An arbitrary-angle fast beamforming method applicable to multi-beam sounding systems

Abstract

The present application provides a fast beamforming method for any angle applicable to a multi-beam sounding system. The beamforming method includes: calculating a frequency index matrix corresponding to a preset angle vector; splitting the frequency index matrix into an integer part matrix and a fractional part matrix; obtaining a weighting matrix based on the fractional part matrix and weighting the array element received data matrix; and outputting an output beam corresponding to the preset angle vector based on the integer part matrix and the weighted array element received data matrix. The present application proposes an arbitrary angle beamforming algorithm based on the fast Fourier transform. By studying the relationship between the angle and the spatial domain frequency, this algorithm splits the frequency index matrix of the spatial domain frequency into an integer part and a fractional part, and further designs the weighting vectors for each angle according to the fractional part, solving the problem of limited beam angles in DFT beamforming.

Description

Technical Field

[0001] The present invention relates to the technical field of beamforming, and particularly relates to a method for fast beamforming at any angle applicable to a multi-beam sounding system. Background Art

[0002] Seabed topography survey is the basis of all marine engineering activities. Its most basic task is to measure the seabed depth and map the seabed topographic map. With the continuous strengthening of human activities in ocean resource development and research, the significance of marine surveying and mapping has no longer been limited to navigation safety and scientific research, but is more related to the ownership of marine resources and territorial sovereignty.

[0003] A multi-beam sounding system is an efficient seabed mapping tool. It can simultaneously form multiple beams within a certain spatial range. Each time an acoustic wave is emitted, depth data of up to hundreds of seabed measurement points can be obtained, turning the sounding technology from "point-line" measurement into "line-plane" measurement, and greatly promoting the measurement efficiency of seabed three-dimensional topography and the quality of seabed telemetry.

[0004] Beamforming technology is a key technology required for multi-beam sounding sonar. The purpose of sonar beamforming is to make the array composed of multiple array elements obtain directivity in a predetermined direction through appropriate processing. For a transmitting system, having directivity means that the transmitted energy can be concentrated in a certain direction, so that a smaller transmitted power can be used to detect targets at a farther distance. If the receiving system has directivity, the system can receive signals directionally, thereby suppressing signals and interference from other directions. In addition, the directivity of the receiving system can be used to accurately determine the target azimuth. If the receiving system forms multiple beams, multiple targets can be resolved. The multi-beam sounding system works based on this principle.

[0005] Existing multi-beam sounding systems mostly use conventional beamforming algorithms to process the original data collected by the system to obtain beam outputs at preset angles. The conventional beamforming algorithm uses the method of weighted summation of multi-channel data, which has good robustness and high imaging accuracy. However, when the observation scene is large and the number of preformed beams is large, the computing load of the system is very large, and it is difficult to ensure the real-time performance of the system implementation.

[0006] Conventional beamforming is achieved by weighted summation of the data received by the array elements. In order to improve the calculation speed of the conventional beamforming algorithm, the DFT beamforming algorithm has emerged. Although the DFT beamforming algorithm can use the FFT to accelerate the calculation of beamforming, it can only obtain beam outputs at N fixed angles. The reason why the DFT beamforming cannot form beam outputs at arbitrary angles is that the frequency index of the DFT needs to be an integer. When the frequency index of the DFT corresponding to the calculated angle is not an integer, the DFT beamforming algorithm will fail. Therefore, this method cannot be directly applied to multi-beam sounding systems.

[0007] The commonly used DFT beamforming algorithm cannot form beam outputs at arbitrary angles. At the same time, the conventional beamforming algorithm uses the method of weighted summation of multi-channel data, which has good robustness and high imaging accuracy. However, when the observation scene is large and the number of pre-formed beams is large, the computing load of the system is very large, and it is difficult to ensure the real-time performance of the system implementation. Summary of the Invention

[0008] The purpose of this application is to solve the defects existing in the prior art.

[0009] This application provides a method for fast beamforming at arbitrary angles applicable to a multi-beam sounding system. Aiming at the problems existing in the DFT beamforming algorithm, an arbitrary angle beamforming algorithm based on the fast Fourier transform is proposed on this basis.

[0010] This application provides a method for fast beamforming at arbitrary angles applicable to a multi-beam sounding system. The multi-beam sounding system uses array elements to receive and process raw data to obtain output beams at preset angles. The beamforming method includes: determining an array element received data matrix and a preset angle vector of the output beam, where the preset angle vector includes at least one preset angle; calculating a frequency index matrix corresponding to the preset angle vector based on the existing beam angle algorithm; splitting the elements of the frequency index matrix into an integer part and a decimal part, where the integer part forms a frequency index integer matrix and the decimal part forms a frequency index decimal matrix; obtaining a weighting matrix based on the frequency index decimal matrix, and weighting the array element received data matrix to obtain a weighted array element received data matrix; outputting the output beam corresponding to the preset angle vector based on the frequency index integer matrix and the weighted array element received data matrix.

[0011] In a feasible embodiment, the obtaining a weighting matrix based on the frequency index decimal matrix, weighting the array element received data matrix to obtain a weighted array element received data matrix includes: performing an FFT transformation on the array element received data matrix to obtain an array element received data spectrum matrix; obtaining a weighting matrix based on the frequency index decimal matrix, performing an FFT transformation on the weighting matrix to obtain a weighted spectrum matrix; performing a windowing process near the peak of the weighted spectrum matrix to obtain a windowed weighted spectrum matrix; using the windowed weighted spectrum matrix to perform a convolution process on the array element received data spectrum matrix to obtain a weighted array element received data matrix.

[0012] In a feasible embodiment, splitting the elements of the frequency index matrix into an integer part and a fractional part, where the integer part forms a frequency index integer matrix and the fractional part forms a frequency index fractional matrix, includes: splitting the elements of the frequency index matrix into an integer part and a fractional part, where the integer part is the integer closest to the element of the frequency index matrix, and the fractional part is the difference between the element of the frequency index matrix and the integer part; forming the integer part into a frequency index integer matrix and the fractional part into a frequency index fractional matrix.

[0013] In a feasible embodiment, the beamforming method further includes: establishing a mapping relationship between the preset angle vector and the weighting matrix and presetting it into the multi-beam sounding system; when pre-outputting an output beam at a certain angle, obtaining the corresponding weighting matrix according to the mapping relationship.

[0014] In a feasible embodiment, calculating the frequency index matrix corresponding to the preset angle vector based on the existing beam angle algorithm includes: for a linear array with evenly distributed array elements, the array element spacing is d, and the number of array elements is N, then the conventional beamforming algorithm can be expressed by the following formula: where s k，n represents the signal sampled by the nth array element at the kth sampling moment, and β m represents the phase difference compensated between adjacent array elements. By adjusting the value of β m , the beam can be directed to different directions; for the DFT beamforming method, directly performing a discrete Fourier transform on the array element dimension data to obtain N beam outputs, and the fast Fourier transform can be used to accelerate this calculation process. The beam angle output by the DFT beamforming method can be expressed as: where p represents the frequency index of the discrete Fourier transform, and λ is the signal wavelength.

[0015] In a feasible embodiment, splitting the elements of the frequency index matrix into an integer part and a fractional part, where the integer part forms a frequency index integer matrix and the fractional part forms a frequency index fractional matrix, includes: if for any angle θ j , the beam angle is expressed as: where p j =p j，int +p j，dec , p j is an element of the frequency index matrix, p j，int =round(p j ) is the integer closest to p j , that is, the integer part, and p j，dec ∈(-0.5, 0.5) is the difference between p j and pj，int The difference therebetween, i.e., the fractional part; the integer part forms a frequency index integer matrix, and the fractional part forms a frequency index fractional matrix.

[0016] In a feasible embodiment, obtaining a weighting matrix based on the frequency index fractional matrix, and weighting the array element received data matrix to obtain a weighted array element received data matrix, includes: for any angle θ j The beamforming can be rewritten as: If we let denote the element of the weighted array element received data matrix, where k, n, and j respectively represent discrete time, array element index, and beamforming angle index; the weighted array element received data matrix is represented by the matrix: x k，n = s k，n ·W, where s n，k = [s 0，k , s 1，k , …, s N-1，k T denotes the array element received data matrix, (·) represents dot product operation, W = [w1, w2, …, w J denotes the weighting matrix, where x k，n denotes the obtained weighted array element received data matrix.

[0017] In a feasible embodiment, outputting the output beam corresponding to the preset angle vector based on the frequency index integer matrix and the weighted array element received data matrix, includes: the output beam corresponding to the preset angle vector is Y k = FFT[x k，n , where x k，n denotes the weighted array element received data matrix, FFT(·) represents fast Fourier transform, and the complex term of the fast Fourier transform contains the frequency index integer matrix; the output beam corresponding to the angle θ j can be expressed as: B j，k = Y k (p j，int , j), where Y k (p j，int , j) represents the element in the p k -th row and the j-th column of the matrix Y j，int .

[0018] In a feasible embodiment, performing windowing processing on the vicinity of the peak of the weighted spectrum matrix to obtain a windowed weighted spectrum matrix, includes: letting S k (p) and W F (p, j) be the array element received data spectrum matrix and the weighted spectrum matrix respectively, then the angle θ​j The corresponding beam output is obtained as follows: Among them, when determining the preformed beam angle, W F (p, j) can be preset as a known matrix in the system. To calculate the beam output in a certain direction, only the corresponding values need to be taken from the weighted spectrum matrix W F and used to perform weighted summation on the element received data spectrum matrix S k It is possible to perform windowing processing on W F and only take the data near the peak for calculation. In fact, each column j of the matrix W F is regarded as the spectrum of the signal with frequency Since p j，dec ∈[-0.5, 0.5], therefore the main energy of the spectrum will be concentrated in Therefore, the window function can be selected according to the position where the spectrum energy is concentrated. Among them, the narrower the window length is selected, the lower the calculation amount will be, but the error will increase accordingly.

[0019] This application provides a fast beamforming method for any angle applicable to a multi-beam sounding system. The beamforming method includes: calculating a frequency index matrix corresponding to a preset angle vector based on an existing beam angle algorithm; splitting the elements of the frequency index matrix into an integer part and a decimal part, and respectively forming a frequency index integer matrix and a frequency index decimal matrix; obtaining a weighted matrix based on the frequency index decimal matrix, and weighting the element received data matrix; and outputting an output beam corresponding to the preset angle vector based on the frequency index integer matrix and the weighted element received data matrix. This application aims at the problems existing in the DFT beamforming algorithm and proposes an arbitrary angle beamforming algorithm based on the fast Fourier transform on this basis. By studying the relationship between the angle and the spatial frequency, this algorithm splits the frequency index matrix of the spatial frequency into an integer part and a decimal part, and further designs the weighted vectors for each angle according to the decimal part, solving the problem of limited beam angles in DFT beamforming and increasing its practicability in multi-beam sounding sonars.

[0020] To solve the problems of slow calculation speed and poor system real-time performance when using the conventional beamforming method in a multi-beam sounding system with a large number of preformed beams, this application proposes an arbitrary angle beamforming algorithm based on the fast Fourier transform. The arbitrary angle beamforming algorithm utilizes the advantage of fast calculation speed of the fast Fourier transform to improve the calculation speed of beamforming. At the same time, a weighted matrix is designed for the disadvantage that the fast Fourier transform can only calculate the beam output at fixed angles, enabling it to calculate the beam output at any angle while using the fast Fourier transform algorithm. This method can improve the real-time performance of the system when the number of preformed beams in a multi-beam sounding sonar is large and is easy to implement in engineering. Description of the Drawings

[0021] Figure 1 It is a schematic flowchart of a fast beamforming method at any angle applicable to a multi-beam sounding system according to Embodiment 1 of the present invention;

[0022] Figure 2 It is the beamforming flowchart of the preset angle θ j of the present invention in Embodiment 1;

[0023] Figure 3 It is the flowchart of the FFT-AABF algorithm according to Embodiment 2 of the present invention;

[0024] Figure 4a It is the beamforming result of the FFT-AABF algorithm when the preset angle of the embodiment of the present invention is 0°;

[0025] Figure 4b It is the beamforming result of the conventional beamforming algorithm when the preset angle of the embodiment of the present invention is 0°;

[0026] Figure 4c It is the beamforming result of the DFT beamforming algorithm when the preset angle of the embodiment of the present invention is 0°;

[0027] Figure 5a It is the beamforming result of the FFT-AABF algorithm when the preset angle of the embodiment of the present invention is 10°;

[0028] Figure 5b It is the beamforming result of the conventional beamforming algorithm when the preset angle of the embodiment of the present invention is 10°;

[0029] Figure 5c It is the beamforming result of the DFT beamforming algorithm when the preset angle of the embodiment of the present invention is 10°;

[0030] Figure 6a It is the beamforming result of the FFT-AABF algorithm when the preset angle of the embodiment of the present invention is 30°;

[0031] Figure 6b It is the beamforming result of the conventional beamforming algorithm when the preset angle of the embodiment of the present invention is 30°;

[0032] Figure 6c It is the beamforming result of the DFT beamforming algorithm when the preset angle of the embodiment of the present invention is 30°;

[0033] Figure 7a It is the beamforming result when the threshold value of the FFT-AABF algorithm of the embodiment of the present invention is set to 0;

[0034] Figure 7b The threshold value for the FFT - AABF algorithm of the embodiment of the present invention is set to the beamforming result with a 10 dB drop in peak energy;

[0035] Figure 7c The threshold value for the FFT - AABF algorithm of the embodiment of the present invention is set to the beamforming result with a 3 dB drop in peak energy. Detailed implementation manners

[0036] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. All other embodiments obtained by those skilled in the art of the present technology field without creative efforts based on the embodiments of the present invention belong to the scope of protection of the present invention.

[0037] In order to enable the public to have a better understanding of the present invention, some specific details are described in detail in the following detailed description of the present invention. Those skilled in the art can fully understand the present invention without the description of these details. Detailed implementation manner 1

[0039] The embodiment of the present application provides a fast beamforming method at any angle applicable to a multi - beam sounding system. The multi - beam sounding system uses array elements to receive original data and processes it to obtain output beams at preset angles. Figure 1 It is a schematic flowchart of a fast beamforming method at any angle applicable to a multi - beam sounding system according to an embodiment of the present invention. As Figure 1 shown, the fast beamforming method at any angle includes the following steps:

[0040] Step S110, determining the array element received data matrix and the preset angle vector of the output beam, where the preset angle vector includes at least one preset angle;

[0041] Step S120, calculating the frequency index matrix corresponding to the preset angle vector based on the existing beam angle algorithm;

[0042] Step S130, splitting the elements of the frequency index matrix into an integer part and a decimal part. The integer part forms a frequency index integer matrix, and the decimal part forms a frequency index decimal matrix;

[0043] Step S140, obtaining a weighting matrix based on the frequency index decimal matrix, and weighting the array element received data matrix to obtain a weighted array element received data matrix;

[0044] In step S150, an output beam corresponding to the preset angle vector is output based on the frequency index integer matrix and the weighted array element received data matrix.

[0045] In step S120, the beam angle algorithm is further described. Conventional beamforming is achieved by weighted summation of the array element received data. Specifically, considering a uniformly distributed linear array with an element spacing of d and the number of array elements being N, the conventional beamforming algorithm can be expressed by the following formula:

[0046]

[0047] where s k，n represents the signal sampled by the nth array element at the kth sampling moment, and β m represents the phase difference compensated between adjacent array elements. By adjusting the value of β m , the beam can be directed to different directions.

[0048] To improve the calculation speed of the conventional beamforming algorithm, the DFT beamforming algorithm emerged. This algorithm directly performs a discrete Fourier transform on the array element dimension data to obtain N beam outputs. The fast Fourier transform can be used to accelerate this calculation process. The beam angles output by this method can be expressed by the following formula:

[0049]

[0050] where p represents the frequency index of the discrete Fourier transform, δ is the result of taking the remainder of N divided by 2, that is, when N is even, δ = 0, and when N is odd, δ = 1, and λ is the signal wavelength. It can be seen from Equation (2) that although the DFT beamforming algorithm can use the FFT to accelerate the calculation of beamforming, it can only obtain N beam outputs at fixed angles. The reason why the DFT beamforming cannot form beam outputs at arbitrary angles is that the frequency index p of the DFT needs to be an integer. When the p corresponding to the angle θ calculated using the relationship in Equation (2) is not an integer, the DFT beamforming algorithm will fail. Therefore, this method cannot be directly applied in a multi-beam sounding system.

[0051] To solve the problems of the DFT beamforming algorithm, this application proposes an arbitrary angle beamforming algorithm based on the fast Fourier transform to improve the DFT beamforming algorithm.

[0052] The phase difference in Equation (1) can be expressed in the following form:

[0053]

[0054] where θ m is the angle corresponding to the phase β m . Then Equation (1) can be rewritten as:

[0055]

[0056] Let Since θ m ∈[-90°, 90°], when f s ∈[-0.5, 0.5], at this time, f s can be called the spatial domain frequency. Perform discrete Fourier transform (DFT) on the array element dimension signal s k，n at time k:

[0057]

[0058] where is the digital frequency.

[0059] If we let:

[0060]

[0061] Combining equations (4) and (5), it can be seen that when the relationship in equation (6) exists, the beamforming result of the angle θ m is equivalent to the spectral data of the corresponding frequency point of p m after performing DFT on the array element dimension signal. According to the relationship described in equation (6), the beamforming result at a fixed angle can be obtained using DFT, and these fixed angles can be calculated by the following formula:

[0062]

[0063] The above method is called DFT beamforming. Therefore, the beamforming can be calculated using the FFT algorithm, and the benefit is the improvement of the calculation speed. However, the main disadvantage of this method is that it can only form beams at fixed angles, and these angles are determined by the arcsine function of N discrete points of .

[0064] In step S130, to solve the problem that DFT beamforming cannot output beams at arbitrary angles, this application proposes a new DFT beamforming method. From equation (7), it can be seen that the reason why DFT beamforming cannot output beams at arbitrary angles is that p m must be an element of the set , that is, p m needs to be an integer. For any angle θ j , equation (6) can be written as:

[0065]

[0066] where

[0067] p j= p j，int + p j，dec (9)

[0068] p j，int = round(p j ) is the integer closest to the distance p j , and p j，dec ∈ (-0.5, 0.5) is the difference between p j and p j，int .

[0069] In step S140, based on equation (9), the beamforming for any angle θ j can be rewritten as:

[0070]

[0071] If we let

[0072]

[0073] where k, n, j represent discrete time, array element index, and beamforming angle index respectively, and x k，n，j is the element in the weighted array element received data matrix.

[0074] In step S150, based on the frequency index integer matrix and the weighted array element received data matrix, the output beam corresponding to the preset angle vector is output. Based on equation (11), the output beam equation (10) can become:

[0075]

[0076] At this time, the beamforming of the angle θ j can be regarded as the value of the DFT of x k，n，j at the array element dimension at the frequency point corresponding to p j，int . Therefore, performing DFT after weighting the array signal can obtain the beamforming at any angle. This process can Figure 2 be represented by the flowchart shown.

[0077] To make the formula expression more concise, define

[0078] W = [w1, w2,..., w J (13)

[0079] as the weighting matrix, where Using equation (13), equation (10) can be represented in matrix form as:

[0080] Y k = FFT[s n，k · W] (14)

[0081] where s n，k = [s 0，k , s 1，k ,..., s N-1，k T , (·) represents the dot product operation, and FFT(·) represents the fast Fourier transform. Then the beam output corresponding to the angle θ j can be expressed as:

[0082] B j，k = Y k (p j，int , j) (15)

[0083] where Y k (p j，int , j) represents the element in the p k -th row and j-th column of the matrix Y j，int . Specific Embodiment 2

[0085] To solve the problem of high computational complexity in Specific Embodiment 1, the present application provides another specific embodiment.

[0086] For convenience, we refer to the arbitrary angle beamforming algorithm based on the fast Fourier transform proposed in Specific Embodiment 2 as FFT-AABF (Arbitrary Angle Beamforming based on Fast Fourier Transform). The algorithm for implementing beamforming requires a total of five steps. The first step is to calculate the frequency index of the corresponding spatial domain frequency for the pre-set angle and divide it into an integer part and a fractional part; the second step is to calculate the weighting matrix using the fractional part, the third step is to transform the weighting matrix to the frequency domain using FFT and window it, the fourth step is to calculate the spectrum of the input array signal, and the fifth step is to convolve the array signal spectrum with the weighting matrix spectrum to obtain the beam output corresponding to each angle. The algorithm flow chart is as Figure 3 shown. The first two steps of this algorithm are the same as those in Specific Embodiment 1, and the third, fourth, and fifth steps are further described.

[0087] Specific Embodiment 1 solves the problem that the DFT beamforming cannot calculate the beam output at arbitrary angles. However, as can be seen from the Figure 2 flow chart shown, currently, according to this process, one FFT needs to be calculated for each calculation of the beam at an angle, and only one of the N frequency points calculated is the result required. Therefore, the calculation efficiency is low according to the above process. In fact, from the perspective of computational complexity, the above process for beamforming the signals of N channels in a certain time slice requires two steps of weighting and FFT, and it takes ​The proposed method requires N log2 N complex multiplications and N log2 N additions, while the conventional beamforming only requires N complex multiplications and (N - 1) complex additions.

[0088] The reason for the high computational complexity of the method in Embodiment 1 is the repeated calculation of FFT and the low utilization rate of the calculation results. To improve the computational efficiency, we consider converting the calculation to the frequency domain. Specifically, since there is a corresponding relationship between the time domain and the frequency domain of a signal, the spectrum of the signal obtained by multiplying two time-domain signals is equivalent to the convolution of the two signals in the frequency domain. Let S k (p) and W F (p, j) be the spectra of s k，n and w j，n respectively, then the beam output corresponding to the angle θ j can be calculated by the following formula:

[0089]

[0090] Observing the above formula, it can be seen that the beam output can still be regarded as a weighted summation form. When the preformed beam angle is determined, W F (p, j) can be pre-calculated as a known matrix and does not require computational resources during beamforming. Calculating the beam output in a certain direction only requires taking the corresponding values in the matrix W F and performing weighted summation on the signal spectrum S k . Therefore, for the array element dimension signal in a certain time slice, this method only needs to perform one FFT operation and several multiplication and addition operations.

[0091] Equation (16) describes the convolution operation between S k and W F . The theoretical computational complexity of this equation is N multiplications and N - 1 additions. However, both S k and W F are finite-length sequences. To further reduce the computational complexity, we can choose to window W F and only take the data near the peak for calculation. In fact, the j-th column of the matrix W F can be regarded as the spectrum of the signal with frequency . Since p j，dec ∈ [-0.5, 0.5], the main energy of the spectrum of will be concentrated in . Therefore, the window function can be selected according to the position where the spectrum energy is concentrated. The narrower the window length is selected, the lower the computational complexity will be, but the error will increase accordingly. We summarize the process of the FFT-AABF algorithm in Table 1.

[0092] Table 1 Flow chart of FFT-AABF algorithm

[0093]

[0094] Example 1

[0095] In this example, the FFT-AABF algorithm of the present application is implemented through computer simulation experiments, and a comparative analysis is carried out with the conventional beamforming algorithm and the DFT beamforming algorithm.

[0096] The number of array elements N is set to 8, the number of snapshots (the number of sampling points per channel) K is set to 100, the signal center frequency is set to 300 kHz, the sampling frequency is set to 1.5 MHz, and the signal-to-noise ratio is set to 10 dB. We simulated the beamforming results of the above three methods at preset angles of 0°, 10°, and 30° respectively. Among them, Figure 4a is the beamforming result of the FFT-AABF algorithm when the preset angle of the embodiment of the present invention is 0°; Figure 4b is the beamforming result of the conventional beamforming algorithm when the preset angle of the embodiment of the present invention is 0°; Figure 4c is the beamforming result of the DFT beamforming algorithm when the preset angle of the embodiment of the present invention is 0°; Figure 5a is the beamforming result of the FFT-AABF algorithm when the preset angle of the embodiment of the present invention is 10°; Figure 5b is the beamforming result of the conventional beamforming algorithm when the preset angle of the embodiment of the present invention is 10°; Figure 5c is the beamforming result of the DFT beamforming algorithm when the preset angle of the embodiment of the present invention is 10°; Figure 6a is the beamforming result of the FFT-AABF algorithm when the preset angle of the embodiment of the present invention is 30°; Figure 6b is the beamforming result of the conventional beamforming algorithm when the preset angle of the embodiment of the present invention is 30°; Figure 6c is the beamforming result of the DFT beamforming algorithm when the preset angle of the embodiment of the present invention is 30°. Both the FFT-AABF algorithm and the conventional beamforming algorithm can control the receiving beam in any direction. Therefore, in the simulation, the beam scanning angle ranges of the two methods are both set to -90° to 90°, and the scanning angle interval is set to 1°.

[0097] First, the above three algorithms are simulated without windowing, and the simulation results are as shown in Figure 4a , Figure 4b , Figure 4c , as shown in Figure 5a , Figure 5b , Figure 5c , as shown in Figure 6a , Figure 6b , Figure 6cAs shown. It can be seen from the simulation results that both the FFT-AABF algorithm and the conventional beamforming algorithm can perform scanning in the range of -90° to 90°, while the DFT beamforming algorithm can only calculate the beam outputs at N fixed angles. The DFT beamforming algorithm has a fast calculation speed, but compared with the previous two algorithms, its disadvantage is that it is difficult to achieve equiangular or equidistant beams required by the multi-beam sounding system, and there will inevitably be an angle estimation error when the preset angle does not appear at the corresponding angle of the DFT beamforming. For example, in Figure 6c , the preset angle is 30°, however, 30° does not exist among the angles corresponding to each beam of the DFT beamforming, and the closest angle is 36.8°, so the DFT beamforming forms a pseudo peak at the 36.8° position. Although the number of output beams can be increased by zero-padding operation, it is still impossible to calculate the beam output in any specified direction. The FFT-AABF algorithm solves this problem. By comparing the FFT-AABF algorithm and the conventional beamforming algorithm without windowing, it can be seen that at different preset angles, the FFT-AABF algorithm can achieve the same angle estimation accuracy as the conventional beamforming, indicating that the performance of this algorithm in this application is consistent with that of the conventional beamforming algorithm without windowing.

[0098] Next, the influence of windowing on the performance of the FFT-AABF algorithm is studied. In this embodiment, the values in the frequency-domain matrix W FW of the weight vector are screened according to energy, and the values higher than the threshold are selected to participate in the convolution operation. The threshold values are respectively selected as 0 (equivalent to no threshold), the value corresponding to a 10 dB drop in peak energy, and the value corresponding to a 3 dB drop in peak energy as the screening thresholds, and the simulation results are respectively as Figure 7a , Figure 7b , Figure 7c shown. It can be seen from the simulation results that when the threshold value is set to 0, all the values in the matrix W FW are retained, so there is no error compared with the conventional beamforming algorithm; when the threshold value is set to the value corresponding to a 10 dB drop in peak energy, compared with the conventional beamforming result, there is an obvious error in the beam output of the FFT-AABF algorithm at the null point, but it still coincides with the conventional beamforming result near the peaks of the main lobe and sidelobes; when the threshold value is set to the value corresponding to a 3 dB drop in peak energy, larger errors begin to appear in the sidelobes of the FFT-AABF algorithm, but it still coincides with the conventional beamforming result near the peak of the main lobe. This simulation shows that windowing the matrix W FW will cause errors in the beam output, and the narrower the window length, the greater the introduced error, but the error is concentrated in the sidelobes and has little impact on the beam output result of the main lobe. Therefore, the method of windowing can be used to reduce the algorithm calculation complexity under the condition of ensuring the performance of the beam main lobe.

[0099] Finally, by comparing with the conventional beamforming algorithm, the influence of windowing on the operation speed of the FFT-AABF algorithm is studied. When performing beamforming on a time slice, for the conventional beamforming algorithm, N complex multiplications and (N - 1) complex additions are required for each angle. For the FFT-AABF algorithm, the same amount of calculation is needed without windowing. However, windowing can effectively improve the calculation speed of the FFT-AABF algorithm.

[0100] For the data on a time slice, the conventional beamforming algorithm requires NJ complex multiplications and (N - 1)J complex additions to calculate the beams in J directions. Assume that the number of non-zero elements in the matrix W FW after windowing in the FFT-AABF algorithm is N no , obviously 0 < N no < NJ. At this time, when this algorithm also calculates the beams in J directions, it only needs N no complex multiplications and about N no - J complex additions. Therefore, the computational complexity of the windowed FFT-AABF algorithm is lower than that of the conventional beamforming algorithm.

[0101] Through MATLAB simulation, the running time of the FFT-AABF algorithm after windowing the matrix W FW with different thresholds for 8-channel data is compared, and it is compared with the conventional beamforming algorithm. In the simulation, the number of beams J is set to 181. The simulation results are shown in Tables 2 and 3. Table 2 gives the comparison of the number of multiplication and addition calculations of the two algorithms in the simulation. When the threshold of the FFT-AABF algorithm is 0, the number of multiplication and addition operations is the same as that of the conventional beamforming. As the threshold value increases, the number of multiplication and addition operations of this algorithm decreases significantly. Table 3 gives the comparison of the actual running time of the two algorithms. The running time is obtained by statistically performing 100,000 experiments on each algorithm in the same environment. From the results, it can be seen that the operation time of the conventional beamforming algorithm and the FFT-AABF algorithm when the threshold is 0 is the same, both are 2.5 ms. As the threshold value increases, the operation time of the FFT-AABF algorithm decreases significantly. When the threshold is -10 dB, the operation time is 1.6 ms, and when the threshold is -3 dB, the operation time is 0.5 ms.

[0102] Table 2 Comparison of Computational Amounts between FFT-AABF Algorithm and Conventional Beamforming Algorithm

[0103]

[0104] Table 3 Comparison of Running Times between FFT-AABF Algorithm and Conventional Beamforming Algorithm

[0105]

[0106] Compared with the DFT beamforming algorithm, the FFT-AABF algorithm proposed in this application maps the beam angle to spatial frequency, divides the spatial frequency into an integer part and a fractional part, and designs a weight matrix using the fractional part to weight the array signals, solving the problem that the DFT beamforming cannot calculate the beam output in any arbitrarily specified direction. At the same time, in order to improve the operation speed of the algorithm, the time-domain weighting is converted to the frequency domain, and the calculation amount of the algorithm is effectively reduced by windowing. As an improved algorithm of DFT beamforming, the proposed FFT-AABF algorithm improves the flexibility of the original algorithm and makes it a beamforming algorithm suitable for multi-beam sounding systems.

[0107] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative effort.

[0108] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solution, in essence, or the part that contributes to the prior art can be embodied in the form of a software product, which can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0109] The specific embodiments described above further elaborate on the purpose, technical solution, and beneficial effects of the present invention. Therefore, it is understood that the above description is only one of the specific embodiments of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for fast beamforming at any angle applicable to a multi-beam sounding system, wherein the multi-beam sounding system uses array elements to receive and process raw data to obtain output beams at preset angles, characterized in that Including: Determine the received data matrix of the array elements and the preset angle vector of the output beam, where the preset angle vector includes at least one preset angle; Based on the existing beam angle algorithm, calculate the frequency index matrix corresponding to the preset angle vector; Split the elements of the frequency index matrix into an integer part and a fractional part, where the integer part forms a frequency index integer matrix and the fractional part forms a frequency index fractional matrix; Based on the frequency index fractional matrix, obtain a weighting matrix, and weight the received data matrix of the array elements to obtain a weighted received data matrix of the array elements; Based on the frequency index integer matrix and the weighted received data matrix of the array elements, output the output beam corresponding to the preset angle vector; Among them, the calculating the frequency index matrix corresponding to the preset angle vector based on the existing beam angle algorithm includes: The array elements are a linear array with uniform distribution, the element spacing is d, and the number of array elements is N. Then the conventional beamforming algorithm can be expressed by the following formula: where s k,n represents the signal sampled by the nth array element at the kth sampling moment, and β m represents the phase difference compensated between adjacent array elements. By adjusting the value of β m , the beam can be directed to different directions; The DFT beamforming method directly performs a discrete Fourier transform on the element dimension data to obtain N beam outputs. The fast Fourier transform can be used to accelerate this calculation process. The beam angle output by the DFT beamforming method can be expressed as: where p represents the frequency index of the discrete Fourier transform, and λ is the signal wavelength; The splitting the elements of the frequency index matrix into an integer part and a fractional part, where the integer part forms a frequency index integer matrix and the fractional part forms a frequency index fractional matrix, includes: If for any angle θ j , the beam angle is expressed as: where p j = p j,int + p j,dec , p j is an element of the frequency index matrix, p j,int = round(p j ) is the integer closest to p j , that is, the integer part. p j,dec where \(p\in(-0.5,0.5)\) j The difference between j,int and \(p\) is the fractional part. The integer part forms a frequency index integer matrix, and the fractional part forms a frequency index fractional matrix.

2. The beamforming method according to claim 1, wherein The obtaining a weighting matrix based on the frequency index fractional matrix, and weighting the received data matrix of the array elements to obtain a weighted received data matrix of the array elements, includes: Perform FFT transformation on the received data matrix of the array elements to obtain a received data spectrum matrix of the array elements; Based on the frequency index fractional matrix, obtain a weighting matrix, perform FFT transformation on the weighting matrix to obtain a weighted spectrum matrix; Perform windowing processing on the vicinity of the peak of the weighted spectrum matrix to obtain a windowed weighted spectrum matrix; Use the windowed weighted spectrum matrix to perform convolution processing on the received data spectrum matrix of the array elements to obtain a weighted received data matrix of the array elements.

3. The beamforming method according to claim 1, characterized in that, The splitting the elements of the frequency index matrix into an integer part and a fractional part, where the integer part forms a frequency index integer matrix and the fractional part forms a frequency index fractional matrix, includes: The splitting the elements of the frequency index matrix into an integer part and a fractional part, where the integer part is the integer closest to the element of the frequency index matrix, and the fractional part is the difference between the element of the frequency index matrix and the integer part; Form the integer part into a frequency index integer matrix, and the fractional part into a frequency index fractional matrix.

4. The beamforming method according to claim 1, wherein Also including: Establish the mapping relationship between the preset angle vector and the weighting matrix, and preset it into the multi-beam sounding system; When pre-outputting the output beam at a certain angle, obtain the corresponding weighting matrix according to the mapping relationship.

5. The beamforming method according to claim 1, characterized in that The obtaining a weighting matrix based on the frequency index fractional matrix, and weighting the received data matrix of the array elements to obtain a weighted received data matrix of the array elements, includes: Arbitrary angle θ j The beamforming can be rewritten as: If we let represent the element of the weighted array element received data matrix, where k, n, and j represent discrete time, array element index, and beamforming angle index respectively; The weighted array element received data matrix is represented by the matrix: x k,n = s k,n ·W, where s k,n = [s 0,k , s 1,k , …, s N-1,k T represents the array element received data matrix, (·) represents the dot product operation, W = [w1, w2, …, w J represents the weighting matrix, where x k,n represents the obtained weighted array element received data matrix.​ 6. The beamforming method according to claim 5, wherein The outputting the output beam corresponding to the preset angle vector based on the frequency index integer matrix and the weighted received data matrix of the array elements, includes: The output beam corresponding to the preset angle vector is Y k = FFT[x k,n , where x k,n represents the weighted array element received data matrix, FFT(·) represents the fast Fourier transform, and the complex term of the fast Fourier transform includes the frequency index integer matrix; Angle θ j The corresponding output beam can be expressed as: B j,k = Y k (p j,int , j), where Y k (p j,int , j) represents the element in the p k -th row and the j j,int -th column of the matrix Y 7. The beamforming method according to claim 6, wherein The performing windowing processing on the vicinity of the peak of the weighted spectrum matrix to obtain a windowed weighted spectrum matrix, includes: Let S k (p) and W F (p,j) be the spectral matrix of the received data of the array elements and the weighted spectral matrix respectively. Then, for the angle θ j the corresponding beam output is obtained as follows: where, when determining the preformed beam angle, W F (p,j) can be preset as a known matrix in the system. To calculate the beam output in a certain direction, only the corresponding values need to be taken from the weighted spectral matrix W F and used to perform weighted summation on the spectral matrix S k of the received data of the array elements; Windowing can be performed on W F and only the data near the peak is taken for calculation. In fact, each column of matrix W F is regarded as the spectrum of a signal with a frequency of . Since p j,dec ∈[-0.5,0.5], the main energy of the spectrum of will be concentrated at Therefore, the window function can be selected according to the position where the spectrum energy is concentrated. Among them, the narrower the window length is selected, the lower the computational amount is, but the error will increase accordingly.

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