High-speed mobile AUV underwater acoustic communication method based on OTFS

Abstract

The invention relates to the technical field of AUV underwater acoustic communication, in particular to a high-speed mobile AUV underwater acoustic communication method based on OTFS. Comprising the following steps: generating a modulation symbol # imgabs0 # on a time delay-Doppler domain, and converting the modulation symbol of the time delay-Doppler domain into a time domain signal # imgabs1 #; inputting the time domain signal # imgabs2 # into an underwater acoustic channel to obtain an output # imgabs3 # of the underwater acoustic channel; optimizing an underwater acoustic channel parameter estimation value through a VSBL channel estimation algorithm; and S3, correcting the output value of the underwater acoustic channel through the corresponding estimation value of the underwater acoustic channel obtained in the step S3, and converting the corrected signal into a modulation symbol # imgabs4 # of a time delay-Doppler domain to complete information transmission. The method can effectively cope with channel changes caused by high-speed movement, improves the communication stability of the system in a non-stationary underwater environment, and achieves high robustness, high precision and low complexity in AUV underwater acoustic communication.

Description

Technical Field

[0001] The present invention relates to the technical field of AUV underwater acoustic communication, and particularly to a high-speed mobile AUV underwater acoustic communication method based on OTFS. Background Art

[0002] Currently, autonomous underwater vehicles are widely used in the field of ocean exploration. The unmanned submersibles that navigate autonomously in water have the functions of autonomous navigation, autonomous guidance, and autonomous detection. At the same time, underwater acoustic communication, as a communication technology that can effectively cope with the underwater environment, has the advantages of strong anti-interference ability and high reliability, and is widely used in military, seabed exploration and other fields. The AUV platform itself has the characteristics of flexible movement, but relative movement will have a serious impact on the communication quality of the AUV. How to effectively address the communication problem of the AUV under high-speed movement is of great practical significance for the platform system to achieve the best performance.

[0003] Most traditional AUV communication schemes rely on simple linear or non-linear channel estimation methods, such as the least squares method (LS) or MMSE. These methods are often difficult to accurately estimate the rapidly changing channel in a high-speed mobile environment, especially in the case of severe multipath fading and frequency offset. Since traditional methods cannot fully utilize the sparse characteristics of the channel, the estimation results may have large errors, affecting the overall communication performance.

[0004] The communication system of the AUV mobile platform mainly relies on underwater acoustic communication technology. Traditional communication technologies mainly combine multiple technologies such as OFDM, MIMO, TDMA / FDMA, etc. to improve communication rate, capacity, and robustness to adapt to complex underwater environments. When applying existing underwater acoustic communication technologies to a high-speed mobile AUV platform, the following problems usually exist: (1) The high-speed movement of the AUV will make the multipath effect of the signal more complex, and traditional underwater acoustic communication technologies usually have difficulty effectively suppressing multipath interference; (2) Under the high-speed movement of the AUV, the robustness of traditional communication systems is poor and is easily affected by dynamic changes, resulting in communication interruption or data loss; (3) For a high-speed mobile AUV, traditional channel estimation methods usually require a large amount of signal processing and calculation to adapt to the rapid change of the channel; (4) Traditional channel estimation methods of OFDM (such as estimation based on pilot signals) are sensitive to frequency offset and Doppler effect. In a high-speed mobile environment, traditional OFDM channel estimation may not be able to adapt to the rapidly changing channel characteristics. Summary of the Invention

[0005] The object of the present invention is to overcome the above-mentioned defects existing in the prior art, and a high-speed mobile AUV underwater acoustic communication method based on OTFS is proposed, which can effectively cope with the channel changes brought about by high-speed movement, improve the communication stability of the system in a non-stationary underwater environment, and achieve high robustness, high precision and low complexity in AUV underwater acoustic communication.

[0006] The technical solution of the present invention is: a high-speed mobile AUV underwater acoustic communication method based on OTFS, which includes the following steps: S1. Generate modulation symbols in the time-delay - Doppler domain , and convert the modulation symbols in the time-delay - Doppler domain into time-domain signals ; S2. Input the time-domain signal into the underwater acoustic channel to obtain the output of the underwater acoustic channel ; S3. Optimize the estimated value of the underwater acoustic channel parameters through the VSBL channel estimation algorithm; S4. Correct the output value of the underwater acoustic channel through the estimated value of the underwater acoustic channel obtained in step S3, and convert the corrected signal into modulation symbols in the time-delay - Doppler domain , and complete the information transmission.

[0007] In the present invention, in step S1, the conversion of the signal is achieved through the following steps: S1.1. Convert the modulation symbol into a time-frequency domain signal : ; Among them, represents the index of discrete time and frequency points; represents the index of the converted time-frequency grid points; represents the number of subcarriers in the Doppler domain; represents the number of subcarriers in the time-delay domain; represents the imaginary unit; represents the scaling factor of the phase shift in the frequency domain; S1.2. Convert into a time-domain signal through the Heisenberg transform: ; Among them, represents time; represents the transmission waveform; represents the total duration or time window of the signal; represents a constant related to the Doppler shift or time-frequency shift; represents the frequency offset.

[0008] Input the time-domain signal into the underwater acoustic channel, and the output of the underwater acoustic channel is: , where represents the underwater acoustic channel in the delay-Doppler domain; represents the transformed index, which is usually used for the received signal or the transformed grid; represents the expression of the signal in the time-frequency grid; represents the noise term of the signal in the time-frequency domain.

[0009] The VSBL channel estimation algorithm in step S3 includes the following steps: S3.1. Define the variational parameters , and , and initialize the parameters in the above variational parameters. Among them, the parameter represents the underwater acoustic communication vector, the parameter represents the hyperparameter vector element, and the parameter represents the noise precision; S3.2. Use the variational parameter and the variational parameter to update the variational parameter ; S3.3. Use the variational parameter updated in step S3.2 to update the variational parameter , and obtain the updated variational parameter ; S3.4. Use the variational parameter updated in step S3.2 to update the variational parameter , and obtain the updated variational parameter ; S3.5. Repeat steps S3.2 to S3.4. Each time it is repeated, one iteration optimization of the variational parameters , and is achieved until the ELBO converges; After the iteration process ends, output the final channel response estimation value : .

[0010] In the said step S3.1, the initialization of the parameter comes from the following formula: , where Denote the measurement matrix; n denotes the noise vector; Obtain the initial value of the parameter according to the output of the underwater acoustic channel; The initial value of the parameter and the parameter adopts an identity matrix or a zero matrix.

[0011] In the step S3.2, the variational parameter and the variational parameter are used to update the variational parameter The formula is: , where denotes a constant; denotes the current iteration number, k = 1, 2, …, , denotes the maximum iteration number; denotes the estimated value of the parameter k- after 1 iteration. When k- 1 = 0, it denotes the initial value of the parameter ; The calculation formula of is: In the above formula, The calculation formula of is: The calculation formula of is: where A denotes a diagonal matrix; The calculation formula of is: where a denotes the shape parameter of the Gamma distribution corresponding to ; it determines the shape of the distribution and affects the distribution of the probability density function; b denotes the scale parameter of the Gamma distribution corresponding to and determines the scaling size of the distribution; The calculation formula of is: where c denotes the shape parameter of the Gamma distribution corresponding to ; d denotes the shape parameter of the Gamma distribution corresponding to The scale parameter of the Gamma distribution; According to the above formula, solve for the expected value: ; where, The calculation formula for ; The calculation formula for ; Using the properties of the Gamma distribution, The calculation formula for ; The calculation formula for , where, represents the updated value of the shape parameter of the Gamma distribution corresponding to , represents the updated values of the shape parameter and scale parameter of the Gamma distribution corresponding to ; The calculation formula for ; The calculation formula for ; The calculation formula for ; where, represents the updated value of the shape parameter of the Gamma distribution corresponding to , represents the updated value of the scale parameter of the Gamma distribution corresponding to ; Substitute the above formula into the expected value calculation formula and , to obtain: ; ; The variational parameter is a Gaussian distribution, so: , where, represents the mean related to , represents the mean related to Related variance; Derived from the above formula: , , Therefore, , .

[0012] In the step S3.3, when updating the variational parameter for the variational parameter , , where, represents the conditional probability distribution of the current observation given the previous state ; represents the prior probability distribution of the state ; represents a constant value; Combined with the expected value , , the updated variational parameter is obtained: , where the calculation formula of is: the calculation formula of .

[0013] In the step S3.4, when updating the variational parameter for the variational parameter , the updated variational parameter is calculated from the following expected value equation: , The updated variational parameter is: , where, the calculation formula of is: the calculation formula of , where, denotes the trace of the matrix, i.e., the sum of the diagonal elements of the matrix.

[0014] In the step S3.5, the estimated channel response is given by the variational parameters optimized by iteration; The iterative optimization process continues uninterrupted until the change in ELBO between consecutive iterations is less than a predefined threshold , when the ELBO interpolation in two adjacent iterative processes is less than , the iterative process ends; When the number of iterations reaches , the iterative process ends.

[0015] The specific implementation process of step S4 is as follows: S4.1. The final estimated value of the channel response output by the VSBL channel estimation algorithm is used to correct the output value of the underwater acoustic channel, and the corrected signal is: ; S4.2. Through the Wigner transform, the signal is converted into a time-domain signal : ; S4.3. Through the symplectic Fourier transform, the time-domain signal is converted into a modulation symbol in the delay-Doppler domain, and thus the signal transmission process is completed: .

[0016] The beneficial effects of the present invention are as follows: (1) The OTFS communication system adopted in the present application uses time-frequency-space scheduling signals, enabling the signals to more effectively resist multipath interference. In an underwater high-speed mobile environment, due to the relatively severe multipath effect and frequency-selective fading of signals, OTFS can reconstruct signal paths in the time-frequency plane, reducing the impact of the multipath effect on communication quality, thereby improving the stability and reliability of the system; (2) The VSBL channel estimation algorithm proposed in this application combines sparse Bayesian channel estimation (SBL) with variational inference, which can bring out the advantages of both: SBL itself can effectively utilize the sparse characteristics of the channel, while variational inference can optimize the Bayesian inference process by introducing an approximate posterior distribution, thereby improving the accuracy and efficiency of estimation. The combined method can reduce the computational complexity, reduce the computational overhead of parameter updates when dealing with high-dimensional and sparse channels, and make the channel estimation applicable to real-time communication systems, better adapting to the dynamically changing underwater acoustic channel environment; (3) The VSBL channel estimation algorithm can more accurately estimate the active signal paths in a complex multipath environment, which enables the AUV to maintain a high channel estimation accuracy in a high-speed dynamic environment, thereby reducing the performance loss caused by channel estimation errors; (4) The combination of OTFS and the VSBL channel estimation algorithm can better adapt to the channel changes brought about by high-speed movement: among them, the SBL method can update the channel state in real time, the variational inference optimization can quickly adapt to the non-stationary changes of the channel, and OTFS can provide flexible signal reconstruction in the time-frequency space. This combination enables the system to achieve stable communication during the high-speed movement of the AUV, especially performing excellently in a rapidly changing underwater environment; (5) Through the combination of the VSBL method and OTFS, the system can provide stronger robustness, can effectively cope with non-stationary channels, frequency offsets, noise, and multipath interference, ensuring the communication quality and maintaining stable transmission even in high-speed and harsh underwater environments. The accuracy of channel estimation is improved. Description of the Drawings

[0017] Figure 1 is the flowchart of the method described in this application; Figure 2 is a comparison graph of the relationship curves of the root mean square error (RMSE) and signal-to-noise ratio (SNR) between the method proposed in this application and the existing method in the OFDM system under the same conditions; Figure 3 is a comparison graph of the relationship curves of the root mean square error (RMSE) and signal-to-noise ratio (SNR) between the method proposed in this application and the existing method in the OTFS system under the same conditions. Detailed Embodiments

[0018] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the following will describe the detailed embodiments of the present invention in conjunction with the drawings.

[0019] Specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar generalizations without departing from the spirit of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0020] The high-speed mobile AUV underwater acoustic communication method proposed in this application adopts the orthogonal time-frequency-space (OTFS) modulation technology and builds an OTFS underwater acoustic communication framework on the AUV platform. OTFS modulates signals in the time-delay-Doppler domain, enabling the communication system to fully utilize the full-time-frequency diversity gain of the channel, thereby enhancing the anti-Doppler ability and improving the stability of data transmission. The framework includes modules such as OTFS signal mapping, time-frequency transformation, modulation, and transmission design at the transmitting end, as well as signal demodulation, time-delay-Doppler domain equalization, and error correction at the receiving end to ensure stable data reception under high-speed mobile conditions.

[0021] The method described in this application mainly includes the following steps.

[0022] The first step is to generate modulation symbols in the time-delay-Doppler domain , and convert the modulation symbols in the time-delay-Doppler domain into through two transformations.

[0023] First, the modulation symbol is converted into a time-frequency domain signal through the inverse symplectic Fourier transform: ; where represents the indices of discrete time and frequency points and represents the sampling points in the OTFS domain; represents the converted time-frequency grid point index; represents the number of subcarriers in the Doppler domain; represents the number of subcarriers in the delay domain; represents the imaginary unit; represents the scaling factor representing the frequency-domain phase shift.

[0024] Secondly, is converted into a time-domain signal through the Heisenberg transform.

[0025] ; where represents time and is used for the time-domain signal; represents the transmission waveform; represents the total duration or time window of the signal; represents a constant related to the Doppler shift or time-frequency shift; Indicates the frequency offset.

[0026] Second step, input the time-domain signal into the underwater acoustic channel, and the output of the underwater acoustic channel is: ; wherein, represents the underwater acoustic channel in the delay-Doppler domain; represents the transformed index, which is usually used for the received signal or the transformed grid; represents the expression of the signal in the time-frequency grid; represents the noise term of the signal in the time-frequency domain, which usually represents the interference or noise in the system.

[0027] Third step, optimize the estimated value of the underwater acoustic channel parameters through the VSBL channel estimation algorithm. In this application, by optimizing the variational parameters, various statistical characteristics of the channel parameters are better captured, so that the estimated value of the underwater acoustic channel parameters continuously approaches the true channel characteristics, improving the accuracy of channel estimation.

[0028] Specifically, the VSBL channel estimation algorithm includes the following steps.

[0029] First, define the variational parameters , and , and initialize the parameters in the above variational parameters. Among them, the parameter represents the underwater acoustic communication vector, the parameter represents the hyperparameter vector element, and the parameter represents the noise precision.

[0030] The initialization of the parameter comes from the following formula: , wherein, represents the measurement matrix; n represents the noise vector.

[0031] According to the output of the underwater acoustic channel, obtain the initial value of the parameter . The initial values of the parameter , as well as the parameter can adopt the identity matrix or the zero matrix.

[0032] Second, use the variational parameter and the variational parameter to update the variational parameter .

[0033] , wherein, represents a constant; represents the current iteration number, k = 1, 2, …, , represents the maximum number of iterations; represents after k- 1 iteration, the estimated value of the parameter When k- 1 = 0, it represents the initial value of the parameter .

[0034] The calculation formula of , In the above formula, The calculation formula of , The calculation formula of , where A represents a diagonal matrix used to control the channel response accuracy.

[0035] The calculation formula of , where a represents the shape parameter of the Gamma distribution corresponding to ; it determines the shape of the distribution and affects the distribution of the probability density function; b represents the scale parameter of the Gamma distribution corresponding to and determines the scaling size of the distribution.

[0036] The calculation formula of , where c represents the shape parameter of the Gamma distribution corresponding to ; d represents the scale parameter of the Gamma distribution corresponding to .

[0037] According to the above formula, the expected value can be solved: ; where The calculation formula of ; The calculation formula of ; Using the properties of the Gamma distribution, The calculation formula of ; The calculation formula for is: where represents the updated value of the shape parameter of the Gamma distribution corresponding to and represents the updated values of the shape parameter and scale parameter of the Gamma distribution corresponding to .

[0038] The calculation formula for is: The calculation formula for is: The calculation formula for is: where represents the updated value of the shape parameter of the Gamma distribution corresponding to and represents the updated value of the scale parameter of the Gamma distribution corresponding to .

[0039] Substituting the above formulas into the expected value calculation formula and , we can obtain: ; .

[0040] The variational parameter is a Gaussian distribution, so: , where represents the mean related to and represents the variance related to .

[0041] Derived from the above formula derivation: , , therefore, , .

[0042] Third, use the variational parameters updated by the above steps to update the variational parameters and obtain the updated variational parameters .

[0043] ; Among them, represents the conditional probability distribution of the current observable quantity under the condition given by the previous state ; represents the prior probability distribution of the state ; represents a constant value

[0044] Combined with the expected value , , obtain the updated variational parameters : .

[0045] Among them The calculation formula of is: , Among them The calculation formula of is: .

[0046] Fourth, use the variational parameters updated by the above steps to update the variational parameters and obtain the updated variational parameters .

[0047] Using the same average value, the updated variational parameters can be calculated from the following expected value equation

[0048] , The updated variational parameters are: .

[0049] Among them, The calculation formula of is: .

[0050] The calculation formula of is: .

[0051] Among them, Denotes the trace of a matrix, i.e., the sum of the diagonal elements of the matrix.

[0052] Fifth, repeat steps two to four. Each repetition realizes one iteration optimization of the variational parameters 、 and until the ELBO converges.

[0053] Estimated channel response Is given by the variational parameters after iterative optimization. The iterative optimization process continues until the change in ELBO between consecutive iterations is less than a predefined threshold , i.e., when the ELBO interpolation between two adjacent iterations is less than , the iterative process ends. In this embodiment, .

[0054] In addition, a maximum number of iterations is also set in this application. When the number of iterations reaches , the iterative process ends. In this embodiment, , to prevent an infinite iteration loop.

[0055] Sixth, after the iterative process ends, output the final estimated value of the channel response : .

[0056] Fourth, using the channel response estimate obtained in the third step, correct the output value of the underwater acoustic channel. The corrected signal is successively transformed into modulation symbols in the delay-Doppler domain through the Wigner transform and the symplectic Fourier transform , completing the information transmission.

[0057] First, by correcting the output value of the underwater acoustic channel, the corrected signal is: .

[0058] Second, through the Wigner transform, transform the signal into a time-domain signal : .

[0059] Finally, through the symplectic Fourier transform, transform the time-domain signal into modulation symbols in the delay-Doppler domain , thus completing the signal transmission process.

[0060] .

[0061] Through the method of the present invention, communication within the same high-speed moving AUV can be achieved, and communication between the high-speed moving AUV and the water platform, as well as communication between different high-speed moving AUVs, can also be achieved, ensuring that the AUV maintains a high-quality communication link during high-speed movement.

[0062] To verify the superiority of the method described in this application, this application provides a comparison chart of the relationship curves between the root mean square error (RMSE) and the signal-to-noise ratio (SNR) of the VSBL channel estimation algorithm proposed in this application and the existing method under the OFDM framework under the same conditions, as Figure 2 shown. And under the same conditions, a comparison chart of the relationship curves between the root mean square error (RMSE) and the signal-to-noise ratio (SNR) of the VSBL channel estimation algorithm proposed in this application and the existing method under the OTFS framework, as shown in Figure 3: The simulation parameters in Table 1 were used during the comparative experiment.

[0063] Table 1 Simulation parameter conditions Parameter Value Number of symbols in the delay domain M 128 Number of symbols in the Doppler domain N 64 Modulation scheme 4QAM Frequency spacing / Hz 15.6 Bandwidth / kHz 2 Center frequency / kHz 12 Center frequency / kHz 48 Maximum delay 10 Doppler shift 10 These parameters were consistently used in the simulation experiments of the OFDM and OTFS systems to ensure a fair comparison and evaluation of the variational Bayesian channel estimation method.

[0064] Figure 2 and Figure 3 The simulation results described in show that compared with the compressed sensing (CS), orthogonal matching pursuit (OMP), least squares method (LS), and minimum mean square error estimation (MMSE) algorithms, the VSBL channel estimation algorithm proposed in this application exhibits excellent performance, whether implemented in the OFDM or OTFS system.

[0065] In addition, the performance of the VSBL channel estimation algorithm proposed in this application in the OTFS system exceeds that in the OFDM system. This indicates that the VSBL channel estimation algorithm of this application exhibits better anti-interference ability and higher signal recovery accuracy in multipath delay UAC. This improvement is attributed to the time-frequency separation characteristics of the OTFS system, which enables them to perform better in a multipath propagation environment.

[0066] In summary, the communication method described in this application has broad application potential in actual underwater acoustic communication systems and provides a solution for improving the performance of underwater communication systems.

[0067] The above has introduced in detail the high-speed mobile AUV underwater acoustic communication method based on OTFS provided by the present invention. Specific examples are applied in this article to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention. It should be noted that for those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and modifications can still be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention. The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A high-speed mobile AUV underwater acoustic communication method based on OTFS, characterized in that: The following steps are involved: S1. Generate modulation symbols in the delay-Doppler domain , converting the modulation symbols in the delay-Doppler domain into time domain signals ; S2, the time domain signal Input the underwater acoustic channel and get the output of the underwater acoustic channel ; S3, optimizing the estimated values ​​of underwater acoustic channel parameters through the VSBL channel estimation algorithm; S4: Correct the output value of the underwater acoustic channel according to the corresponding estimated value of the underwater acoustic channel obtained in step S3, and convert the corrected signal into a modulation symbol in the delay-Doppler domain. , completing the information transmission.

2. The high-speed mobile AUV underwater acoustic communication method based on OTFS according to claim 1 is characterized in that: In step S1, the signal conversion is achieved through the following steps: S1.1, through the inverse sigmoid Fourier transform, the modulation symbol Convert to time-frequency domain signal : ； in, An index representing discrete time and frequency points; Represents the index of the time-frequency grid point after conversion; Indicates the number of Doppler domain subcarriers; Indicates the number of delay domain subcarriers; represents an imaginary unit; Scaling factor representing the phase shift in the frequency domain; S1.2, through Heisenberg transformation Convert to time domain signal : ； in, Indicates time; represents the transmission waveform; represents the total duration or time window of the signal; represents a constant related to Doppler shift or time-frequency shift; Indicates frequency offset.

3. The high-speed mobile AUV underwater acoustic communication method based on OTFS according to claim 1 is characterized in that: The time domain signal Input the underwater acoustic channel, and the output of the underwater acoustic channel is: , in, represents the delay-Doppler domain underwater acoustic channel; Represents the transformed index, usually used to receive signals or transformed grids; Represents the expression of the signal in the time-frequency grid; Represents the noise term of the signal in the time-frequency domain.

4. The high-speed mobile AUV underwater acoustic communication method based on OTFS according to claim 1 is characterized in that: The VSBL channel estimation algorithm in step S3 includes the following steps: S3.

1. Defining variational parameters , and , and initialize the parameters in the above variational parameters, where the parameters represents the underwater acoustic communication vector, and the parameters Represents the hyperparameter vector element, parameter Indicates noise accuracy; S3.

2. Using variational parameters and the variational parameters Variational parameters Make updates; S3.

3. Update the variational parameters obtained using step S3.2 Variational parameters Update and obtain the updated variational parameters ; S3.

4. Update the variational parameters obtained using step S3.2 Variational parameters Update and obtain the updated variational parameters ; S3.5, repeat steps S3.2 to S3.4, and achieve the variational parameters each time. , and An iterative optimization is performed until ELBO converges; After the iteration process is completed, the final channel response estimate is output : 。 5. The high-speed mobile AUV underwater acoustic communication method based on OTFS according to claim 4 is characterized in that: In step S3.1, the parameters The initialization comes from the following formula: ， in, represents the measurement matrix; n represents the noise vector; According to the output of the underwater acoustic channel, obtain the parameters The initial value of parameter , and parameters The initial value of is the identity matrix or the zero matrix.

6. The high-speed mobile AUV underwater acoustic communication method based on OTFS according to claim 4 is characterized in that: In step S3.2, the variational parameter and the variational parameters Variational parameters The formula for updating is: ， in, represents a constant; Indicates the current iteration number, k =1,2,…, , Indicates the maximum number of iterations; Indicates passing k- Parameters after 1 iteration The estimated value of k- 1=0 indicates parameter The initial value of The calculation formula is: ， In the above formula, The calculation formula is: ， The calculation formula is: ， Where A represents a diagonal matrix; The calculation formula is: ， Among them, a represents the corresponding The shape parameter of the Gamma distribution; determines the shape of the distribution and affects the distribution of the probability density function; b represents the corresponding The scale parameter of the Gamma distribution determines the size of the distribution; The calculation formula is: ， in, c Indicates the corresponding The shape parameter of the Gamma distribution; d Indicates the corresponding The scale parameter of the Gamma distribution; According to the above formula, solve the expected value: ； in, The calculation formula is: ； The calculation formula is: ； Using the properties of the Gamma distribution, The calculation formula is: ， The calculation formula is: ， in, Indicates the corresponding The updated value of the shape parameter of the Gamma distribution, Indicates the corresponding Updated values ​​for the shape and scale parameters of the Gamma distribution; The calculation formula is: ； The calculation formula is: ； The calculation formula is: ； in, Indicates the corresponding The updated value of the shape parameter of the Gamma distribution, Indicates the corresponding Updated value of the scale parameter of the Gamma distribution; Substitute the above formula into the expected value calculation formula and ,get: ； ； Variational parameters is a Gaussian distribution, so: ， in, Representation and The mean of the correlation, Representation and The variance of the correlation; The above formula can be derived as follows: ， ， therefore, ， 。 7. The high-speed mobile AUV underwater acoustic communication method based on OTFS according to claim 4 is characterized in that: In step S3.3, the updated variational parameters are used Variational parameters When updating, ， in, Indicates the previous state Under given conditions, the current observation The conditional probability distribution of ; Indicates status The prior probability distribution of ; Represents a constant value; Combined with expected value , ， Get the updated variational parameters : ， in The calculation formula is: ， The calculation formula is: 。 8. The high-speed mobile AUV underwater acoustic communication method based on OTFS according to claim 4 is characterized in that: In step S3.4, the updated variational parameters are used Variational parameters When updating, the updated variational parameters are calculated from the following expected value equation: : ， Updated variational parameters for: ， in, The calculation formula is: ， The calculation formula is: ， in, represents the trace of a matrix, which is the sum of the diagonal elements of the matrix.

9. The high-speed mobile AUV underwater acoustic communication method based on OTFS according to claim 4 is characterized in that: In step S3.5, Estimated channel response The variational parameters after iterative optimization given; The iterative optimization process continues until the change in ELBO between consecutive iterations is less than a predefined threshold. , when the ELBO interpolation value in two consecutive iterations is less than , the iteration process ends; When the number of iterations reaches When , the iteration process ends.

10. The high-speed mobile AUV underwater acoustic communication method based on OTFS according to claim 4, characterized in that: The specific implementation process of step S4 is as follows: S4.

1. The final channel response estimate output by the VSBL channel estimation algorithm , correct the output value of the underwater acoustic channel, and the corrected signal for: ； S4.2, through Wigner transformation, the signal Convert to time domain signal : ； S4.3, through the symplectic Fourier transform, the signal time domain signal Convert to Delay-Doppler Domain Modulation Symbols , and the signal transmission process is completed: 。

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