SBL algorithm's runtime is significantly improved to 174.745 ms, while the method of this invention runs in 13.584 ms, still significantly lower than SBL and OMP. In terms of computational complexity, the method of this invention has a computational complexity of [missing information]. This method eliminates the need for iteration, significantly reducing computational burden, especially in high-order and high-dimensional scenarios, thus meeting the low-complexity requirements of real-time underwater communication. In summary, by avoiding iteration during the inference phase, the running time and computational complexity of this invention are significantly lower than the SBL method under different refined Doppler coefficients. Specifically, running time is reduced by at least 73%, and computational complexity is significantly reduced. Although the computational complexity of the method in this invention is slightly higher than that of the traditional OMP method, it saves at least 60% of the running time, and the normalized mean square error of channel estimation is significantly better than that of the OMP method. The method of this invention can achieve a synergy of "high-precision estimation + low-complexity operation" under different fractional diffusion scenarios, solving the pain points of high complexity and poor real-time performance of traditional transmission methods (OMP, SBL), ensuring the real-time performance of the entire underwater acoustic OTFS transmission method, and meeting the actual needs of underwater real-time communication transmission.

[0146] This invention belongs to the field of underwater communication transmission technology, specifically addressing the technical challenges of poor fractional diffusion adaptation, low channel estimation accuracy, high computational complexity, and poor engineering feasibility in existing underwater acoustic transmission systems. It differs from technical improvements that focus primarily on data transmission logic. This invention outperforms existing underwater acoustic OTFS transmission systems in four core dimensions: estimation accuracy, computational complexity, engineering feasibility, and anti-interference capability. It effectively adapts to the inherent characteristics of long delay spread, Doppler spread, and fractional diffusion in underwater acoustic channels. Experiments show that this invention can achieve stable and efficient underwater communication transmission while maintaining low complexity and short operating time.

[0147] The above embodiments are merely preferred embodiments of the present invention and should not be considered as limiting the scope of the present invention. All equivalent variations and improvements made within the scope of the present invention should still fall within the patent coverage of the present invention.

Claims

1. A hydroacoustic OTFS communication transmission system based on generative neural networks, characterized in that, It includes a transmitting device, a receiving device, a channel estimation device, and a channel equalization device, which work together to form an end-to-end underwater acoustic OTFS communication transmission. The transmitting device is used to perform OTFS modulation, carrier modulation, and transmission on the signal to be transmitted by the underwater platform based on Zak transform. The receiving device is used to receive the signal transmitted through the underwater acoustic channel, resample and downconvert the received signal to obtain the baseband signal, and perform discrete Zak transform and OTFS demodulation on the baseband signal. The channel estimation device is used to estimate the time delay, channel gain, and Doppler factor of each path in the underwater acoustic channel based on the signal after discrete Zak transform, using a generative neural network combined with a fractional dictionary matrix. The channel equalization device is used to perform channel equalization processing on the OTFS demodulated signal based on the channel estimation information, decode and recover the original data, and complete the underwater acoustic OTFS communication transmission. The transmitting device includes an inverse discrete Zak transform unit, a cyclic prefix addition unit, a transmit pulse shaping unit, an up-conversion module, and a transducer connected in series. The receiving device includes a hydrophone, a resampling module, a downconversion module, a receiving matched filter unit, a cyclic sequence prefix removal unit, and a discrete Zak transform unit connected in series. The channel estimation device includes a fractional dictionary construction module, a neural network processing module, and an optimization calculation module, with each module connected in series. The neural network processing module contains a pre-trained generative neural network, and the fractional dictionary construction module constructs a refined grid and a fractional dictionary matrix for the fractional diffusion effect of the underwater acoustic channel. The refined grid constructed by the fractional dictionary construction module has a time delay dimension step size of [missing value]. The step size of the Doppler dimension is Among them, the time delay dimension refinement coefficient , It is a symbol period. Indicates frequency interval, ; and Let represent the number of grids in the time delay dimension and the Doppler dimension, respectively; based on the refined time delay and Doppler grids, construct a time delay dictionary set and a Doppler dictionary set; the time delay dictionary set... Doppler dictionary set ;in, This represents the maximum index value in the latency dimension. Represents the maximum index value of the Doppler dimension; the overall dictionary size is... ,in, Indicates the size of the latency dimension dictionary. Indicates the size of the Doppler dimension dictionary; The generative neural network adopts an encoder-decoder architecture. The encoder includes three linear layers and two convolutional layers, and the decoder includes three linear layers. The encoder is used to receive underwater acoustic pilot observation samples, extract signal features, and output the mean and variance of the posterior distribution of latent variables. The posterior samples of latent variables are obtained through reparameterized sampling. The decoder is used to receive the posterior samples of latent variables, output the parameters of the generation side, and realize unsupervised learning of the prior structure of the underwater acoustic sparse channel. The optimization calculation module is used to collaboratively optimize model parameters through multiple constraints. The core is to construct observation consistency constraints, KL divergence constraints between latent variable posterior and standard prior, and KL divergence constraints between conditional posterior and generated prior. These three are combined to form the training objective function, and the network parameters are updated through the Adam optimizer. In the inference stage, the conditional posterior mean is calculated by combining the fractional dictionary matrix, the generated prior parameters output by the decoder, and the compressed sensing observation model to obtain the sparse channel representation. Then, the channel estimation result is converted and output through the mapping relationship from dictionary to channel. No iteration is required, which reduces the computational complexity and adapts to the real-time transmission requirements of the system. The channel equalization device includes a channel equalization module and a signal recovery module connected in series.

2. The underwater acoustic OTFS communication transmission system based on generative neural networks according to claim 1, characterized in that, The fractional dictionary construction module is used to construct a refined grid and a corresponding fractional dictionary matrix for the fractional diffusion effect of the underwater acoustic channel; the neural network processing module includes a pre-trained generative neural network to extract features from the underwater acoustic pilot observation samples and output latent variable distribution parameters that characterize the prior structure of the underwater acoustic sparse channel; the optimization calculation module is used to optimize the model through observation consistency constraints and divergence constraints and output the channel estimation results.

3. A method for underwater acoustic OTFS communication transmission based on generative neural networks, characterized in that... The underwater acoustic OTFS communication transmission system based on generative neural networks as described in any one of claims 1 to 2, the method comprising the following steps: Step 1: At the transmitting end, prepare the signal to be transmitted from the underwater platform. Perform OTFS modulation based on Zak transform to obtain an interference-resistant OTFS modulated signal for transmission. ,in, Indicates a delay index. Indicates Doppler index, It is time; the OTFS modulation includes the signal to be transmitted. Perform inverse discrete Zak transform, add a cyclic prefix to suppress inter-frame interference, and then perform pulse modulation to obtain the OTFS modulated signal. ; Step 2: Use an underwater acoustic communication transmitter to transmit the OTFS modulated signal obtained in Step 1. After carrier modulation, the signal is transmitted via a transducer to the underwater acoustic channel. The transmitted signal is represented as follows: ; Step 3: At the receiving end, the signal The signal is transmitted to the receiving end via an underwater acoustic channel. The receiving end resamples and downconverts the received signal to obtain the baseband signal. Step 4: Perform matched filtering on the baseband signal and remove the cyclic prefix, then perform OTFS demodulation based on Discrete Zak Transform to obtain the OTFS demodulated signal. ; Step 5: Demodulated signal based on OTFS Mapped to the time-delay-Doppler domain, the time delay, channel gain, and Doppler factor of each path in the channel are estimated by a generative neural network combined with a fractional dictionary matrix. The estimation process includes: constructing a refined grid and a corresponding fractional dictionary matrix for the fractional diffusion effect of the underwater acoustic channel; extracting underwater acoustic pilot observation samples and inputting them into the generative neural network to extract latent variables and generate constraint parameters; optimizing the model through observation consistency constraints and divergence constraints; and outputting the channel estimation results based on the optimized model. Step 6: Based on the channel estimation results obtained in Step 5, perform channel equalization processing on the OTFS demodulated signal obtained in Step 4 to eliminate two-dimensional interference and transmission distortion in the time delay-Doppler domain, decode and recover the original data, and complete the underwater acoustic OTFS communication transmission.

4. The underwater acoustic OTFS communication transmission method based on generative neural networks according to claim 3, characterized in that, Step 1 is described in detail as follows: Step 1.1: At the transmitting end, the data symbols from the modulation set are first mapped to a discrete-time delay-Doppler grid, and each symbol is denoted as... ;in, Indicates a delay index. , The number of grid cells in the time delay dimension; Indicates Doppler index, , The number of grid cells in the Doppler dimension; Step 1.2, Data Symbols Perform inverse discrete Zak transform; to suppress inter-frame interference, remove the last element from the sequence. Each sample is copied and prepended to form a cyclic prefix CP; This represents the number of samples corresponding to the cyclic prefix; Step 1.3: Perform pulse amplitude modulation on the inverse discrete Zak transform result after adding the cyclic prefix to obtain the OTFS modulated signal. .

5. The underwater acoustic OTFS communication transmission method based on generative neural networks according to claim 3, characterized in that, Channel response of the underwater acoustic channel in step 3 Represented as: in, It is the total number of paths in the channel. Represents the Dirac function, Represents the time delay variable. It is time. , and They represent the first Channel gain, delay, and Doppler factor for each path. For path indexing, .

6. The underwater acoustic OTFS communication transmission method based on generative neural networks according to claim 3, characterized in that, Step 5 specifically includes the following steps: Step 5.1: To accommodate the fractional diffusion effect, a refined mesh is introduced in both the time delay and Doppler dimensions, with the step size set to the same as the step size of the refined mesh in the time delay dimension. Step size for refining the mesh with Doppler dimensions Where the time delay dimension refinement coefficient is set , It is a symbol period. Indicates frequency interval, ; and These represent the number of grids in the time delay dimension and the Doppler dimension, respectively; Step 5.2: Construct a time delay and Doppler dictionary set based on the refined time delay and Doppler grid. in, Represents the set of delay dictionaries. This represents the maximum index value in the latency dimension. This represents the maximum index value of the Doppler dimension; Overall dictionary size ,in and These represent the size of the time delay and Doppler dimension dictionary, respectively; Step 5.3: Based on the time delay, the Doppler dictionary set, and the signal to be transmitted by the underwater platform... Construct a fractional dictionary matrix from the pilot component. From the signal Extracting the pilot component yields underwater acoustic pilot observation samples. And set the initial number of iterations. ; Step 5.4: Sample underwater acoustic pilot observations Input the encoder network to obtain the mean of the posterior distribution of the latent variables. and variance ;in, For encoder network parameters; Step 5.5: Based on the mean of the posterior distribution of the latent variables and variance Constructing the posterior distribution of latent variables Furthermore, a reparameterization method was used for sampling to obtain the posterior samples of the latent variables. ; Step 5.6: The posterior sample of the latent variables... Input to decoder network, output parameters of generator side , used to constrain the distribution structure of sparse channels; where, These are the decoder network parameters; Step 5.7: Based on the underwater acoustic pilot observation samples Fractional dictionary matrix and decoder output Construct and calculate the first The conditional posterior distribution of the sparse channel representation at the next iteration Key statistics, including the conditional posterior mean With conditional posterior covariance The aforementioned statistics are used to couple the prior generated by the neural network with the compressed sensing linear observation model, thereby enabling the computation of posterior inference for sparse channels. in The representation of a sparse channel in a fractional-order dictionary matrix; Step 5.8: Based on the conditional posterior mean With conditional posterior covariance Construct observation consistency constraints and calculate the expected log-likelihood term. ;in, It is the first Sparse Channel Representation in Sub-iteration The conditional posterior distribution, It is an underwater acoustic pilot observation sample. about Log-likelihood, From the measurement equation and noise statistics definition; Step 5.9: Calculate the posterior and prior distributions of the latent variables. KL divergence constraint latent variable distribution between: in, It is the KL divergence. It is the first The posterior distribution of the latent variables at the nth iteration For encoder parameters, Indicates the number of iterations; Representing latent variables, This represents the underwater acoustic pilot frequency observation sample; Representing latent variables The prior distribution is set as a standard Gaussian distribution. Indicates the summation index; Represents the hidden dimension of a generative neural network; Indicates the first The variance of the posterior distribution of the latent variable during the nth iteration is... The logarithm of each element; and The first The mean of the posterior distribution of the latent variables at the next iteration and variance The One element; Step 5.10: Construct and compute the conditional posterior distribution of the sparse channel representation. Compared to the generative prior distribution determined solely by latent variables KL divergence between: in, Denotes KL divergence, Indicates the first The conditional posterior distribution of the sparse channel representation at the next iteration; Indicates the decoder network parameters; Indicates the number of iterations; Representation of the sparse channel in a fractional dictionary matrix; Represents the posterior sample of the latent variable; This represents the underwater acoustic pilot frequency observation sample; Indicates the first The prior distribution generated in the next iteration is determined only by the latent variables; The logarithm of a determinant; Indicates the first The decoder generates parameters during the next iteration; Indicates the first The covariance of the conditional posterior distribution at the next iteration; Indicates the overall size of the dictionary; This represents the computation of the trace of a matrix; This indicates the construction of a diagonal matrix; Indicates the first The decoder generates the inverse of the parameters in the next iteration; Indicates the first The mean of the conditional posterior distribution at the next iteration; Indicates the first Transpose of the mean of the conditional posterior distribution at the next iteration; The conditional posterior distribution With prior distribution The KL divergence between them is used to align the sparse posterior inferred by compressed sensing with the prior structure characterized by the generative network, so that the network learns more effective generative constraints for sparse channels. Step 5.11: Combine the three parts from steps 5.8-5.10 to form the training objective function, update the network parameters, and output the channel estimate after training is complete. .

7. The underwater acoustic OTFS communication transmission method based on generative neural networks according to claim 6, characterized in that, The training objective function in step 5.11 is: in, and For the first The network parameters of the encoder and decoder at the next iteration For the expected log-likelihood term, Indicates underwater acoustic pilot observation samples about Log-likelihood, No. The posterior distribution of the latent variables at the nth iteration Representing latent variables The prior distribution, )and For the conditional posterior distribution and the generated prior distribution. It is the KL divergence.

Images