A Doppler Fast Estimation Method and System for Direct Sequence Spread Spectrum Underwater Acoustic Communication Based on GPU

Abstract

The present invention discloses a method and system for fast Doppler estimation in direct-sequence spread-spectrum underwater acoustic communication based on GPU, including: modeling the received signal passing through the direct-sequence spread-spectrum underwater acoustic communication system; resampling and performing FFT operations on the local pilot signal in sequence, and storing the FFT operation result based on the device memory preloading method of GPU to obtain the Doppler matching matrix; adopting a two-step Doppler estimation process. In the coarse search stage, cross ambiguity function calculation is performed based on GPU complex multiplication, modulus normalization calculation with reduction in parallel based on GPU is carried out, and the to-be-estimated coarse Doppler factor is obtained through threshold detection; in the fine search stage, multiple Doppler branches near the coarse Doppler factor are selected, cross ambiguity function calculation is performed based on GPU complex multiplication, modulus normalization calculation with reduction in parallel based on GPU is carried out, and the to-be-estimated fine Doppler factor is obtained through threshold detection.

Description

Technical Field

[0001] The present invention belongs to the cross - field of underwater acoustic communication physical layer technology and GPU scientific computing, and particularly relates to a method and system for fast Doppler estimation of direct - sequence spread - spectrum underwater acoustic communication based on GPU. Background Art

[0002] Underwater acoustic communication is the best choice for long - distance underwater wireless communication. However, the complex characteristics of the underwater acoustic channel, such as time - varying, frequency - varying, and space - varying, bring many challenges to the realization of reliable communication. The speed of sound wave propagation in water is relatively slow, and the undulation of water flow and the relative movement between the signal transmitter and receiver will bring obvious Doppler frequency shift to the underwater acoustic signal, which has a great impact on the realization of high - reliability underwater acoustic communication. Therefore, it is particularly important to achieve fast and accurate Doppler estimation for underwater acoustic communication systems.

[0003] Currently, the commonly used Doppler estimation in underwater acoustic communication is mostly achieved by inserting known waveforms into the communication signal. One method is to insert Doppler - insensitive waveforms at the front and back of the communication signal to form preamble and postamble sequences. The receiver detects the change in the interval between the preamble and postamble sequences to obtain the average Doppler scale estimation of the entire communication signal. For example, using a linear frequency modulation (LFM) signal as the preamble and postamble sequences of a single - carrier underwater acoustic communication signal can achieve relatively accurate Doppler estimation at a low computational cost. The method of measuring the interval change has low estimation accuracy and regards the Doppler factor within the entire communication data packet as constant, resulting in poor estimation effect for the Doppler in the case of variable - speed movement of the communication machine.

[0004] Another method is to insert a Doppler-sensitive waveform with a sharp ambiguity function before the communication signal as a preamble sequence. At the receiving end, the Doppler scale estimate is obtained by calculating the cross ambiguity function (CAF) between the received signal and the preamble sequence calibrated by the Doppler scaling factor and searching for the index of the maximum branch of the correlation peak. The direct sequence spread spectrum (DSSS) underwater acoustic communication system uses a pseudo-random sequence (PN) for spectrum spreading. The PN sequence has a relatively sharp ambiguity function. Using the PN sequence as a pilot can ensure the consistency of the DSSS communication signal. Therefore, the DSSS underwater acoustic communication system often uses the CAF method for Doppler estimation. The CAF method can achieve high estimation accuracy and can also achieve good estimation results for Doppler in a variable-speed motion scenario under the condition of high-density pilot insertion. However, this method requires multiple searches in the delay-Doppler factor grid and has a relatively high computational complexity, which will cause a considerable computational overhead in hardware implementation.

[0005] The graphics processing unit (GPU) is specifically used for highly parallel computing and has been widely used in the fields of signal processing and data-intensive computing in recent years.

[0006] In summary, for the direct sequence spread spectrum underwater acoustic communication system, the difficulty in using the cross ambiguity function method for fast Doppler estimation lies in reducing the computational complexity and avoiding the computational overhead in hardware implementation. Parallel optimization of the Doppler estimation algorithm and deployment on the GPU platform is a better solution. Summary of the Invention

[0007] The object of the present invention is to overcome the defects of the prior art and propose a method and system for fast Doppler estimation of direct sequence spread spectrum underwater acoustic communication based on GPU.

[0008] In view of this, the present invention proposes a method for fast Doppler estimation of direct sequence spread spectrum underwater acoustic communication based on GPU. The method includes:

[0009] Step 1) Model the received signal passing through the direct sequence spread spectrum underwater acoustic communication system;

[0010] Step 2) Resample and perform FFT operations on the local pilot signal in sequence. Based on the device memory preloading method of GPU, store the FFT operation result to obtain a Doppler matching matrix;

[0011] Step 3) Adopt a two-step Doppler estimation process. In the coarse search stage, calculate the cross ambiguity function based on GPU complex multiplication, perform modulus normalization calculation based on GPU parallel reduction, and obtain the coarse Doppler factor to be estimated through threshold detection.

[0012] Step 4) In the fine search stage, select multiple Doppler branches near the coarse Doppler factor, calculate the cross ambiguity function based on GPU complex multiplication, perform modulus normalization calculation based on GPU parallel reduction, and obtain the fine Doppler factor to be estimated through threshold detection.

[0013] Preferably, the received signal in step 1) is modeled as:

[0014]

[0015] where is the transmitted signal, N pa is the number of channel multipaths, A p (t) and τ p represent the amplitude and delay of the p-th path respectively, α is the Doppler factor, n(t) is the additive noise, and t represents the time domain.

[0016] Preferably, the length of the local pilot signal in step 2) is N s T s , the resampling factor is the calibrated Doppler factor α j , j = 1, 2,..., J - 1, J is the number of Doppler factors to be estimated; perform N FFT point FFT operation, where N FFT is an integer power of 2 and greater than the signal sampling points; the size of the Doppler matching matrix is N FFT ×J.

[0017] Preferably, step 3) includes:

[0018] In the coarse search stage, divide the Doppler branches to be estimated into K groups, with J branches in each group, the Doppler estimation accuracy is Δα1, and the Doppler search range of each group is greater than twice the main peak width of the ambiguity function; where is the Q-channel signal;

[0019] Calculate the cross ambiguity function based on GPU complex multiplication, perform modulus normalization calculation based on GPU parallel reduction, calculate the energy integral of the normalized cross ambiguity function of the k-th group of Doppler branches, and adopt the threshold detection method. If the variance of the k-th group is significantly higher than the average variance threshold, take the branch with the minimum energy integral within this group which is the coarse Doppler factor to be estimated

[0020] Preferably, step 4) includes:

[0021] Select J' Doppler branches for fine search near the to-be-estimated coarse Doppler factor Perform cross ambiguity function calculation based on GPU complex multiplication, perform modulus normalization calculation of reduction in parallel based on GPU, select the minimum value of the energy integration of the normalized cross ambiguity function of J' branches, and the branch where the minimum value is located generates the to-be-estimated fine Doppler factor

[0022] Preferably, the method is designed based on the heterogeneous parallel algorithm of GPU.

[0023] On the other hand, the present invention proposes a direct sequence spread spectrum underwater acoustic communication Doppler fast estimation system based on GPU, including:

[0024] A modeling unit for modeling the received signal passing through the direct sequence spread spectrum underwater acoustic communication system;

[0025] An operation and storage unit for resampling and FFT operation on the local pilot signal in sequence, and storing the FFT operation result based on the device memory preloading method of GPU to obtain the Doppler matching matrix;

[0026] A coarse search unit for adopting a two-step Doppler estimation process. In the coarse search stage, perform cross ambiguity function calculation based on GPU complex multiplication, perform modulus normalization calculation of reduction in parallel based on GPU, and obtain the to-be-estimated coarse Doppler factor through threshold detection; and

[0027] A fine search unit for, in the fine search stage, selecting multiple Doppler branches near the coarse Doppler factor, performing cross ambiguity function calculation based on GPU complex multiplication, performing modulus normalization calculation of reduction in parallel based on GPU, and obtaining the to-be-estimated fine Doppler factor through threshold detection.

[0028] Compared with the prior art, the advantages of the present invention are as follows:

[0029] Facing the real-time processing requirements of underwater acoustic communication signals, from the perspective of engineering implementation, the present invention innovatively applies GPU to the Doppler estimation task of underwater acoustic communication signals, optimizes from three aspects: algorithm improvement, operation unit, and GPU platform deployment, and tests and verifies the algorithm performance using measured data. The test and verification results show that the present invention has reliability and effectiveness. The present invention greatly improves the processing efficiency of the direct sequence spread spectrum underwater acoustic communication receiver, solves the key problem of real-time Doppler estimation of the received signal, and provides support for the research and development of underwater acoustic communication systems. Description of the Drawings

[0030] Figure 1 is the block diagram of the direct-sequence spread-spectrum underwater acoustic communication system used in the present invention;

[0031] Figure 2 is the schematic diagram of the calculation process of the mutual ambiguity function Doppler estimation method used in the present invention;

[0032] Figure 3 is the schematic diagram of the implementation method of the device memory preloading method based on GPU proposed by the present invention;

[0033] Figure 4 is the schematic diagram of the calculation process of the cross ambiguity function calculation method based on GPU complex multiplication proposed by the present invention;

[0034] Figure 5 is the schematic diagram of the calculation process of the modulus normalization calculation method based on GPU parallel reduction proposed by the present invention;

[0035] Figure 6 is the schematic diagram of the calculation process of the heterogeneous parallel algorithm design based on GPU proposed by the present invention;

[0036] Figure 7 is the relative velocity between the two communication parties;

[0037] Figure 8 is the result of Doppler estimation of measured data using 5 methods;

[0038] Figure 9 is the average calculation time of Doppler estimation and the method speedup ratio under 5 methods;

[0039] Figure 10 is the receiver operation time and the method speedup ratio under 5 methods. Detailed Implementation Manner

[0040] The present invention proposes a fast Doppler estimation method for direct-sequence spread-spectrum underwater acoustic communication based on GPU, which realizes accurate and fast estimation of the Doppler of direct-sequence spread-spectrum underwater acoustic communication signals.

[0041] To achieve the above object, the present invention designs a fast Doppler estimation method for direct-sequence spread-spectrum underwater acoustic communication signals on a CPU+GPU heterogeneous platform. The method includes: an improved two-step Doppler estimation method based on the cross ambiguity function, a device memory preloading method based on GPU, a cross ambiguity function calculation method based on GPU complex multiplication, a modulus normalization calculation method based on GPU parallel reduction, and a heterogeneous parallel algorithm design based on GPU.

[0042] The improved two-step Doppler estimation method based on the cross ambiguity function reduces the number of Doppler estimation branches at the algorithm level, is suitable for deployment on the GPU platform, and improves the execution efficiency of the Doppler algorithm;

[0043] The device memory preloading method based on GPU is used to pre-store the calibrated Doppler matching matrix to reduce repeated calculations, avoid frequent data interactions, and reduce the overhead of computing resources and storage resources during hardware implementation;

[0044] The cross ambiguity function calculation method based on GPU complex multiplication is used for calculating the Doppler cross ambiguity function within the algorithm, and is optimized using the parallel computing advantage of GPU to further reduce the calculation time;

[0045] The modulus normalization calculation method based on GPU parallel reduction is used to calculate the normalized modulus of the cross ambiguity function, and mainly uses the fast reduction algorithm to improve the calculation efficiency;

[0046] The heterogeneous parallel algorithm design based on GPU is used for the deployment of the Doppler fast estimation algorithm on the GPU platform.

[0047] The actual measured data is used to verify the present invention, and it is proved that the method proposed in this paper can achieve accurate and fast estimation of the Doppler of the direct sequence spread spectrum underwater acoustic communication signal.

[0048] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0049] Embodiment 1

[0050] Embodiment 1 of the present invention proposes a Doppler fast estimation method for direct sequence spread spectrum underwater acoustic communication based on GPU, and this method includes:

[0051] Step 1) Model the received signal passing through the direct sequence spread spectrum underwater acoustic communication system;

[0052] Step 2) Resample and perform FFT operations on the local pilot signal in sequence. Based on the device memory preloading method of GPU, store the FFT operation result to obtain the Doppler matching matrix;

[0053] Step 3) Adopt a two-step Doppler estimation process. In the coarse search stage, calculate the cross ambiguity function based on GPU complex multiplication, perform modulus normalization calculation based on GPU parallel reduction, and obtain the to-be-estimated coarse Doppler factor through threshold detection;

[0054] Step 4) In the fine search stage, select multiple Doppler branches near the coarse Doppler factor, calculate the cross ambiguity function based on GPU complex multiplication, perform modulus normalization calculation based on GPU parallel reduction, and obtain the to-be-estimated fine Doppler factor through threshold detection.

[0055] The present invention includes an improved two-step Doppler estimation method based on the cross ambiguity function, a device memory preloading method based on GPU, a cross ambiguity function calculation method based on GPU complex multiplication, a modulus normalization calculation method based on GPU parallel reduction, and a heterogeneous parallel algorithm design based on GPU. First, a direct sequence spread spectrum underwater acoustic system model applicable to the invention is briefly introduced.

[0056] The direct sequence spread spectrum underwater acoustic communication system is as Figure 1 shown. Among them, the signal is generated by means of IQ modulation. The I channel is used to transmit actual information, and the Q channel transmits a known PN sequence for frame synchronization, Doppler estimation, and channel estimation. Among them, the I-channel baseband spread spectrum signal S I (t) is expressed as where, T c is the chip pulse width of the spreading code, T s is the symbol duration,

[0057] T s =LT c , and g(t) is the pulse shaping function.

[0058]

[0059] The Q-channel signal is generated by a known PN sequence with a length of N s ×L. The baseband spread spectrum signal S Q (t) is expressed as:

[0060]

[0061] The I and Q baseband signals are respectively carrier modulated and superimposed to obtain the transmitted signal, where f c is the carrier center frequency.

[0062]

[0063] The signal after passing through the underwater acoustic channel is modeled as follows, where N pa is the number of channel multipaths, A p (t) and τ p respectively represent the amplitude and delay of the p-th path, α is the Doppler factor, and n(t) is the additive noise,

[0064]

[0065] Regarding the improved two-step Doppler estimation method based on the cross ambiguity function, Figure 2 For the mutual ambiguity function Doppler estimation method, first, for the calculation of r MF (α,τ), the frequency-domain implementation form is as follows, where and respectively represent the Fourier transform and the inverse Fourier transform.

[0066]

[0067] The calculation process of the improved two-step Doppler estimation method based on the cross ambiguity function proposed by the present invention is as follows: (1) In the coarse search stage, the Doppler branches to be estimated are divided into K groups, with J branches in each group, the Doppler estimation accuracy is Δα1, and the Doppler search range of each group is greater than twice the main peak width of the ambiguity function; (2) Calculate the energy integral of the normalized cross ambiguity function of the k-th group of Doppler branches. By using the threshold detection method, if the variance of the k-th group is significantly higher than the average variance threshold, select the branch with the minimum energy integral within this group as the rough Doppler factor to be estimated (3) After obtaining the rough Doppler factor , near select J' Doppler branches for fine search with the Doppler estimation accuracy Δα2, and select the minimum value of the energy integral of the normalized cross ambiguity function of the J' branches. The branch where the minimum value is located generates the fine Doppler factor to be estimated

[0068] The implementation method of the device memory preloading method based on GPU is as Figure 3 shown. First, resample the local pilot signal with a length of N s T s , and the resampling factor is the calibrated Doppler factor α , j = 1, 2,..., J - 1. Among them, the size of the Doppler factor increases from α1 to α j and the interval is the fine search accuracy Δα2. Perform N j point FFT operation on the resampled signal, where N FFT is an integer power of 2 and N FFT > α FFT × N J × N s T s . Transmit the FFT result from the host memory to the device memory in sequence to obtain a Doppler matching matrix with a size of N FFT × J.

[0069] The schematic diagram of the calculation process of the cross ambiguity function calculation method based on GPU complex multiplication is as Figure 4 shown.

[0070] The schematic diagram of the calculation process of the modulus normalization calculation method based on GPU parallel reduction is as Figure 5 shown.

[0071] The schematic diagram of the calculation process of the GPU-based heterogeneous parallel algorithm design is as follows Figure 6 as shown

[0072] Figure 6 It is mainly divided into two parts: coarse search and fine search. In the coarse search stage is the received signal is the local pilot signal after resampling, and the resampling factor is α k,j , F[·] represents the FFT operation, J is the number of coarse search Doppler branches. The "CAF normalization energy calculation" calculates the CAF normalization energies r_MF_NORM and ss_MF_NORM within the kth group. Kernel_variance is the kernel function used to calculate the variance v of r_MF_NORM k . When v k is greater than the threshold v threshold , the minimum value index of ss_MF_NORM is calculated by the kernel function Kernel_min to obtain the coarse search Doppler factor In the fine search stage, J' is the number of fine search Doppler branches. The "CAF normalization energy calculation" calculates the CAF normalization energy ss_MF_NORM, and the minimum value index of ss_MF_NORM is calculated by the kernel function Kernel_min to obtain the fine search Doppler factor

[0073] Embodiment 2

[0074] Embodiment 2 of the present invention proposes a direct sequence spread spectrum underwater acoustic communication Doppler rapid estimation system based on GPU, which is implemented based on the method of Embodiment 1. The system includes:

[0075] A modeling unit for modeling the received signal passing through the direct sequence spread spectrum underwater acoustic communication system;

[0076] An operation and storage unit for sequentially resampling and performing FFT operations on the local pilot signal, and storing the FFT operation results based on the GPU device memory preloading method to obtain the Doppler matching matrix;

[0077] A coarse search unit for adopting a two-step Doppler estimation process. In the coarse search stage, cross ambiguity function calculation is performed based on GPU complex multiplication, modulus normalization calculation with parallel reduction based on GPU is performed, and the to-be-estimated coarse Doppler factor is obtained through threshold detection;

[0078] A fine search unit is used to select multiple Doppler branches near the coarse Doppler factor during the fine search stage, calculate the cross ambiguity function based on GPU complex multiplication, perform modulus normalization calculation based on GPU parallel reduction, and obtain the fine Doppler factor to be estimated through threshold detection.

[0079] Deploy the heterogeneous parallel algorithm on the GPU platform: (1) The algorithm framework is an improved two-step Doppler estimation method based on the cross ambiguity function. The estimation of the Doppler factor is completed in two stages: coarse search and fine search; (2) Optimize the spatial storage using the device memory preloading method of the GPU; (3) Optimize the CAF normalization energy calculation module using the cross ambiguity function calculation method based on GPU complex multiplication and the modulus normalization calculation method based on GPU parallel reduction.

[0080] Verify the reliability of the present invention and use the method of the present invention to estimate the Doppler factor of measured data. The relative speed between the communication parties is as Figure 7 shown, and the Doppler estimation results of 5 methods are as Figure 8 shown. The 5 methods are: ① CPU method 1; ② CPU method 2; ③ GPU method 1; ④ GPU method 2; ⑤ the method of the present invention. Figure 9 It shows that the method of the present invention has the same Doppler estimation accuracy as the other 4 methods, verifying the reliability of the present invention.

[0081] Verify the effectiveness of the present invention and compare the Doppler estimation times of the method of the present invention with those of the other 4 methods. The average calculation time of Doppler estimation, the running time of the receiver, and the method acceleration ratio under different methods are as Figure 9 、 Figure 10 shown. Figure 9 、 Figure 10 The results shown verify the effectiveness of the present invention.

[0082] Summary:

[0083] The present invention provides a method for fast Doppler estimation of direct sequence spread spectrum underwater acoustic communication signals based on a CPU+GPU heterogeneous platform. The method includes: an improved two-step Doppler estimation method based on the cross ambiguity function, which is used to reduce the number of Doppler estimation branches; a device memory preloading method based on the GPU, which is used to pre-store the calibrated Doppler matching matrix; a cross ambiguity function calculation method based on GPU complex multiplication, which is used to calculate the Doppler cross ambiguity function; a modulus normalization calculation method based on GPU parallel reduction, which is used to calculate the normalized modulus of the cross ambiguity function; and a heterogeneous parallel algorithm design based on the GPU, which is used to deploy the Doppler fast estimation algorithm on the GPU platform. The present invention utilizes the advantage of high parallel computing efficiency of the GPU to provide an accurate and efficient method for Doppler estimation of direct sequence spread spectrum underwater acoustic communication signals. This method can accurately estimate the Doppler of measured underwater acoustic communication signals, greatly reduce the time of Doppler estimation, improve the processing efficiency of the receiver, and provide strong support for the real-time processing of received underwater acoustic communication signals and the research and development of underwater acoustic communication system equipment.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A GPU-based direct sequence spread spectrum underwater acoustic communication Doppler fast estimation method, the method comprising: Step 1) Modeling the received signal of the direct sequence spread spectrum underwater acoustic communication system; Step 2) resampling and FFT operation are performed on the local pilot signal in sequence, and the FFT operation result is stored to obtain the Doppler matching matrix based on the device memory preloading method of the GPU; Step 3) adopts a two-step Doppler estimation process. In the coarse search stage, the cross ambiguity function is calculated based on GPU complex multiplication, the reduced modulus normalization calculation is performed based on GPU parallelization, and the coarse Doppler factor to be estimated is obtained through threshold detection; Step 4) In the fine search stage, multiple Doppler branches near the coarse Doppler factor are selected, cross ambiguity function calculation is performed based on GPU complex multiplication, and reduced modulus normalization calculation is performed based on GPU parallelization, and the fine Doppler factor to be estimated is obtained through threshold detection; The step 3) comprises: In the coarse search stage, the Doppler branches to be estimated are divided into K groups, each with J branches, the Doppler estimation accuracy is Δα1, and the Doppler search range of each group is greater than Twice the width of the main peak of the fuzziness function; where, is the Q channel signal of the local pilot signal; The cross ambiguity function is calculated based on GPU complex multiplication, and the reduced modulus normalization calculation is performed based on GPU parallelization to calculate the energy integral of the normalized cross ambiguity function of the kth group of Doppler branches. The threshold detection method is used. If the variance of the kth group is significantly higher than the average variance threshold, the branch with the smallest energy integral in the group is selected. The rough Doppler factor to be estimated is The step 4) comprises: The rough Doppler factor to be estimated Select J′ Doppler branches for fine search with Doppler estimation accuracy Δα2 nearby, calculate cross ambiguity function based on GPU complex multiplication, perform reduced modulus normalization calculation based on GPU parallelization, select the minimum value of the energy integral of the normalized cross ambiguity function of J′ branches, and the branch with the minimum value generates the fine Doppler factor to be estimated.

2. The GPU-based direct sequence spread spectrum underwater acoustic communication Doppler fast estimation method according to claim 1 is characterized in that: The received signal of step 1) Modeled as: in, is the transmitted signal, N pa is the number of multipath channels, A p and τ p They represent the amplitude and delay of the pth path respectively, α is the Doppler factor, n(t) is the additive noise, and t represents the time domain.

3. The GPU-based direct sequence spread spectrum underwater acoustic communication Doppler fast estimation method according to claim 2 is characterized in that: The Q-path signal of the local pilot signal in step 2) The length is N s T s , the resampling factor is the calibration Doppler factor α j ,j=1,2,...,J-1, J is the number of Doppler factors to be estimated; perform N FFT Point FFT operation, where N FFT is an integer power of 2 and is greater than the number of signal sampling points; the size of the Doppler matching matrix is ​​N FFT ×J.

4. The GPU-based direct sequence spread spectrum underwater acoustic communication Doppler fast estimation method according to claim 1 is characterized in that: The method is based on the heterogeneous parallel algorithm design of GPU.

5. A system based on the GPU-based direct sequence spread spectrum underwater acoustic communication Doppler fast estimation method according to claim 1, characterized in that: include: A modeling unit, used for modeling a received signal of a direct sequence spread spectrum underwater acoustic communication system; The operation storage unit is used to perform resampling and FFT operation on the local pilot signal in sequence, and store the FFT operation result to obtain the Doppler matching matrix based on the device memory preloading method of the GPU; A coarse search unit is used to adopt a two-step Doppler estimation process. In the coarse search stage, a cross ambiguity function is calculated based on GPU complex multiplication, a reduced modulus normalization calculation is performed based on GPU parallelization, and a coarse Doppler factor to be estimated is obtained through threshold detection; and The fine search unit is used to select multiple Doppler branches near the coarse Doppler factor in the fine search stage, calculate the cross ambiguity function based on GPU complex multiplication, perform reduced modulus normalization calculation based on GPU parallelism, and obtain the fine Doppler factor to be estimated through threshold detection.

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