Adaptive underwater acoustic OFDM signal frame synchronization and compensation method based on HFM signal

Abstract

The invention relates to the technical field of underwater acoustic communication, and discloses an adaptive underwater acoustic OFDM (Orthogonal Frequency Division Multiplexing) signal frame synchronization and compensation method based on an HFM (High Frequency Modulation) signal. The invention provides a double-stage synchronization strategy of rough synchronization probable interval and fine synchronization accurate optimization. In the coarse synchronization stage, preliminary frame synchronization is rapidly completed by identifying the approximate time window where the synchronization head is located, the calculation complexity is reduced, and the processing efficiency is improved. And in the fine synchronization stage, the position of the synchronization head is accurately positioned based on an accurate optimization algorithm, so that high-precision frame synchronization of the signal is realized. And a compensation mechanism is introduced, dynamic adjustment is carried out for multipath interference and signal distortion in an underwater acoustic channel, and the synchronization performance is further improved. According to the adaptive underwater acoustic OFDM signal frame synchronization and compensation method based on the HFM signal provided by the invention, the influence of an underwater acoustic channel multipath effect and path attenuation difference on communication is reduced, the communication quality is improved, the requirements of an underwater acoustic system on high reliability and stability are met, and the method has a wide application prospect.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic communication, and in particular to an adaptive underwater acoustic OFDM signal frame synchronization and compensation method based on HFM signal. Background Art

[0002] With the rapid development of underwater acoustic communication technology, orthogonal frequency division multiplexing (OFDM) technology has become a research direction that has attracted much attention in the field of underwater acoustic communication due to its high spectrum utilization and excellent anti-multipath interference ability. However, in underwater acoustic channels, due to its unique physical characteristics, including narrow available bandwidth, severe multipath delay, and large propagation loss, traditional communication technology is difficult to meet actual needs, and the advantages of OFDM technology make it an ideal solution for underwater acoustic communication.

[0003] Nevertheless, the variability of underwater acoustic channels also brings new challenges to OFDM systems, especially the Doppler effect, which is particularly destructive to signals. The Doppler effect not only destroys the orthogonality between OFDM subcarriers, but also introduces inter-symbol interference (ICI), which significantly reduces system performance. In addition, OFDM technology is extremely sensitive to time and frequency synchronization deviations. In underwater acoustic communication systems, accurate signal synchronization design becomes a key issue that determines the overall performance of the system.

[0004] Therefore, it is necessary to provide an adaptive underwater acoustic OFDM signal frame synchronization and compensation method based on HFM signal to solve the above technical problems. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides an adaptive underwater acoustic OFDM signal frame synchronization and compensation method based on HFM signal. In this method, the frequency modulation signal (HFM) is introduced into the underwater acoustic communication system due to its excellent anti-frequency deviation ability and high correlation characteristics. The HFM signal has the characteristics of broadband and continuous frequency change, which makes it show strong anti-interference ability in complex underwater acoustic channels. By using the HFM signal as a preamble code, this method can provide reliable support in the signal detection and synchronization stages, and further combine the calculation of the synchronization sequence and the Doppler factor to dynamically compensate the received signal, effectively overcome the influence of channel degradation on signal transmission, and thus significantly improve the stability and reliability of the underwater acoustic communication system in complex environments.

[0006] The method for adapting underwater acoustic OFDM signal frame synchronization and compensation based on HFM signal provided by the present invention comprises the following steps: S1. Signal frame structure design: The PC generates an up-and-down frequency sweep HFM signal as the OFDM signal of the preamble code and transmits it in the underwater acoustic channel in the form of sound waves through the transmitting transducer; S2, Doppler estimation (coarse synchronization): The receiving transducer intercepts the sound wave signal and starts the Doppler estimation (coarse synchronization) stage. First, the received signal is cross-correlated with the up-and-down scanning HFM signal generated by the transmitting end, and the two generated results are subjected to the last correlation process. The result obtained at this time reflects the correlation degree of the up-and-down scanning HFM signal on the time line. Based on the peak value obtained by the last correlation, the Doppler factor under this path can be obtained; S3, Doppler compensation (fine synchronization): The calculated Doppler factor is used to resample the received signal, and the resampled signal is cross-correlated with s(t) generated by the transmitter. The strongest path is traced back and the peak points are stored in chronological order. The first path greater than the set threshold is determined as the path corresponding to the first sound line. At this time, all paths are traversed, and the minimum residual criterion is used to continuously judge the size of the updated residual and the threshold until the residual is less than the set threshold, and finally the Doppler factors of all paths are obtained; S4. Hydroacoustic channel modeling: The gateway buoy is placed in the predetermined experimental sea area to monitor the temperature, salinity and other physical parameters of the water body to provide environmental data for the characteristics of hydroacoustic propagation; after data preprocessing, these data are input into the Bellhop model to calculate the corresponding channel gain matrix (hmat); the obtained frequency domain channel gain matrix is ​​subjected to IFFT to obtain the hydroacoustic channel impulse response in the target sea area; a fusion method is used to weighted average the delay of the first propagation path obtained based on the Bellhop model and the delay of the first path determined by Doppler compensation to improve the accuracy and reliability of delay estimation; all paths are traversed, and the residual minimum criterion is used to continuously judge the size of the updated residual and the threshold until the residual is less than the set threshold, and finally the Doppler factor of all paths is obtained.

[0007] Preferably, the signal frame structure design step is specifically as follows: The pilot signal used in the adaptive underwater acoustic OFDM frame based on HFM signal is the up-and-down frequency sweep HFM signal. For an underwater acoustic OFDM symbol block, the up-and-down frequency sweep HFM signal + time slot + down-and-down frequency sweep HFM signal + time slot + 3-frame OFDM signal are used, and the time slot uses a blank sequence. It is assumed that the start and end frequencies of the HFM signal are and , the sweep frequency is , , T is the time length of an HFM signal, is the time interval between two HFM signals.

[0008] Preferably, the Doppler estimation (coarse synchronization) step is specifically as follows: S2.1, at the receiving end, cross-correlation operations are performed on the up-scanning HFM signal (HFM +) and the down-scanning HFM signal (HFM -) with the received pilot signal to obtain a cross-correlation output of the received signal; S2.2. Perform a cross-correlation operation on the output result of the cross-correlation of the up-scan HFM signal and the output result of the cross-correlation of the down-scan HFM signal, and determine the time interval by the peak value after the cross-correlation between the two, so as to estimate the Doppler frequency shift, and characterize the correlation degree of the cross-correlation results of the up-scan HFM and down-scan HFM signals. According to the fact that the output results of the cross-correlation of the up-scan HFM signal and the down-scan HFM signal at the receiving end are basically consistent, the output correlation degree of the cross-correlation of the up-scan HFM signal and the down-scan HFM signal is the highest by finding the peak moment, and then calculate the time interval between the two HFM signals at the receiving end, so as to satisfy the relationship between the Doppler factor and the time interval: .

[0009] Preferably, the Doppler compensation (fine synchronization) step is specifically as follows: S3.1. Based on the Doppler factor calculated in step S2, the received signal is resampled, and a cross-correlation operation is performed on the resampled signal and s(t) generated by the transmitting end. The cross-correlation result is defined as X(n). In the cross-correlation result, the path corresponding to the peak point is defined as nmax. S3.2, in a multipath underwater channel environment, assuming that the maximum delay of the system is, taking the strongest path nmax as a reference, find the point corresponding to the first path by tracing back; S3.3. Extract all peak points of X(n) within the range and store them into the set check in chronological order. In the set, search for the first point that is greater than the preset threshold. The moment corresponding to this point is the point corresponding to the first path.

[0010] Preferably, the fusion method in step S4 comprises the following steps: First, the delay of the first propagation path obtained based on the Bellhop model and the delay of the first path determined by Doppler compensation are weighted averaged to obtain the starting position of the first path; then: P1: After determining the starting point of the first path, we can start traversing each path. The first path is: And let the corresponding amplitude under this path be ; P2: The calculation range is: ; P3: Update residual: ; P4: P1-P3 are repeated continuously. The fusion method is used to determine the position of the delay point of each path. That is, the delay of the propagation path obtained based on the Bellhop model and the delay of the path determined by Doppler compensation are weighted averaged. Based on this, the residual is updated until the residual is less than the set threshold. At this time, the Doppler factor corresponding to each path is obtained.

[0011] Compared with the related art, the adaptive underwater acoustic OFDM signal frame synchronization and compensation method based on HFM signal provided by the present invention has the following beneficial effects: 1. Improve frame synchronization accuracy and communication stability: Through the two-stage synchronization strategy of "rough synchronization approximate range, fine synchronization precise optimization", this solution effectively solves the synchronization problem caused by multipath effect and signal attenuation in the underwater acoustic channel. The rough synchronization stage quickly identifies the approximate range of the synchronization head, and the fine synchronization stage accurately optimizes the synchronization head position, which significantly improves the signal frame synchronization accuracy and overall communication stability; 2. Effectively reduce the interference of Doppler effect on communication: In the Doppler estimation process, through multiple cross-correlation operations of up and down scanning HFM signals, the scheme can accurately calculate the Doppler factor and use resampling processing to adjust the received signal to reduce the impact of Doppler effect on signal transmission. This compensation mechanism effectively improves the robustness of the communication link; 3. Comprehensive optimization of computing efficiency and communication performance: The solution uses up and down frequency sweep HFM signals as preamble codes and accurately extracts path information through multiple correlation and backtracking algorithms. The process improves synchronization performance while reducing computational complexity, improving the processing efficiency of the system, meeting the high reliability requirements of underwater acoustic communications, and showing broad application potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A flowchart of a method for adapting underwater acoustic OFDM signal frame synchronization and compensation based on HFM signal provided by the present invention; Figure 2 is a schematic diagram of an OFDM signal frame structure; Figure 3 It is a schematic diagram of the correlation between the up-scan HFM signal, the down-scan HFM signal and the receiving end signal; Figure 4 For HFM UP & HFM DOWN Schematic diagram of the cross-correlation of ; Figure 5 This is the channel impulse response result diagram of a certain sea area. DETAILED DESCRIPTION

[0013] The present invention proposes a method for adapting underwater acoustic OFDM signal frame synchronization and compensation based on HFM signal, which includes: Step 1: The PC generates an OFDM signal with an up-and-down frequency sweep HFM signal as a preamble code and transmits it in the underwater acoustic channel in the form of sound waves through a transmitting transducer; Step 2: The receiving transducer intercepts the sound wave signal and starts the Doppler estimation (coarse synchronization) stage. First, the received signal is cross-correlated with the up-and-down scanning HFM signal generated by the transmitting end, and the two generated results are subjected to the last correlation process. The result obtained at this time reflects the correlation degree of the up-and-down scanning HFM signal on the time line. Based on the peak value obtained by the last correlation, the Doppler factor under this path can be obtained; Step 3: Use the calculated Doppler factor to resample the received signal. Perform a cross-correlation operation on the resampled signal and s(t) generated by the transmitter, trace back based on the strongest path, and store the peak points in chronological order. The first path that is greater than the set threshold is determined as the path corresponding to the first sound line. The delay of each path obtained based on the Bellhop model and the delay of each path determined by Doppler compensation are averaged. At this time, all paths are traversed, and the minimum residual criterion is used to continuously judge the size of the updated residual and the threshold until the residual is less than the set threshold, and finally the Doppler factors of all paths are obtained; Step 4: Underwater acoustic channel modeling.

[0014] The present invention will be further described below in conjunction with the accompanying drawings and implementation modes.

[0015] The embodiment of the present invention provides a method for adapting underwater acoustic OFDM signal frame synchronization and compensation based on HFM signal, which meets the requirements of underwater acoustic communication. The whole flow chart is as follows: Figure 1 As shown, the steps of the gauge method will be described in detail below.

[0016] 1. Signal frame structure design: Hyperbolic FM signals are often used as pilot signals in underwater acoustic communications due to their excellent Doppler insensitivity. In addition, since their autocorrelation function is approximately a narrow pulse-shaped function, hyperbolic FM signals are also used in underwater acoustic channel detection to obtain information such as the time delay of each propagation path in the channel. Next, we use the autocorrelation characteristics of hyperbolic FM signals to design a signal frame structure that is suitable for underwater acoustic communications. At the same time, due to the Doppler insensitivity of hyperbolic FM signals, the proposed synchronization method also has a certain anti-Doppler capability.

[0017] First, the pilot signal used in the adaptive underwater acoustic OFDM signal frame based on the HFM signal is the up and down frequency sweeping HFM signal, where it is assumed that and are the start and end frequencies of the HFM signal, , is the sweep frequency. OFDM signal frame structure Figure 2 As shown, where T is the time length of an HFM signal, is the time interval between two HFM signals.

[0018] For an underwater acoustic OFDM symbol block, we use: up-scanning HFM signal + time slot + down-scanning HFM signal + time slot + 3 frames of OFDM signal. In fact, the use of blank sequence in the time slot can not only ensure that the tailing phenomenon of the previous signal will not affect the next signal under poor channel conditions, but also save energy at the transmitter.

[0019] 2. Doppler estimation (coarse synchronization): After passing through the underwater acoustic channel, at the receiving end, we cross-correlate the up-scan HFM signal (HFM+) and the down-scan HFM signal (HFM-) with the received pilot signal to obtain the cross-correlation output of the received signal. Further, we cross-correlate the output result of the up-scan HFM signal with the output result of the down-scan HFM signal. The peak value after the cross-correlation between the two can be used to determine the time interval and thus estimate the Doppler shift. Figure 3 The results of cross-correlation between the up-scan HFM signal (HFM+) and the down-scan HFM signal (HFM-) and the received pilot signal are shown.

[0020] The output results of correlator 1 and correlator 2 are known, and they are input into correlator 3 to perform cross-correlation operation again. The output result of correlator 3 represents the correlation degree of the cross-correlation results of the up-scan HFM and down-scan HFM signals. Since the interval between the up-scan HFM signal and the down-scan HFM signal is extremely short in the pilot signal part, it can be approximately considered that the channel characteristics remain unchanged during this period. Figure 4 The output of correlator 3 is shown.

[0021] Under this assumption, the cross-correlation output results of the up-scan HFM signal and the down-scan HFM signal at the receiving end are basically the same. By finding the peak moment, it can be determined that the output correlation degree of the cross-correlation of the up-scan HFM signal and the down-scan HFM signal is the highest at this time. From this, the time interval between the two HFM signals at the receiving end can be calculated and recorded as , that is, the relationship between the Doppler factor and the time interval is: (1) 3. Doppler compensation (fine synchronization): Based on the Doppler factor calculated in the previous steps, the received signal is resampled. The resampled signal is cross-correlated with s(t) generated by the transmitter, and the cross-correlation result is defined as X(n). In the cross-correlation result, the path corresponding to the peak point is defined as nmax.

[0022] In a multipath underwater channel environment, due to the influence of path length difference, reflection gain, Doppler effect, interference effect, environmental noise and receiver frequency selectivity during signal propagation, the later arriving path may have stronger energy due to less attenuation, constructive interference or signal aggregation, while the earlier direct path may be subject to greater attenuation or interference, resulting in the strongest path not necessarily being the first path. Assuming the maximum delay of the system is , then taking the strongest path nmax as a reference, we can find the point corresponding to the first path by backtracking forward.

[0023] Extract all peak points of X(n) within the range and store them in the set check in chronological order. In the set, search for the first point that is greater than the preset threshold, and the time corresponding to this point is the point corresponding to the first path.

[0024] 4. Underwater acoustic channel modeling: First, the gateway buoy is precisely arranged in the predetermined experimental sea area so as to comprehensively measure the hydroacoustic environmental parameters of the sea area. The gateway buoy is equipped with high-precision temperature and salinity sensors, which can monitor the temperature, salinity and other physical parameters of the water body in real time, thereby providing important environmental data for the hydroacoustic propagation characteristics. These data will be used as input, and after appropriate data preprocessing, they will be input into the Bellhop model. The Bellhop model calculates the corresponding channel gain matrix (hmat) based on the input hydroacoustic environmental parameters. The matrix describes the gain of each path when the sound wave propagates in the water area, including factors such as multipath effects and attenuation. Furthermore, in order to convert these channel gain information into the hydroacoustic channel impulse response in the time domain, the obtained frequency domain channel gain matrix needs to be IFFT.

[0025] Through this series of refined experimental steps and data processing, the impact response of the underwater acoustic channel in the target sea area will eventually be obtained, which will provide important theoretical basis and experimental reference for the design and optimization of actual underwater acoustic communication systems. Figure 5 The channel impulse response result diagram of a certain sea area is shown. It can be observed that the sea surface reflection wave and the seabed reflection wave arrive almost at the same time.

[0026] in, Figure 5 The horizontal axis in the middle represents the channel delay caused by the multipath effect, the vertical axis represents the observation time during the entire simulation process, and the color bar on the left corresponds to the amplitude.

[0027] By observing the impulse response of the channel, we can see that there are 7 main paths in total, although the direct path It reaches the receiving end first, but its energy is less than that after a reflection path on the sea surface. , after a seabed reflection path has weakened, and The small time delay between them forms a main path with relatively concentrated energy. The maximum delay of the entire channel is about 27ms. Each main path shows obvious time variation, and the attenuation of signal energy shows a positive linear relationship with the increase of delay. Each main path contains 20 scattering paths. The time delay difference between them is very small. Overall, the main path is formed by this cluster of scattering paths.

[0028] In order to obtain a more accurate overall delay, a fusion method is used to perform a weighted average of the delay of the first propagation path obtained based on the Bellhop model and the delay of the first path determined by Doppler compensation. The core purpose of this process is to minimize the deviation caused by a single method by combining two different delay estimation results, and to improve the accuracy and reliability of delay estimation, that is, each path traversed later adopts this fusion method. The fusion method also includes the following steps: Step 1: After determining the starting point of the first path, we can start traversing each path. The first path is: (2) And let the corresponding amplitude under this path be .

[0029] Step 2: Calculate the amplitude: (3) Step 3: Update the residual: (4) Step 4: Repeat steps 1-3 continuously, and use a fusion method to determine the location of the delay point of each path, that is, take a weighted average of the delay of the propagation path obtained based on the Bellhop model and the delay of the path determined by Doppler compensation, and then update the residual based on this until the residual is less than the set threshold. At this time, the Doppler factor corresponding to each path is obtained.

[0030] Compared with the related art, the adaptive underwater acoustic OFDM signal frame synchronization and compensation method based on HFM signal provided by the present invention has the following beneficial effects: 1. Improve frame synchronization accuracy and communication stability: Through the two-stage synchronization strategy of "rough synchronization approximate range, fine synchronization precise optimization", this solution effectively solves the synchronization problem caused by multipath effect and signal attenuation in the underwater acoustic channel. The rough synchronization stage quickly identifies the approximate range of the synchronization head, and the fine synchronization stage accurately optimizes the synchronization head position, which significantly improves the frame synchronization accuracy of the signal and the overall communication stability.

[0031] 2. Effectively reduce the interference of Doppler effect on communication: In the Doppler estimation process, through multiple cross-correlation operations of up and down scanning HFM signals, the scheme can accurately calculate the Doppler factor and use resampling processing to adjust the received signal to reduce the impact of Doppler effect on signal transmission. This compensation mechanism effectively improves the robustness of the communication link.

[0032] 3. Comprehensive optimization of computational efficiency and communication performance: The solution uses the upper and lower frequency sweep HFM signal as the preamble code, and accurately extracts the path information through multiple correlation and backtracking algorithms. Its process improves the synchronization performance while reducing the computational complexity and improving the processing efficiency of the system. It meets the high reliability requirements of underwater acoustic communication and shows a wide range of application potential.

[0033] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for adaptive underwater acoustic OFDM signal frame synchronization and compensation based on HFM signal, characterized in that: The following steps are involved: S1. Signal frame structure design: The PC generates an up-and-down frequency sweep HFM signal as the OFDM signal of the preamble code and transmits it in the underwater acoustic channel in the form of sound waves through the transmitting transducer; S2, Doppler estimation: The receiving transducer intercepts the sound wave signal and starts the Doppler estimation stage. First, the received signal is cross-correlated with the up-and-down scanning HFM signal generated by the transmitting end, and the two generated results are subjected to the last correlation process. The result obtained at this time reflects the correlation degree of the up-and-down scanning HFM signal on the time line. Based on the peak value obtained by the last correlation, the Doppler factor under this path can be obtained; S3, Doppler compensation: The calculated Doppler factor is used to resample the received signal, and the resampled signal is cross-correlated with s(t) generated by the transmitter. The strongest path is traced back and the peak points are stored in chronological order. The first path greater than the set threshold is determined as the path corresponding to the first sound line. At this time, all paths are traversed, and the minimum residual criterion is used to continuously judge the size of the updated residual and the threshold until the residual is less than the set threshold, and finally the Doppler factors of all paths are obtained; S4. Underwater acoustic channel modeling: The gateway buoy is placed in the predetermined experimental sea area to monitor the temperature and salinity physical parameters of the water body to provide environmental data for the underwater acoustic propagation characteristics; After data preprocessing, these data are input into the Bellhop model to calculate the corresponding channel gain matrix; Perform IFFT on the obtained frequency domain channel gain matrix to obtain the underwater acoustic channel impulse response in the target sea area; adopt a fusion method to perform weighted averaging on the delay of the first propagation path obtained based on the Bellhop model and the delay of the first path determined by Doppler compensation to improve the accuracy and reliability of delay estimation; All paths are traversed, and the minimum residual criterion is used to continuously judge the size of the updated residual and the threshold until the residual is less than the set threshold, and finally the Doppler factors of all paths are obtained.

2. The method for adaptive underwater acoustic OFDM signal frame synchronization and compensation based on HFM signal as claimed in claim 1, characterized in that: The signal frame structure design steps are specifically as follows: The pilot signal used in the adaptive underwater acoustic OFDM frame based on HFM signal is the up-and-down frequency sweep HFM signal. For an underwater acoustic OFDM symbol block, the up-and-down frequency sweep HFM signal + time slot + down-and-down frequency sweep HFM signal + time slot + 3-frame OFDM signal are used, and the time slot uses a blank sequence. Among them, it is assumed that the start and end frequencies of the HFM signal are and , the sweep frequency is , , T is the time length of an HFM signal, is the time interval between two HFM signals.

3. The method for adaptive underwater acoustic OFDM signal frame synchronization and compensation based on HFM signal as claimed in claim 1, characterized in that: The Doppler estimation step is specifically as follows: S2.1, at the receiving end, respectively performing cross-correlation operations on the up-scanning HFM signal and the down-scanning HFM signal with the received pilot signal to obtain a cross-correlation output of the received signal; S2.

2. Perform a cross-correlation operation on the output result of the cross-correlation of the up-scan HFM signal and the output result of the cross-correlation of the down-scan HFM signal, and determine the time interval by the peak value after the cross-correlation between the two, so as to estimate the Doppler frequency shift, and characterize the correlation degree of the cross-correlation results of the up-scan HFM and down-scan HFM signals. According to the fact that the output results of the cross-correlation of the up-scan HFM signal and the down-scan HFM signal at the receiving end are basically consistent, the output correlation degree of the cross-correlation of the up-scan HFM signal and the down-scan HFM signal is the highest by finding the peak moment, and then calculate the time interval between the two HFM signals at the receiving end, so as to satisfy the relationship between the Doppler factor and the time interval: .

4. The method for adaptive underwater acoustic OFDM signal frame synchronization and compensation based on HFM signal as claimed in claim 1, characterized in that: The Doppler compensation step is specifically as follows: S3.

1. Based on the Doppler factor calculated in step S2, the received signal is resampled, and a cross-correlation operation is performed on the resampled signal and s(t) generated by the transmitting end. The cross-correlation result is defined as X(n). In the cross-correlation result, the path corresponding to the peak point is defined as nmax. S3.2, in a multipath underwater channel environment, assuming that the maximum delay of the system is, taking the strongest path nmax as a reference, find the point corresponding to the first path by tracing back; S3.

3. Extract all peak points of X(n) within the range and store them into the set check in chronological order. In the set, search for the first point that is greater than the preset threshold. The moment corresponding to this point is the point corresponding to the first path.

5. The method for adaptive underwater acoustic OFDM signal frame synchronization and compensation based on HFM signal as claimed in claim 1, characterized in that: The fusion method in step S4 comprises the following steps: First, the delay of the first propagation path obtained based on the Bellhop model and the delay of the first path determined by Doppler compensation are weighted averaged to obtain the starting position of the first path; then: P1: After determining the starting point of the first path, we can start traversing each path. The first path is: , and let the corresponding amplitude under this path be ; P2: The calculation range is: ; P3: Update residual: ; P4: P1-P3 are repeated continuously. The fusion method is used to determine the position of the delay point of each path. That is, the delay of the propagation path obtained based on the Bellhop model and the delay of the path determined by Doppler compensation are weighted averaged. Based on this, the residual is updated until the residual is less than the set threshold. At this time, the Doppler factor corresponding to each path is obtained.

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