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

Abstract

A multipath channel modeling method for mobile underwater acoustic communication based on sound field calculation is presented, involving underwater sound waves. Channel modeling is performed by inputting environmental parameters including ocean sound velocity profiles and seabed topography, as well as modeling parameters such as the initial coordinates and trajectory equations of the signal transmitter and receiver. Ocean sound field calculations are performed using kernels such as ray tracing models, normal mode models, or wavenumber integral models, calculating the sound field at each trajectory sampling time based on the modeling parameters. The frequency domain sound field results are converted into a channel impulse response using inverse Fourier transform, and the time-varying impulse response of the overall multipath channel is recovered using local spline interpolation. The transmitted signal is convolved with the time-varying impulse response of the multipath channel, and a common propagation delay is added to obtain the simulation results of the received signal. Through accurate sound field calculation and multipath channel modeling, signal transmission under specific marine environments can be simulated without actual marine environmental measurements, reducing marine field testing costs and improving R&D efficiency.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic communication, and more particularly to a method for multipath channel modeling of mobile underwater acoustic communication based on sound field calculation. Background Technology

[0002] With the continuous development and utilization of marine resources, the importance of marine communication technology is becoming increasingly prominent. However, the complexity and variability of the marine environment pose significant challenges to the design and optimization of communication systems. Underwater acoustic multipath channel modeling is one of the key methods guiding the design of marine communication systems and evaluating their performance. Deterministic underwater acoustic multipath channel modeling methods based on the mathematical theory of Helmholtz equations can become one of the efficient technical means to reduce the investment in marine environmental measurements and improve the efficiency of marine communication R&D.

[0003] Traditional methods for designing and evaluating marine communication systems often rely on extensive field data of the marine environment, which is not only costly but also time-consuming and labor-intensive. Developing a modeling method that can simulate signal transmission under specific marine conditions is of great significance for reducing the cost of marine field testing and improving research and development efficiency. Summary of the Invention

[0004] The purpose of this invention is to address the problem of significant manpower, material resources, and time investment required for marine field measurements during the design of marine communication systems. It provides a multipath channel modeling method for mobile underwater acoustic communication based on sound field calculation, capable of simulating signal transmission under specific marine environments. This method, through accurate sound field calculation and multipath channel modeling, can simulate signal transmission under specific marine conditions without the need for actual marine environmental measurements, thereby significantly reducing marine field measurement costs and improving R&D efficiency.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for modeling multipath channels in mobile underwater acoustic communication based on sound field calculation, comprising:

[0007] S1: Channel modeling parameter settings: Input modeling parameters, including environmental parameters such as ocean sound velocity profile and seabed topography, as well as the motion trajectory equations of the starting coordinates and time-varying coordinates of the signal transmitter and receiver. You also need 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 marine environment: ray tracing model, normal mode model and wavenumber integral model, initialize the relevant parameters of the selected kernel, and generate the environment file required for different kernels as input based on these parameters, and calculate the acoustic field at each trajectory sampling time according to the modeling parameters.

[0009] S3: Calculate the channel impulse response: Through inverse Fourier transform, the frequency domain sound field results are converted into the channel impulse response at the trajectory sampling time. Due to the movement of the transmitter and receiver, there is a delay offset in the channel impulse response at adjacent trajectory sampling points. In order to accurately simulate the changes in 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 recovered 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 to simulate the signal propagation process in the channel, and pad the result with zeros to add a common propagation delay to obtain the final simulation result of the received signal.

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

[0012] First, set the relevant parameters for 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 the motion trajectory equations of the coordinates, etc.

[0014] Then, set the necessary parameters for model calculation, including the selected kernel name, relevant parameters for different kernels, and simulation duration;

[0015] Finally, based on the relevant parameters of the transmitted signal and the motion trajectory equations of the transmitter / receiver, the trajectory sampling point interval is calculated using the following formula:

[0016]

[0017]

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

[0019] Further, step S2 includes the following steps:

[0020] First, select a suitable channel modeling method kernel based on the requirements of the marine environment, initialize the kernel-related parameters, and the model will generate environment files for different kernels based on the parameters as input.

[0021] Secondly, the sound field at each trajectory sampling point is calculated to prepare for 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 perspectives.

[0023] If we choose the ray tracing model as the kernel, then the Helmholtz equation can be expressed as:

[0024]

[0025] In the formula, Indicates sound pressure level. It is the second partial derivative of sound pressure in space. It's the speed of sound. yes The angular frequency of the sound source. It is the Dirac function, representing the location of the sound source. A point source at a given location. To obtain the ray equation, we seek a solution in the series form of the Helmholtz equation:

[0026]

[0027] in, Represents phase delay, Represents amplitude. This is the index of the terms in the series expansion. This expression is usually divergent, but in some cases it is an asymptotic approximation of the exact solution; its derivative is:

[0028]

[0029] in, , These represent the gradients of phase delay and magnitude, respectively. , Let the second-order partial derivatives of the phase delay and amplitude be represented respectively. Substituting the above equation into the Helmholtz equation, we get... If the terms of the same degree are equal, the equation can be simplified to obtain the functional equation:

[0030]

[0031] And the migration equation:

[0032]

[0033] The zeroth-order coefficients represent the zeroth-order approximation of the sound field. By solving the equation of motion, the propagation time along the sound ray, i.e., the wave phase delay, can be obtained; by solving the migration equation, the amplitude information of the sound ray can be obtained. Therefore, by using 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 mode model is chosen as the kernel, the sound field is represented as a separated variable form in the horizontal and vertical directions:

[0035]

[0036] In the formula, It is the horizontal distance. It's about depth. It is the modal number. It is a modal function. It is the modal amplitude. Represents the radial wave propagation term. This refers to the wave number. Substituting the separated variable form into the Helmholtz equation and processing the depth direction, we obtain the equation for the vertical direction of the normal mode wave:

[0037]

[0038] This represents the local propagation speed of the wave in the vertical direction. It is the second spatial derivative in the vertical direction, describing the curvature of the waveform in that direction. Represents angular frequency. This represents the difference in effective wavenumber, reflecting the propagation characteristics in the medium.

[0039] At the sea surface and seabed, corresponding boundary conditions must be met. Typical boundary conditions include:

[0040] Sea surface: Free boundary conditions ;

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

[0042] The eigenvalues ​​can be obtained by solving the above differential equations using the finite difference method or the Sturm method in conjunction with boundary conditions. and characteristic function By superimposing all modes, the sound field at each location can be obtained. Therefore, choosing the normal mode model as the kernel allows us to obtain the sound pressure field at each trajectory sampling point.

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

[0044]

[0045] in, It refers to sound pressure in the spatial domain. It is the horizontal distance. It's about depth. It is the horizontal wavenumber. This is the sound pressure in the wavenumber domain. Substituting this equation into the Helmholtz equation and simplifying it for the depth direction, we obtain the ordinary differential equation for the vertical direction:

[0046]

[0047] The above equation is an eigenvalue problem. The modal function in the vertical direction can be obtained by solving the eigenvalues ​​and eigenfunctions. and the corresponding wavenumber The specific form is as follows:

[0048]

[0049] in, These are eigenvalues ​​of the horizontal wavenumber. Using appropriate boundary conditions, the results from the wavenumber domain are transformed back to physical space through numerical integration:

[0050]

[0051] In the formula, The modal amplitude is determined by the initial conditions. Therefore, using the wavenumber integral model as the kernel allows us to obtain the sound pressure field value at each trajectory sampling point.

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

[0053] First, to find the delay offset ∆ between two consecutive trajectory sampling points, the channel impulse response on adjacent trajectory sampling points is aligned, and the calculation formula is as follows:

[0054]

[0055]

[0056] In the formula, and These are the trajectory sampling points. and trajectory sampling points On frequency The frequency response at each sampling point is estimated using a binary search algorithm, thereby obtaining 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 recovered by local spline interpolation according to the transmission signal sampling rate.

[0058] Further, step S4 includes the following steps:

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

[0060] Then, zero samples are padded at the beginning of the convolution result to give the result the correct signal length including the common propagation delay, thus obtaining the final simulation result.

[0061] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0062] 1. Significantly Reduced Costs of Marine Real-World Measurements: Traditional marine communication system design and evaluation often rely on a large amount of marine environmental measurement data, which not only requires significant investment of manpower and resources but also consumes a lot of time. This invention, through precise sound field calculations and multipath channel modeling, can simulate signal transmission under specific marine conditions without the need for actual marine environmental measurements, thereby greatly reducing costs.

[0063] 2. Improved R&D Efficiency: Using the modeling method of this invention, researchers can quickly construct simulation models that closely resemble the actual marine environment, enabling rapid evaluation and optimization of the performance of marine communication systems. This significantly shortens the R&D cycle, improves efficiency, and helps accelerate the development of marine communication technology. The mobile underwater acoustic communication multipath channel modeling method based on sound field calculation provided by this invention integrates the influence of the marine environment, underwater acoustics theory, and digital signal processing theory, enabling simulation of signal transmission during the movement of the transmitting and receiving ends in specific marine environments.

[0064] 3. This invention provides three different model kernels—a ray tracing model, a normal mode model, and a wavenumber integral model—each adaptable to different frequency bands of transmitted signals and marine environments at varying depths. Therefore, regardless of whether in shallow waters, deep waters, or complex and varied seabed topography, this invention can provide accurate channel modeling results, exhibiting strong adaptability and a wide range of applications. Its ability to adapt to different frequency bands of transmitted signals and marine environments at varying depths further improves the accuracy and reliability of simulation results.

[0065] 4. This invention integrates the influence of the marine environment, underwater acoustics theory, and digital signal processing theory. Through precise sound field calculation and multipath channel modeling, it can accurately simulate signal transmission when the transmitter and receiver are moving. The simulation results not only reflect the signal propagation process in the channel but also include key information such as common propagation delay, exhibiting high accuracy.

[0066] 5. The successful implementation of this invention not only helps to solve the technical problems in the design process of marine communication systems, but also provides strong technical support for the further development of marine communication technology. Attached Figure Description

[0067] Figure 1 This is a flowchart illustrating the overall process of the multipath channel modeling method for mobile underwater acoustic communication based on sound field calculation, as described in this invention.

[0068] Figure 2 The present invention provides a motion trajectory diagram constructed based on the relative motion of the transmitter and receiver. In diagram (a), the transmitter moves towards the receiver at a horizontal speed of 6 m / s, while the receiver remains stationary; (b) the trajectory of the receiver under condition (a); (c) the transmitter moves uniformly from south to north at a speed of 6 m / s, while the receiver moves towards the transmitter at a horizontal speed of 6 m / s; (d) the trajectory of the receiver under condition (c); (e) the transmitter performs a regular garland motion, while the receiver moves towards the transmitter at a horizontal speed of 6 m / s; and (f) the trajectory of the receiver under condition (e).

[0069] Figure 3 Doppler frequency shift-time plots calculated under the same environmental conditions of Qiandao Lake using different model kernels are presented to characterize the multipath distribution and Doppler phenomenon in the calculation results. Among them, (a) the result obtained by selecting the ray tracing model as the kernel; (b) the result obtained by selecting the normal mode model as the kernel; and (c) the result obtained by selecting the wavenumber integral model as the kernel.

[0070] Figure 4 Time-delay plots of different model kernels running in the Qiandao Lake environment at different frequencies are presented to characterize the channel impulse response of the simulation results. Among them, (a) results are obtained with the ray tracing model as the kernel and a center frequency of 12500Hz; (b) results are obtained with the normal mode model as the kernel and a center frequency of 2500Hz; (c) results are obtained with the wavenumber integral model as the kernel and a center frequency of 2500Hz. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this invention clearer, the following embodiments will be used in conjunction with the accompanying drawings to further illustrate the invention. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Rather, this invention covers any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims.

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

[0073] S1: Channel modeling parameter settings;

[0074] S2: Ocean acoustic field calculation;

[0075] S3: Calculate the channel impulse response;

[0076] S4: Digital Signal Processing;

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

[0078] First, set the relevant parameters for 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 the motion trajectory equations of the coordinates, etc.

[0080] Then, set the necessary parameters for model calculation, including the selected kernel name, relevant parameters for different kernels, and simulation duration;

[0081] Finally, based on the relevant parameters of the transmitted signal and the motion trajectory equations of the transmitter / receiver, the trajectory sampling point interval is calculated using the following formula:

[0082]

[0083]

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

[0085] Further, step S2 includes the following steps:

[0086] First, select a suitable channel modeling method kernel based on the requirements of the marine environment, initialize the kernel-related parameters, and the model will generate environment files for different kernels based on the parameters as input.

[0087] Secondly, the sound field at each trajectory sampling point is calculated to prepare for 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 perspectives.

[0089] If we choose the ray tracing model as the kernel, then the Helmholtz equation can be expressed as:

[0090]

[0091] In the formula, Indicates sound pressure level. It is the second partial derivative of sound pressure in space. It's the speed of sound. yes The angular frequency of the sound source. Let be the Dirac function, representing a point source at position 0. To obtain the ray equation, we seek a series solution to the Helmholtz equation:

[0092]

[0093] in, Represents phase delay, Represents amplitude. This is the index of the terms in the series expansion. This expression is usually divergent, but in some cases it is an asymptotic approximation of the exact solution; its derivative is:

[0094]

[0095] in, , These represent the gradients of phase delay and magnitude, respectively. , Let the second-order partial derivatives of the phase delay and amplitude be represented respectively. Substituting the above equation into the Helmholtz equation, we get... If the terms of the same degree are equal, the equation can be simplified to obtain the functional equation:

[0096]

[0097] And the migration equation:

[0098]

[0099] The zeroth-order coefficients represent the zeroth-order approximation of the sound field. By solving the equation of motion, the propagation time along the sound ray, i.e., the wave phase delay, can be obtained; by solving the migration equation, the amplitude information of the sound ray can be obtained. Therefore, by using 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 mode model is chosen as the kernel, the sound field is represented as a separated variable form in the horizontal and vertical directions:

[0101]

[0102] In the formula, It is the horizontal distance. It's about depth. It is the modal number. It is a modal function. It is the modal amplitude. Represents the radial wave propagation term. This refers to the wave number. Substituting the separated variable form into the Helmholtz equation and processing the depth direction, we obtain the equation for the vertical direction of the normal mode wave:

[0103]

[0104] This represents the local propagation speed of the wave in the vertical direction. It is the second spatial derivative in the vertical direction, describing the curvature of the waveform in that direction. Represents angular frequency. This represents the difference in effective wavenumber, reflecting the propagation characteristics in the medium.

[0105] At the sea surface and seabed, corresponding boundary conditions must be met. Typical boundary conditions include:

[0106] Sea surface: Free boundary conditions ;

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

[0108] The eigenvalues ​​can be obtained by solving the above differential equations using the finite difference method or the Sturm method in conjunction with boundary conditions. and characteristic function By superimposing all modes, the sound field at each location can be obtained. Therefore, using the normal mode model as the kernel can yield the sound pressure field at each trajectory sampling point.

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

[0110]

[0111] in, It refers to sound pressure in the spatial domain. It is the horizontal distance. It's about depth. It is the horizontal wavenumber. This is the sound pressure in the wavenumber domain. Substituting this equation into the Helmholtz equation and simplifying it for the depth direction, we obtain the ordinary differential equation for the vertical direction:

[0112]

[0113] The above equation is an eigenvalue problem. The modal function in the vertical direction can be obtained by solving the eigenvalues ​​and eigenfunctions. and the corresponding wavenumber The specific form is as follows:

[0114]

[0115] in, These are eigenvalues ​​of the horizontal wavenumber. Using appropriate boundary conditions, the results from the wavenumber domain are transformed back to physical space through numerical integration:

[0116]

[0117] In the formula, The modal amplitude is determined by the initial conditions. Therefore, using the wavenumber integral model as the kernel allows us to obtain the sound pressure field value at each trajectory sampling point.

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

[0119] First, to find the delay offset ∆ between two consecutive trajectory sampling points, the channel impulse response on adjacent trajectory sampling points is aligned, and the calculation formula is as follows:

[0120]

[0121]

[0122] In the formula, and These are the trajectory sampling points. and trajectory sampling points On frequency The model effectively estimates the frequency response at each sampling point using a binary search algorithm, thereby obtaining 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 recovered by local spline interpolation according to the transmission signal sampling rate.

[0124] Further, step S4 includes the following steps:

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

[0126] Then, zero samples are padded at the beginning of the convolution result to give the result the correct signal length including the common propagation delay, thus obtaining the final simulation result.

[0127] Figure 2 The present invention provides a motion trajectory diagram constructed based on the relative motion of the transmitter and receiver. In this diagram, (a) the transmitter moves towards the receiver at a horizontal velocity of 6 m / s, while the receiver remains stationary; (b) the trajectory of the receiver under condition (a); (c) the transmitter moves uniformly from south to north at a velocity of 6 m / s, while the receiver moves towards the transmitter at a horizontal velocity of 6 m / s; (d) the trajectory of the receiver under condition (c); (e) the transmitter performs a regular garland motion, while the receiver moves towards the transmitter at a horizontal velocity of 6 m / s; and (f) the trajectory of the receiver under condition (e). Figure 2 As can be seen, the present invention can describe the relative motion of the transmitter and receiver in a good way.

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

[0129] Figure 4 Time-delay plots of different model kernels running in the Qiandao Lake environment at different frequencies are presented to characterize the channel impulse response of the simulation results. Specifically, (a) results are obtained using the ray tracing model as the kernel at a center frequency of 12500Hz; (b) results are obtained using the normal mode model as the kernel at a center frequency of 2500Hz; and (c) results are obtained using the wavenumber integral model as the kernel at a center frequency of 2500Hz. Figure 4 It can be seen that the main arrival paths obtained from different model kernels are all three, with a time delay spread of approximately 15 ms. All 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 at lower frequencies, resulting in a relatively wider single path. Furthermore, the normal mode theory cannot accurately trace the propagation path of the sound wave; therefore, the arrival delay of the first arrival path and the results obtained from the ray tracing method contain errors.

[0130] The multipath channel modeling method for mobile underwater acoustic communication based on sound field calculation provided by this invention integrates the influence of the marine environment, underwater acoustic theory, and digital signal processing theory. It can simulate the signal transmission situation when the transmitter and receiver are moving in a specific marine environment. This method can simulate the time-varying underwater acoustic multipath channels generated by transmitters and receivers at different depths under different motion trajectories in a global marine environment, thereby simulating the transmission of underwater acoustic signals.

[0131] 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 method for modeling multipath channels in mobile underwater acoustic communication based on sound field calculation, characterized in that... Includes the following steps: S1: Channel modeling parameter settings: Input modeling parameters, including ocean sound velocity profile, seabed topography and environmental parameters, starting coordinates of the signal transmitter and receiver, motion trajectory equations of coordinates changing over time, and sampling interval of the motion trajectory for channel modeling; The channel modeling parameter settings include the following steps: (1) Set the relevant parameters of the transmitted 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 motion trajectory equation of the coordinates; (3) Set the necessary parameters for model calculation, including the selected kernel name, relevant parameters of different kernels, and simulation duration; (4) Calculate the trajectory sampling point interval based on the relevant parameters of the transmitted signal and the motion trajectory equations of the transmitting / receiving end. The calculation formula is as follows: In the formula, The time interval between trajectory sampling points. The horizontal shift distance that causes the maximum amplitude frequency shift in the channel frequency response. The speed of movement of the transmitter / receiver The sampling period of the transmitted signal. For multipath delay spread of the channel, This is the initial distance between the transmitter and receiver; S2: Ocean acoustic field calculation: Select the kernel of the channel modeling method according to the requirements of the marine environment: ray tracing model, normal mode model and wavenumber integral model, initialize the relevant parameters of the selected kernel, and generate the environment file required for different kernels as input based on these parameters, and calculate the acoustic field at each trajectory sampling time according to the modeling parameters. The ocean acoustic field calculation includes the following steps: (1) Select the appropriate channel modeling method kernel according to the requirements of the marine environment, initialize the kernel-related parameters, and 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 subsequent calculation of the channel impulse response: The computational methods of different model kernels are all based on solving the wave equation from different perspectives; If the ray tracing model is chosen as the kernel, the Helmholtz equation is expressed as: In the formula, Indicates sound pressure level. It is the second partial derivative of sound pressure in space. It's the speed of sound. yes The angular frequency of the sound source. It is the Dirac function, representing the location of the sound source. A point source at that location; To obtain the ray equation, we need to find a solution in the series form of the Helmholtz equation: in, Represents phase delay, Represents amplitude. It is the index of the series expansion term; this expression is usually divergent, but in some cases it is an asymptotic approximation of the exact solution, and its derivative is: in, , These represent the gradients of phase delay and magnitude, respectively. , Let the second-order partial derivatives of the phase delay and amplitude be represented respectively. Substituting the above equation into the Helmholtz equation, we get... Since terms of the same degree are equal, we can simplify to obtain the equation: And the migration equation: The zeroth-order coefficients represent the zeroth-order approximation of the sound field. By solving the equation of process function, the propagation time along the sound ray, i.e. the wave phase delay, is obtained. By solving the migration equation, the amplitude information of the sound ray 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 mode model is chosen as the kernel, the sound field is represented as a separated variable form in the horizontal and vertical directions: In the formula, It is the horizontal distance. It's about depth. It is the modal number. It is a modal function. It is the modal amplitude. Represents the radial wave propagation term. It is the wave number; substituting the separated variable form into the Helmholtz equation and processing the depth direction, we obtain the equation for the vertical direction of the normal mode wave: in, This represents the local propagation speed of the wave in the vertical direction. It is the second spatial derivative in the vertical direction, describing the curvature of the waveform in that direction. Represents angular frequency. This item represents the difference in effective wavenumber, reflecting the propagation characteristics in the medium; At the sea surface and seabed, corresponding boundary conditions need to be met; typical boundary conditions include: Sea surface: Free boundary conditions ; Seabed: Depending on the characteristics of the seabed, it is a free boundary, a rigid boundary, or other types of boundary conditions; The above differential equations are solved using the finite difference method or the Sturm method in conjunction with boundary conditions, and the eigenvalues ​​are obtained. and characteristic function By superimposing all modes, the sound field at each location can be obtained; therefore, the normal mode model is selected as the kernel to obtain the sound pressure field at each trajectory sampling point. If the wavenumber integral model is chosen as the kernel, the sound field is decomposed into integral forms in the horizontal and vertical directions: in, It refers to sound pressure in the spatial domain. It is the horizontal distance. It's about depth. It is the horizontal wavenumber. This is the sound pressure in the wavenumber domain; substituting this equation into the Helmholtz equation and simplifying it for the depth direction, we obtain the ordinary differential equation for the vertical direction: The above equation is an eigenvalue problem. The modal function in the vertical direction can be obtained by solving the eigenvalues ​​and eigenfunctions. and the corresponding wavenumber The specific form is as follows: in, These are eigenvalues ​​of the horizontal wavenumber; by combining them with the corresponding boundary conditions, the results in the wavenumber domain are transformed back into physical space through numerical integration: In the formula, The modal amplitude is determined by the initial conditions; therefore, the wavenumber integral model is used as the kernel to obtain the sound pressure field value at each trajectory sampling point. S3: Calculate the channel impulse response: Convert the frequency domain sound field results into the channel impulse response at the trajectory sampling time through inverse Fourier transform, and align the arrival delay of the channel impulse response at each point to ensure the continuity of the channel impulse response; after alignment, use local spline interpolation to recover the time-varying impulse response of the overall multipath channel according to the transmission signal sampling rate. The calculation of the channel impulse response includes the following steps: (1) To find the delay offset between two consecutive trajectory sampling points The channel impulse response, aligned with adjacent trajectory sampling points, is calculated using the following formula: In the formula, and These are the trajectory sampling points. and trajectory sampling points On frequency The frequency response at each sampling point is estimated using a binary search algorithm, thereby obtaining the delay offset. ; (2) Integrate the delay offset results into the channel impulse response of each trajectory sampling point, and use local spline interpolation to recover the time-varying impulse response of the overall multipath channel according to the transmission signal sampling rate; S4: Digital signal processing: Convolve the transmitted signal with the time-varying impulse response of the multipath channel obtained in step S3 to simulate the signal propagation process in the channel, and pad the result with zeros to add a common propagation delay to obtain the final simulation result of the received signal.

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

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