Mobile underwater acoustic communication multipath channel modeling method based on sound field calculation

Abstract

The invention discloses a mobile underwater acoustic communication multipath channel modeling method based on sound field calculation, and relates to underwater sound waves. Channel modeling is carried out by inputting environmental parameters including an ocean sound velocity profile, submarine topography and the like, and modeling parameters including initial coordinates, motion trail equations and the like of a signal transmitting end and a signal receiving end. Performing ocean sound field calculation by adopting a ray tracing model, a normal wave model or a wave number integral model and the like, and calculating a sound field at each track sampling moment according to modeling parameters. And converting a frequency domain sound field result into a channel impulse response through inverse Fourier transform, and recovering the time-varying impulse response of the whole multipath channel by using local spline interpolation. And carrying out convolution on the transmitted signal and the time-varying impulse response of the multipath channel, and adding common propagation time delay to obtain a received signal simulation result. Through accurate sound field calculation and multipath channel modeling, the signal transmission condition in a specific marine environment can be simulated without actual marine environment measurement, the marine actual measurement cost is reduced, and the research and development efficiency is improved.

Description

Technical Field

[0001] The invention relates to the field of underwater acoustic wave communication, and in particular to a mobile underwater acoustic communication multipath channel modeling method based on acoustic field calculation. Background Art

[0002] With the continuous development and utilization of marine resources, the importance of marine communication technology has become increasingly prominent. However, the complexity and variability of the marine environment poses great challenges to the design and optimization of communication systems. Underwater acoustic multipath channel modeling is one of the key methods to guide the design of marine communication systems and evaluate the performance of marine communication systems. The deterministic underwater acoustic multipath channel modeling method based on the mathematical theory of the Helmholtz equation can become one of the efficient technical means to reduce the input of marine environmental measurements and improve the efficiency of marine communication research and development.

[0003] Traditional marine communication system design and evaluation methods often rely on a large amount of marine environment measurement data, which is not only costly, but also time-consuming and labor-intensive. Developing a modeling method that can simulate signal transmission conditions in a specific marine environment is of great significance for reducing the cost of marine measurement and improving R&D efficiency. Summary of the invention

[0004] The purpose of the present invention is to provide a mobile underwater acoustic communication multipath channel modeling method based on acoustic field calculation that can simulate the signal transmission situation in a specific ocean environment, in view of the fact that ocean measurement requires a lot of manpower, material resources and time in the design process of ocean communication systems. Through accurate acoustic field calculation and multipath channel modeling, this method can simulate the signal transmission situation in a specific ocean environment without the need for actual ocean environment measurement, thereby significantly reducing the cost of ocean measurement and improving research and development efficiency.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A mobile underwater acoustic communication multipath channel modeling method based on acoustic field calculation, comprising:

[0007] S1: Channel modeling parameter setting: input modeling parameters, including environmental parameters such as ocean sound velocity profile, seabed topography, and motion trajectory equations of the starting coordinates of the signal transmitter and receiver and the coordinates that change over time. It is also necessary to set parameters such as the sampling interval of the motion trajectory for channel modeling;

[0008] S2: Ocean acoustic field calculation: Select the kernel of the channel modeling method according to the requirements of the ocean environment: ray tracing model, simple normal wave model and wave number integration model, initialize the relevant parameters of the selected kernel, and generate the environment files required by different kernels as input based on these parameters, and calculate the acoustic field at each trajectory sampling moment according to the modeling parameters;

[0009] S3: Calculate the channel impulse response: The frequency domain sound field result is converted into the channel impulse response at the trajectory sampling time through inverse Fourier transform. Due to the movement of the transmitter and the receiver, there is a delay offset in the channel impulse response at adjacent trajectory sampling points. In order to accurately simulate the change of the channel, the arrival delay of the channel impulse response at each point is aligned to ensure the continuity of the channel impulse response; After alignment, the time-varying impulse response of the overall multipath channel is restored according to the sampling rate of the transmitted signal using local spline interpolation;

[0010] S4: Digital signal processing: Convolve the transmitted signal with the time-varying impulse response of the multipath channel obtained in step S3, simulate the propagation process of the signal in the channel, and fill the result with zeros to add the common propagation delay to obtain the final received signal simulation result.

[0011] Furthermore, the step S1 includes the following steps:

[0012] First, set the parameters related to the transmitted signal, including the signal waveform file name, center frequency, bandwidth, and sampling rate;

[0013] Secondly, input basic environmental parameters, including water body sound velocity profile data, seabed topography file name, starting coordinates of the signal transmitter and receiver, and coordinate motion trajectory equations, etc.;

[0014] Then, set the necessary parameters required for model calculation, including the selected kernel name, related parameters of different kernels, and simulation time;

[0015] Finally, according to the relevant parameters of the transmitted signal and the motion trajectory equation of the transmitter / receiver, the trajectory sampling point interval is calculated. The calculation formula is as follows:

[0016]

[0017]

[0018] In the formula, is the time interval of trajectory sampling points, is the horizontal displacement distance that results in the maximum amplitude frequency shift in the channel frequency response, is the movement speed of the transmitter / receiver, is the sampling period of the transmitted signal, is the multipath delay spread of the channel, is the initial distance between the transmitter and the receiver.

[0019] Furthermore, the step S2 comprises the following steps:

[0020] First, according to the marine environment requirements, the appropriate channel modeling method kernel is selected and the kernel related parameters are initialized. The model will generate environment files of different kernels based on the parameters as input;

[0021] Secondly, the sound field at each trajectory sampling point is calculated to prepare for the subsequent calculation of the channel impulse response:

[0022] The calculation methods of different model kernels are all based on solving the wave equation from different angles.

[0023] If the ray tracing model is chosen as the kernel, the Helmholtz equation can be expressed as:

[0024]

[0025] In the formula, Indicates the sound pressure, is the second-order partial derivative of the sound pressure in space, is the speed of sound, yes The angular frequency of the sound source at is the Dirac function, which indicates that the sound source is at position To obtain the ray equation, we seek a solution to the Helmholtz equation in series form:

[0026]

[0027] in, represents the phase delay, represents the amplitude, is the index of the series expansion term. This formula is usually divergent, but in some cases it is an asymptotic approximation to the exact solution, and its derivative gives:

[0028]

[0029] in, , denote the gradient of phase delay and amplitude respectively, , Denote the second-order partial derivatives of phase delay and amplitude respectively. Substituting the above formula into the Helmholtz equation, we get The terms of the same order are equal, and we can simplify the eikonal equation to get:

[0030]

[0031] And the migration equation:

[0032]

[0033] is the zeroth-order coefficient, representing the zeroth-order approximation of the sound field. By solving the eikonal equation, the propagation time along the sound line, that is, the delay of the wave phase, can be obtained; by solving the migration equation, the amplitude information of the sound line can be obtained. Therefore, by selecting the ray tracing model as the kernel, the multipath delay distribution and amplitude of the underwater acoustic channel at each trajectory sampling point can be directly obtained.

[0034] If the normal wave model is chosen as the kernel, the sound field is represented as separate variables in the horizontal and vertical directions:

[0035]

[0036] In the formula, is the horizontal distance, is depth, is the modal number, is the modal function, is the modal amplitude, represents the radial wave propagation term, is the wave number. Substitute the separated variable form into the Helmholtz equation and process the depth direction to obtain the vertical direction equation of the simple normal wave:

[0037]

[0038] represents the local propagation velocity of the wave in the vertical direction, It is the second-order spatial derivative in the vertical direction, describing the curvature of the waveform in this direction. represents the angular frequency, This term represents the difference in effective wave numbers and reflects the propagation characteristics in the medium.

[0039] At the sea surface and the seabed, the corresponding boundary conditions need to be met. Common boundary conditions include:

[0040] Sea surface: free boundary conditions, ;

[0041] Seabed: Depending on the characteristics of the bottom, it may be a free boundary, a rigid boundary, or other types of boundary conditions.

[0042] The eigenvalue can be solved by solving the above differential equations with the finite difference method or Sturm method combined with boundary conditions. and characteristic function , the sound field at each position can be obtained by superimposing all modes. Therefore, choosing the simple normal wave model as the kernel can obtain the sound pressure field at each trajectory sampling point.

[0043] If the wavenumber integral model is selected as the kernel, the sound field can be decomposed into horizontal and vertical integral forms:

[0044]

[0045] in, is the sound pressure in the spatial domain, is the horizontal distance, is depth, is the horizontal wave number, is the sound pressure in the wavenumber domain. Substituting this into the Helmholtz equation and simplifying it in the depth direction, we obtain the ordinary differential equation in the vertical direction:

[0046]

[0047] The above equation is an eigenvalue problem. By solving the eigenvalue and eigenfunction, we can get the modal function in the vertical direction. and the corresponding wave number , the specific form is:

[0048]

[0049] in, is the eigenvalue of the horizontal wavenumber. The results in the wavenumber domain are converted back to the physical space by numerical integration in combination with the corresponding boundary conditions:

[0050]

[0051] In the formula, is the modal amplitude, which is determined by the initial conditions. Therefore, the wave number integral model is selected as the kernel to obtain the sound pressure field value at each trajectory sampling point.

[0052] Furthermore, step S3 includes the following steps:

[0053] First, to find the delay offset ∆ between two consecutive trace sampling points, align the channel impulse responses at adjacent trace sampling points, as follows:

[0054]

[0055]

[0056] In the formula, and They are trajectory sampling points and trajectory sampling points On frequency The frequency response under the condition is effectively estimated through the binary search algorithm, and the frequency response at each sampling point is obtained to obtain the delay offset. ;

[0057] Subsequently, the delay offset results are integrated into the channel impulse response of each trajectory sampling point, and the time-varying impulse response of the overall multipath channel is restored according to the transmission signal sampling rate using local spline interpolation.

[0058] Furthermore, the step S4 comprises the following steps:

[0059] First, the transmit signal is convolved with the channel impulse response obtained in step S3;

[0060] Afterwards, the number of samples is padded with 0 at the beginning of the convolution result so that the result has the correct signal length including the common propagation delay, and the final simulation result is obtained.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] 1. Significantly reduce the cost of ocean measurement: Traditional ocean communication system design and evaluation often rely on a large amount of ocean environment measurement data, which not only requires high human and material investment, but also takes a lot of time. However, the present invention can simulate the signal transmission situation in a specific ocean environment without the need for actual ocean environment measurement through accurate sound field calculation and multipath channel modeling, thereby greatly reducing costs.

[0063] 2. Improve R&D efficiency: With the modeling method of the present invention, researchers can quickly build a simulation model that is highly similar to the actual ocean environment, and then quickly evaluate and optimize the performance of the ocean communication system. It greatly shortens the R&D cycle, improves R&D efficiency, and helps accelerate the development of ocean communication technology. The mobile underwater acoustic communication multipath channel modeling method based on sound field calculation provided by the present invention integrates the impact of the ocean environment, hydroacoustic theory, and digital signal processing theory, and can simulate the signal transmission situation when the transmitter and receiver are moving in a specific ocean environment.

[0064] 3. The present invention provides three different model kernels: ray tracing model, simple normal wave model and wave number integral model. These models can adapt to transmission signals of different frequency bands and marine environments of different depths. Therefore, whether in shallow sea, deep sea or complex and changeable seabed terrain environment, the present invention can provide accurate channel modeling results, with strong adaptability and wide application scope. It can adapt to transmission signals of different frequency bands and marine environments of different depths, further improving the accuracy and authenticity of simulation results.

[0065] 4. The present invention integrates the impact of the marine environment, hydroacoustic theory and digital signal processing theory, and can achieve accurate simulation of signal transmission when the transmitter and receiver are moving through accurate sound field calculation and multipath channel modeling. The simulation results not only reflect the propagation process of the signal in the channel, but also contain key information such as common propagation delay, with high accuracy.

[0066] 5. The successful implementation of the present invention not only helps to solve the technical problems in the design process of the marine communication system, but also provides strong technical support for the further development of marine communication technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 The present invention is a general flow chart of the method for modeling multipath channels of mobile underwater acoustic communication based on sound field calculation.

[0068] Figure 2 The present invention provides a motion trajectory diagram constructed according to the relative motion of the transmitting end and the receiving end. Among them, (a) the transmitting end moves toward the receiving end at a horizontal speed of 6 m / s, and the receiving end is stationary; (b) the motion trajectory of the receiving end under the condition of (a); (c) the transmitting end moves at a uniform speed from south to north at a speed of 6 m / s, and the receiving end moves toward the transmitting end at a horizontal speed of 6 m / s; (d) the motion trajectory of the receiving end under the condition of (c); (e) the transmitting end makes a regular wreath motion, and the receiving end moves toward the transmitting end at a horizontal speed of 6 m / s; (f) the motion trajectory of the receiving end under the condition of (e).

[0069] Figure 3 The Doppler frequency shift-time diagrams calculated by different model kernels for the same Qiandao Lake environmental conditions are given to characterize the multipath distribution and Doppler phenomenon of the calculation results. Among them, (a) the ray tracing model is selected as the result obtained by the kernel; (b) the simple normal wave model is selected as the result obtained by the kernel; (c) the wave number integration model is selected as the result obtained by the kernel.

[0070] Figure 4 The time-delay diagrams obtained by running different model kernels in the Qiandao Lake environment and under different frequency conditions are given to characterize the channel impulse response of the simulation results. Among them, (a) the result obtained when the ray tracing model is selected as the kernel and the center frequency is 12500Hz; (b) the result obtained when the simple normal wave model is selected as the kernel and the center frequency is 2500Hz; (c) the result obtained when the wave number integration model is selected as the kernel and the center frequency is 2500Hz. DETAILED DESCRIPTION

[0071] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following embodiments will further illustrate the present invention in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. On the contrary, the present invention covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present invention as defined by the claims.

[0072] Please refer to Figure 1, a mobile underwater acoustic communication multipath channel modeling method based on acoustic field calculation includes the following steps:

[0073] S1: channel modeling parameter setting;

[0074] S2: Ocean acoustic field calculation;

[0075] S3: Calculate channel impulse response;

[0076] S4: Digital signal processing;

[0077] Furthermore, the step S1 includes the following steps:

[0078] First, set the parameters related to the transmitted signal, including the signal waveform file name, center frequency, bandwidth, and sampling rate;

[0079] Secondly, input basic environmental parameters, including water body sound velocity profile data, seabed topography file name, starting coordinates of the signal transmitter and receiver, and coordinate motion trajectory equations, etc.;

[0080] Then, set the necessary parameters required for model calculation, including the selected kernel name, related parameters of different kernels, and simulation time;

[0081] Finally, according to the relevant parameters of the transmitted signal and the motion trajectory equation of the transmitter / receiver, the trajectory sampling point interval is calculated. The calculation formula is as follows:

[0082]

[0083]

[0084] In the formula, is the time interval of trajectory sampling points, is the horizontal displacement distance that results in the maximum amplitude frequency shift in the channel frequency response, is the movement speed of the transmitter / receiver, is the sampling period of the transmitted signal, is the multipath delay spread of the channel, is the initial distance between the transmitter and the receiver.

[0085] Furthermore, the step S2 comprises the following steps:

[0086] First, according to the marine environment requirements, the appropriate channel modeling method kernel is selected and the kernel related parameters are initialized. The model will generate environment files of different kernels based on the parameters as input;

[0087] Secondly, the sound field at each trajectory sampling point is calculated to prepare for the subsequent calculation of the channel impulse response:

[0088] The calculation methods of different model kernels are all based on solving the wave equation from different angles.

[0089] If the ray tracing model is chosen as the kernel, the Helmholtz equation can be expressed as:

[0090]

[0091] In the formula, Indicates the sound pressure, is the second-order partial derivative of the sound pressure in space, is the speed of sound, yes The angular frequency of the sound source at is the Dirac function, which represents a point source at position 𝑥0. To obtain the ray equation, we seek a solution to the Helmholtz equation in series form:

[0092]

[0093] in, represents the phase delay, represents the amplitude, is the index of the series expansion term. This formula is usually divergent, but in some cases it is an asymptotic approximation to the exact solution, and its derivative gives:

[0094]

[0095] in, , denote the gradient of phase delay and amplitude respectively, , Denote the second-order partial derivatives of phase delay and amplitude respectively. Substituting the above formula into the Helmholtz equation, we get The terms of the same order are equal, and we can simplify the eikonal equation to get:

[0096]

[0097] And the migration equation:

[0098]

[0099] is the zeroth-order coefficient, representing the zeroth-order approximation of the sound field. By solving the eikonal equation, the propagation time along the sound line, that is, the delay of the wave phase, can be obtained; by solving the migration equation, the amplitude information of the sound line can be obtained. Therefore, by selecting the ray tracing model as the kernel, the multipath delay distribution and amplitude of the underwater acoustic channel at each trajectory sampling point can be directly obtained.

[0100] If the normal wave model is chosen as the kernel, the sound field is represented as separate variables in the horizontal and vertical directions:

[0101]

[0102] In the formula, is the horizontal distance, is depth, is the modal number, is the modal function, is the modal amplitude, represents the radial wave propagation term, is the wave number. Substitute the separated variable form into the Helmholtz equation and process the depth direction to obtain the vertical direction equation of the simple normal wave:

[0103]

[0104] represents the local propagation velocity of the wave in the vertical direction, It is the second-order spatial derivative in the vertical direction, describing the curvature of the waveform in this direction. represents the angular frequency, This term represents the difference in effective wave numbers and reflects the propagation characteristics in the medium.

[0105] At the sea surface and the seabed, the corresponding boundary conditions need to be met. Common boundary conditions include:

[0106] Sea surface: free boundary conditions, ;

[0107] Seabed: Depending on the characteristics of the bottom, it may be a free boundary, a rigid boundary, or other types of boundary conditions.

[0108] The eigenvalue can be solved by solving the above differential equations with the finite difference method or Sturm method combined with boundary conditions. and characteristic function , the sound field at each position can be obtained by superimposing all modes. Therefore, the simple normal wave model is selected as the kernel to obtain the sound pressure field at each trajectory sampling point.

[0109] If the wavenumber integral model is selected as the kernel, the sound field can be decomposed into horizontal and vertical integral forms:

[0110]

[0111] in, is the sound pressure in the spatial domain, is the horizontal distance, is depth, is the horizontal wave number, is the sound pressure in the wavenumber domain. Substituting this into the Helmholtz equation and simplifying it in the depth direction, we obtain the ordinary differential equation in the vertical direction:

[0112]

[0113] The above equation is an eigenvalue problem. By solving the eigenvalue and eigenfunction, we can get the modal function in the vertical direction. and the corresponding wave number , the specific form is:

[0114]

[0115] in, is the eigenvalue of the horizontal wavenumber. The results in the wavenumber domain are converted back to the physical space by numerical integration in combination with the corresponding boundary conditions:

[0116]

[0117] In the formula, is the modal amplitude, which is determined by the initial conditions. Therefore, the wave number integral model is selected as the kernel to obtain the sound pressure field value at each trajectory sampling point.

[0118] Furthermore, step S3 includes the following steps:

[0119] First, to find the delay offset ∆ between two consecutive trace sampling points, align the channel impulse responses at adjacent trace sampling points, as follows:

[0120]

[0121]

[0122] In the formula, and They are trajectory sampling points and trajectory sampling points On frequency The model uses a binary search algorithm to effectively estimate the frequency response at each sampling point and obtain the delay offset. ;

[0123] Subsequently, the delay offset results are integrated into the channel impulse response of each trajectory sampling point, and the time-varying impulse response of the overall multipath channel is restored according to the transmission signal sampling rate using local spline interpolation.

[0124] Furthermore, the step S4 comprises the following steps:

[0125] First, the transmit signal is convolved with the channel impulse response obtained in step S3;

[0126] Afterwards, the number of samples is padded with 0 at the beginning of the convolution result so that the result has the correct signal length including the common propagation delay, and the final simulation result is obtained.

[0127] Figure 2 The present invention provides a motion trajectory diagram constructed according to the relative motion of the transmitter and the receiver. Among them, (a) the transmitter moves toward the receiver at a horizontal speed of 6 m / s, and the receiver is stationary; (b) the motion trajectory of the receiver under the condition of (a); (c) the transmitter moves at a uniform speed of 6 m / s from south to north, and the receiver moves toward the transmitter at a horizontal speed of 6 m / s; (d) the motion trajectory of the receiver under the condition of (c); (e) the transmitter makes a regular wreath motion, and the receiver moves toward the transmitter at a horizontal speed of 6 m / s; (f) the motion trajectory of the receiver under the condition of (e); Figure 2 It can be seen that the present invention can better describe the relative motion of the transmitting end and the receiving end.

[0128] Figure 3 The Doppler frequency shift-time diagrams calculated by different model kernels for the same Qiandao Lake environmental conditions are given to characterize the multipath distribution and Doppler phenomenon of the calculation results. Among them, (a) the ray tracing model is selected as the result of the kernel; (b) the simple normal wave model is selected as the result of the kernel; (c) the wave number integral model is selected as the result of the kernel; Figure 3 It can be seen that the Doppler frequency shift range of the results obtained by different model kernels is all between 0.1 and 0.35 Hz, which verifies the consistency and effectiveness of different model kernels. The differences between different model kernels in weak multipath can be attributed to the calculation errors of ray tracing theory and normal wave theory for the low-frequency sound wave propagation process.

[0129] Figure 4 The time-delay diagrams obtained by running different model kernels in the Qiandao Lake environment and under different frequency conditions are given to characterize the channel impulse response of the simulation results. Among them, (a) the result obtained when the ray tracing model is selected as the kernel and the center frequency is 12500Hz; (b) the result obtained when the simple normal wave model is selected as the kernel and the center frequency is 2500Hz; (c) the result obtained when the wave number integral model is selected as the kernel and the center frequency is 2500Hz. Figure 4 It can be seen that the main arrival paths of the results obtained by different model kernels are all 3, and the delay spread is about 15 ms. The three model kernels can accurately describe the propagation behavior of sound waves underwater. Due to the different center frequencies of the transmitted signals, the wavelength is longer under low-frequency conditions, and the single path is relatively wide. In addition, the normal wave theory cannot accurately track the propagation path of the sound wave, so there is an error between the arrival delay of the first arrival path and the results obtained by the ray tracing method.

[0130] The mobile underwater acoustic communication multipath channel modeling method based on acoustic field calculation provided by the present invention integrates the influence of the marine environment, the theory of underwater acoustics and the theory of digital signal processing, and can simulate the signal transmission situation when the transmitter and the receiver are moving in a specific marine environment. The method can simulate the time-varying underwater acoustic multipath channels generated by the transmitter and the receiver at different depths under different motion trajectory conditions in the global marine environment, and then simulate the transmission of underwater acoustic signals.

[0131] The above embodiments are only preferred embodiments of the present invention and cannot be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the present invention.

Claims

1. A method for modeling multipath channels of mobile underwater acoustic communication based on acoustic field calculation, characterized in that The following steps are involved: S1: Channel modeling parameter setting: input modeling parameters, including ocean sound velocity profile, seabed terrain environment parameters, starting coordinates of the signal transmitter and receiver, motion trajectory equations of coordinates that change over time, and sampling intervals of motion trajectories for channel modeling; S2: Ocean acoustic field calculation: Select the kernel of the channel modeling method according to the requirements of the ocean environment: ray tracing model, simple normal wave model and wave number integration model, initialize the relevant parameters of the selected kernel, and generate the environment files required by different kernels as input based on these parameters, and calculate the acoustic field at each trajectory sampling moment according to the modeling parameters; S3: Calculate the channel impulse response: Through inverse Fourier transform, the frequency domain sound field result is converted into the channel impulse response at the trajectory sampling time, and the arrival delay of the channel impulse response at each point is aligned to ensure the continuity of the channel impulse response; After alignment, the time-varying impulse response of the overall multipath channel is restored according to the sampling rate of the transmitted signal using local spline interpolation; S4: Digital signal processing: Convolve the transmitted signal with the time-varying impulse response of the multipath channel obtained in step S3, simulate the propagation process of the signal in the channel, and fill the result with zeros to add the common propagation delay to obtain the final received signal simulation result.

2. The method for modeling multipath channels of mobile underwater acoustic communication based on sound field calculation according to claim 1 is characterized in that In step S1, the channel modeling parameter setting includes the following steps: (1) Set the parameters related to the transmission signal, including the signal waveform file name, center frequency, bandwidth, and sampling rate; (2) Input basic environmental parameters, including water body sound velocity profile data, seabed topography file name, starting coordinates of the signal transmitter and receiver, and the coordinate motion trajectory equation; (3) Set the necessary parameters required for model calculation, including the selected kernel name, relevant parameters of different kernels, and simulation time; (4) According to the relevant parameters of the transmitted signal and the motion trajectory equation of the transmitter / receiver, the trajectory sampling point interval is calculated. The calculation formula is as follows: In the formula, is the time interval of trajectory sampling points, is the horizontal displacement distance that results in the maximum amplitude frequency shift in the channel frequency response, is the movement speed of the transmitter / receiver, is the sampling period of the transmitted signal, is the multipath delay spread of the channel, is the initial distance between the transmitter and the receiver.

3. The method for modeling multipath channels of mobile underwater acoustic communication based on sound field calculation according to claim 1 is characterized in that In step S2, the ocean sound field calculation includes the following steps: (1) Select the appropriate channel modeling method kernel according to the marine environment requirements and initialize the kernel related parameters. The model will generate environment files of different kernels based on the parameters as input; (2) Calculate the sound field at each trajectory sampling point to prepare for the subsequent calculation of the channel impulse response: The calculation methods of different model kernels are based on solving the wave equation from different angles; If the ray tracing model is chosen as the kernel, the Helmholtz equation is expressed as: In the formula, Indicates the sound pressure, is the second-order partial derivative of the sound pressure in space, is the speed of sound, yes The angular frequency of the sound source at is the Dirac function, which indicates that the sound source is at position A point source at To obtain the ray equation, find a solution to the Helmholtz equation in series form: in, represents the phase delay, represents the amplitude, is the index of the series expansion term; this formula is usually divergent, but in some cases it is an asymptotic approximation to the exact solution, and its differentiation yields: in, , denote the gradient of phase delay and amplitude respectively, , Denote the second-order partial derivatives of phase delay and amplitude respectively. Substituting the above formula into the Helmholtz equation, we get The terms of the same order are equal, and the eikonal equation is simplified to: And the migration equation: is the zeroth-order coefficient, representing the zeroth-order approximation of the sound field; by solving the eikonal equation, the propagation time along the sound line, that is, the delay of the wave phase, is obtained; by solving the migration equation, the amplitude information of the sound line is obtained; therefore, the ray tracing model is selected as the kernel to directly obtain the multipath delay distribution and amplitude of the underwater acoustic channel at each trajectory sampling point; If the normal wave model is chosen as the kernel, the sound field is represented as separate variables in the horizontal and vertical directions: In the formula, is the horizontal distance, is depth, is the modal number, is the modal function, is the modal amplitude, represents the radial wave propagation term, is the wave number; substitute the separated variable form into the Helmholtz equation and process the depth direction to obtain the vertical direction equation of the simple normal wave: in, represents the local propagation velocity of the wave in the vertical direction, It is the second-order spatial derivative in the vertical direction, describing the curvature of the waveform in this direction. represents the angular frequency, This term represents the difference in effective wave numbers, reflecting the propagation characteristics in the medium; At the sea surface and the seabed, the corresponding boundary conditions need to be met; common boundary conditions include: Sea surface: free boundary conditions, ; Seabed: Depending on the characteristics of the bottom, it can be a free boundary, a rigid boundary, or other types of boundary conditions; The above differential equations are solved by finite difference method or Sturm method combined with boundary conditions to obtain the eigenvalues and characteristic function , superimposing all modes will get the sound field at each position; therefore, the simple normal wave model is selected as the kernel to get the sound pressure field at each trajectory sampling point; If the wavenumber integral model is selected as the kernel, the sound field is decomposed into horizontal and vertical integral forms: in, is the sound pressure in the spatial domain, is the horizontal distance, is depth, is the horizontal wave number, is the sound pressure in the wavenumber domain; substituting this into the Helmholtz equation and simplifying it in the depth direction, we obtain the ordinary differential equation in the vertical direction: The above equation is an eigenvalue problem. By solving the eigenvalue and eigenfunction, we can get the modal function in the vertical direction. and the corresponding wave number , the specific form is: in, is the eigenvalue of the horizontal wavenumber; the result in the wavenumber domain is converted back to the physical space by numerical integration in combination with the corresponding boundary conditions: In the formula, is the modal amplitude, which is determined by the initial conditions; therefore, the wavenumber integration model is selected as the kernel to obtain the sound pressure field value at each trajectory sampling point.

4. The method for modeling multipath channels of mobile underwater acoustic communication based on sound field calculation according to claim 1 is characterized in that In step S3, the calculating of the channel impulse response comprises the following steps: (1) To find the delay offset between two consecutive trajectory sampling points , align the channel impulse responses on adjacent trajectory sampling points, and the calculation formula is as follows: In the formula, and They are trajectory sampling points and trajectory sampling points On frequency The frequency response under the condition is effectively estimated through the binary search algorithm, and the frequency response at each sampling point is obtained to obtain the delay offset. ; (2) The delay offset result is integrated into the channel impulse response of each trajectory sampling point, and the time-varying impulse response of the overall multipath channel is restored according to the transmission signal sampling rate using local spline interpolation.

5. The method for modeling multipath channels of mobile underwater acoustic communication based on sound field calculation according to claim 1 is characterized in that In step S4, the digital signal processing comprises the following steps: (1) Convolve the transmitted signal with the channel impulse response obtained in step S3; (2) Pad the beginning of the convolution result with 0 samples so that the result has the correct signal length including the common propagation delay, and obtain the final simulation result.

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