Wideband MVDR beamforming calculation method

Abstract

This invention discloses a broadband MVDR beamforming calculation method. This method reconstructs the spatial spectrum calculation process of the MVDR algorithm, first establishing a spatial spectrum estimation matrix for the initial frequency points. Then, by precalculating the frequency increment matrix, the independent frequency-point calculations in the traditional algorithm are converted into incremental updates of the Hadamard product. This method addresses the problem of a large number of exponential operations leading to a dramatic increase in computational complexity in broadband MVDR algorithms. By leveraging the associative nature of the Hadamard product, this method reduces the number of complex exponential operations from MFK to 2MK, thereby reducing array computation time while maintaining beamforming accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of array signal processing technology, and specifically relates to a broadband MVDR beamforming calculation method, which is particularly suitable for broadband signal processing scenarios, including but not limited to sonar detection and high-resolution DOA estimation in radar systems. Background Art

[0002] The minimum variance distortionless response (MVDR) algorithm leverages the sensor's spatial information to estimate the direction of arrival (DOA) of the desired signal. This algorithm minimizes the output power while maintaining the distortionless response constraint (maintaining a gain of 1 in the target direction). Finally, by scanning the spatial power spectrum to find the angle corresponding to the power peak, high-resolution DOA estimation is achieved.

[0003] The technical drawback of traditional MVDR calculation methods is that their computational complexity increases cubically with the number of array elements M, the number of frequency bins F, and the number of azimuth angles K. Each frequency bin requires M repeated complex exponential operations, resulting in a total of MFK complex exponential operations. Furthermore, significant latency exists when processing large arrays in real time, making it difficult to meet the real-time requirements of sonar detection systems. Summary of the Invention

[0004] The present invention provides a broadband MVDR beamforming calculation method to solve the above-mentioned technical problems, specifically adopting the following technical solutions:

[0005] A broadband MVDR beamforming calculation method comprises the following steps:

[0006] Receive array signals and calculate covariance matrix;

[0007] According to the steering vector of the initial frequency point and the inverse matrix of the covariance matrix, the initial spatial spectrum estimation matrix is ​​calculated by calculating the Hadamard product;

[0008] Precompute the frequency increment matrix;

[0009] Iteratively updating the spatial spectrum estimation matrix of the next frequency point by using the frequency increment matrix;

[0010] The MVDR spatial broadband power is calculated based on the spatial spectrum estimation matrix.

[0011] Furthermore, the specific method of receiving array signals and calculating the covariance matrix is:

[0012] Receive array signal , is a Matrix, N is the number of snapshots, M is the number of array elements;

[0013] The covariance matrix is ​​calculated using the following formula:

[0014] ;

[0015] in, is the covariance matrix, represents the conjugate transpose.

[0016] Furthermore, the specific method of calculating the initial spatial spectrum estimation matrix by calculating the Hadamard product based on the steering vector of the initial frequency point and the inverse matrix of the covariance matrix is ​​to calculate the initial spatial spectrum estimation matrix by the following formula:

[0017] ;

[0018] in, represents the Hadamard product, represents conjugation, represents the conjugate transpose, for The inverse matrix of is the azimuth The frequency is The steering vector describes the phase difference of the signal reaching each array element.

[0019] Furthermore, the frequency increment matrix is:

[0020]

[0021] Furthermore, the specific method of iteratively updating the spatial spectrum estimation matrix of the next frequency point through the frequency increment matrix is:

[0022] The initial spatial spectrum estimation matrix and the frequency increment matrix are calculated based on the Hadamard product calculation method to obtain the spatial spectrum estimation matrix of the next frequency point.

[0023] Furthermore, the spatial spectrum estimation matrix of the next frequency point is calculated by the following formula:

[0024] ;

[0025] in, Represents the Hadamard product.

[0026] Furthermore, the specific method for calculating the MVDR spatial broadband power according to the spatial spectrum estimation matrix of each frequency point is:

[0027] MVDR spatial broadband power as follows:

[0028] ;

[0029] in, Representation matrix The sum of all elements in .

[0030] Furthermore, the broadband MVDR beamforming calculation method further includes:

[0031] Traverse the azimuth angles to obtain the MVDR spatial broadband power corresponding to each azimuth angle, and calculate the complete spatial power spectrum.

[0032] Furthermore, the broadband MVDR beamforming calculation method further includes:

[0033] Scan the spatial power spectrum to find the angle corresponding to the power peak.

[0034] The broadband MVDR beamforming calculation method of the present application addresses the problem of a sharp increase in computational complexity due to a large number of exponential operations in broadband MVDR algorithms. By utilizing the associative property of the Hadamard product, the number of complex exponential operations is reduced from MFK to 2MK. While maintaining beamforming accuracy, the calculation time for small-scale arrays is reduced by approximately 50%, and for large-scale arrays by approximately 40%. The number of frequency points does not affect the consumption reduction ratio, significantly improving the real-time processing capabilities of broadband array systems such as radar and sonar. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0036] Figure 1 is a flow chart of the broadband MVDR calculation method of the present invention;

[0037] Figure 2 This is a comparison diagram of the spatial spectrum estimation output results of the present invention and the traditional method;

[0038] Figure 3 This is a graph showing the relationship between the computation time and the number of array elements for the present invention and the traditional method;

[0039] Figure 4 This is a graph showing the relationship between the calculation time and the number of frequency points of the present invention and the traditional method. DETAILED DESCRIPTION

[0040] The following describes in detail embodiments of the present application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0041] Assume a For a uniform linear array composed of elements (such as antennas, microphones, sonar sensors), the received signal can be expressed as:

[0042] ;

[0043] ;

[0044] in: Indicates the target signal, represents noise and interference from other directions, Indicates the target direction, represents the target frequency, d represents the array element spacing, c represents the speed of sound, Indicates the corresponding target direction and target frequency The steering vector describes the phase difference of the signal reaching each array element. It represents the signal collected by the M-element array at the receiving end, including the target signal, noise and interference. Discretize into a matrix ,in:

[0045] , N represents the number of beats, Indicates the sampling duration, and fs indicates the sampling duration.

[0046] Assume that the target is a narrowband signal and the signal center frequency Known, in a certain direction When making an estimate, MVDR uses a set of weights Perform weighted summation on the received signals and the output is:

[0047]

[0048] The goal of MVDR is to minimize the output power while ensuring that the signal in the target direction is not distorted. , to achieve the purpose of suppressing noise and interference. ,but MVDR can be viewed as a constrained optimization problem:

[0049]

[0050] Using the Lagrange multiplier method, the optimal weight of MVDR can be derived as:

[0051]

[0052] Substitution , and get the MVDR pair The output power in the direction is:

[0053]

[0054] Traverse the possible azimuths of the target , the output power in the corresponding direction can be calculated .

[0055] If the target is a broadband signal, its frequency range is , we can use the conclusion of narrowband signal MVDR and integrate the frequency to get the MVDR output power of broadband signal:

[0056]

[0057] Changing to discrete form: ;

[0058] ;

[0059] Where f represents the discretized frequency axis, Indicates the number of frequency points, is the left end point of the frequency band, The right end point of the frequency band. is the frequency resolution, usually set to .

[0060] The computational complexity of the MVDR calculation method described above increases cubically with the number of array elements M, the number of frequency points F, and the number of azimuth angles K, O(MFK). Each frequency point requires M repeated complex exponential operations, resulting in a total of MFK complex exponential operations. Furthermore, there is significant latency in real-time processing of large-scale arrays, making it difficult to meet the real-time requirements of sonar detection systems.

[0061] Based on this, Figure 1 As shown, the present application discloses a broadband MVDR beamforming calculation method, comprising the following steps:

[0062] S1: Receive array signals and calculate the covariance matrix.

[0063] Specifically, the specific method of receiving array signals and calculating the covariance matrix is:

[0064] Receive array signal , is a The matrix, N is the number of snapshots, M is the number of array elements. express The signal value received by array element j at time j.

[0065] The covariance matrix is ​​calculated using the following formula:

[0066] ;

[0067] in, is the covariance matrix, represents the conjugate transpose.

[0068] S2: Calculate the initial spatial spectrum estimation matrix by calculating the Hadamard product based on the steering vector of the initial frequency point and the inverse matrix of the covariance matrix.

[0069] Furthermore, the initial spatial spectrum estimation matrix is ​​calculated by calculating the Hadamard product based on the steering vector of the initial frequency point and the inverse matrix of the covariance matrix. The specific method is to calculate the initial spatial spectrum estimation matrix using the following formula:

[0070] ;

[0071] in, represents the Hadamard product, represents conjugation, represents the conjugate transpose, for The inverse matrix of is the azimuth The frequency is The steering vector describes the phase difference of the signal reaching each array element.

[0072] S3: Precompute frequency increment matrix.

[0073] Specifically, the frequency increment matrix is:

[0074]

[0075] S4: Iteratively update the spatial spectrum estimation matrix of the next frequency point through the frequency increment matrix.

[0076] The spatial spectrum estimation matrix of the next frequency point is calculated using the following formula:

[0077] ;

[0078] in, represents the Hadamard product, which is derived as follows:

[0079] ;

[0080]

[0081] S5: Calculate the MVDR spatial broadband power based on the spatial spectrum estimation matrix of each frequency point.

[0082] MVDR spatial broadband power:

[0083]

[0084] The denominator of the above formula is a row vector ,matrix and column vector Multiplication of . , Substitute the following formula:

[0085] ;

[0086] get:

[0087] ;

[0088] Substitute the above formula into have to:

[0089] ;

[0090] in: Representation matrix The sum of all elements in .

[0091] when hour, From step 2, when hour, Obtained by iteration in step 4.

[0092] The above steps calculate the MVDR spatial wideband power for a given azimuth. Furthermore, the azimuths are traversed to obtain the MVDR spatial wideband power corresponding to each azimuth, thereby calculating the complete spatial power spectrum. Furthermore, the spatial power spectrum is scanned to find the angle corresponding to the power peak.

[0093] The following table shows pseudo code for implementing the broadband MVDR calculation method of the present invention.

[0094] Table 1 Pseudo code of the broadband MVDR calculation method of the present invention

[0095]

[0096] The method of the present application is verified by means of specific examples below.

[0097] Example 1 (algorithm accuracy verification experiment):

[0098] This example is used to verify the consistency of the proposed algorithm and the traditional MVDR algorithm in the direction of arrival (DOA) estimation accuracy. The specific implementation is as follows:

[0099] 1. Experimental environment configuration:

[0100] Hardware platform: Intel Xeon Platinum 8260 processor @ 2.40GHz;

[0101] Software environment: g++ 9.4.0 compiler.

[0102] 2. Simulation parameter settings:

[0103] Table 2 Simulation parameter configuration table

[0104]

[0105] 3. Implementation steps:

[0106] An array receiving signal containing Gaussian white noise is generated and processed using the traditional MVDR algorithm and the algorithm of the present invention.

[0107] 4. Experimental results:

[0108] like Figure 2 As shown, the spatial resolution of the algorithm of the present invention is equivalent to that of the traditional algorithm, maintaining a high algorithm accuracy, and is suitable for high-precision sonar detection scenarios.

[0109] Example 2 (computational efficiency verification experiment):

[0110] This embodiment tests the real-time performance of the algorithm under arrays of different sizes, which is divided into two sub-experiments.

[0111] Experiment 2.1 (Test of changing the number of array elements):

[0112] Fixed parameters: 1000 frequencies, 181 azimuths;

[0113] Variable parameters: number of array elements 10~100 elements;

[0114] Test results: When other test conditions remain unchanged and the number of array elements increases from 10 to 100, Figure 3 As shown in the table below, compared with the traditional method, the time consumption of the present invention is reduced from 63.5% to 40.0%.

[0115] Table 3 Relationship between the calculation time and the number of array elements of the present invention and the traditional method

[0116]

[0117] Experiment 2.2 (Frequency conversion point number test):

[0118] Fixed parameters: 20 array elements, 181 azimuth angles;

[0119] Variable parameters: frequency points 10~20000;

[0120] Test results: When other test conditions remain unchanged and the number of frequency points increases from 10 to 20000, Figure 4 As shown in the table below, compared with the traditional method, the time consumption of the present invention is reduced by about 50%.

[0121] Table 4 Relationship between the calculation time and the number of frequency points of the present invention and the traditional method

[0122]

[0123] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the present invention in any form, and any technical solutions obtained by equivalent replacement or equivalent transformation fall within the scope of protection of the present invention.

Claims

1. A broadband MVDR beamforming calculation method, characterized in that: The following steps are involved: Receive array signals and calculate covariance matrix; According to the steering vector of the initial frequency point and the inverse matrix of the covariance matrix, the initial spatial spectrum estimation matrix is ​​calculated by calculating the Hadamard product; Precompute the frequency increment matrix; Iteratively updating the spatial spectrum estimation matrix of the next frequency point by using the frequency increment matrix; The MVDR spatial broadband power is calculated based on the spatial spectrum estimation matrix of each frequency point.

2. The broadband MVDR beamforming calculation method according to claim 1, characterized in that: The specific method of receiving array signals and calculating the covariance matrix is: Receive array signal , is a Matrix, N is the number of snapshots, M is the number of array elements; The covariance matrix is ​​calculated using the following formula: in, is the covariance matrix, represents the conjugate transpose.

3. The broadband MVDR beamforming calculation method according to claim 2, characterized in that: The specific method of calculating the initial spatial spectrum estimation matrix by calculating the Hadamard product based on the steering vector of the initial frequency point and the inverse matrix of the covariance matrix is ​​to calculate the initial spatial spectrum estimation matrix by the following formula: in, represents the Hadamard product, represents conjugation, represents the conjugate transpose, for The inverse matrix of is the azimuth The frequency is The steering vector describes the phase difference of the signal reaching each array element.

4. The broadband MVDR beamforming calculation method according to claim 3, characterized in that: The frequency increment matrix is: 。 5. The broadband MVDR beamforming calculation method according to claim 4, characterized in that: The specific method of iteratively updating the spatial spectrum estimation matrix of the next frequency point by using the frequency increment matrix is: The initial spatial spectrum estimation matrix and the frequency increment matrix are calculated based on the Hadamard product calculation method to obtain the spatial spectrum estimation matrix of the next frequency point.

6. The broadband MVDR beamforming calculation method according to claim 5, characterized in that: The spatial spectrum estimation matrix of the next frequency point is calculated using the following formula: in, represents the Hadamard product.

7. The broadband MVDR beamforming calculation method according to claim 6, characterized in that: The specific method for calculating the MVDR spatial broadband power according to the spatial spectrum estimation matrix of each frequency point is: MVDR spatial broadband power as follows: in, Representation matrix The sum of all elements in .

8. The broadband MVDR beamforming calculation method according to claim 1, wherein: The broadband MVDR beamforming calculation method further comprises: Traverse the azimuth angles to obtain the MVDR spatial broadband power corresponding to each azimuth angle, and calculate the complete spatial power spectrum.

9. The broadband MVDR beamforming calculation method according to claim 8, characterized in that: The broadband MVDR beamforming calculation method further comprises: Scan the spatial power spectrum to find the angle corresponding to the power peak.

Images