A sum-difference beam direction finding and tracking method based on adaptive digital beamforming

Abstract

The application provides a sum-difference beam direction finding method based on adaptive digital beam forming, which first divides a non-regular antenna array into four sub-arrays of upper, lower, left and right by taking x-axis and y-axis as boundaries, and then performs spatial anti-interference on each sub-array through adaptive digital beam forming, so that the array has adaptive anti-interference capability and the subsequent direction finding precision is improved; then the prior direction of the sum-difference beam algorithm is changed through iteration, and the phase and amplitude of the anti-interference beam synthesized by each sub-array are compensated, and then the sum-difference beam iteration is used to solve the target signal direction, until the algorithm converges to the preset threshold range. The signal direction estimation is more accurate when the method converges, so that the high-precision direction finding and tracking problem of the non-regular array in a strong interference environment is solved.

Description

Technical Field

[0001] This invention relates to a direction finding and tracking method for irregular arrays, and particularly to a sum-difference beam direction finding and tracking method based on adaptive digital beamforming (MVDR). Background Technology

[0002] Array signal processing is a crucial component of signal processing, primarily studying the information carried by spatial signals—specifically, processing spatial signals received by spatially arranged antenna arrays to extract information. Direction of arrival (DOA) estimation is a key area of ​​research in array signal processing, with commonly used methods including spatial spectrum estimation and monopulse direction finding. Compared to spatial spectrum estimation, monopulse direction finding can estimate the incident angle of the desired signal within a single pulse echo, exhibiting lower computational complexity and thus finding widespread application in many real-time systems.

[0003] Sum-difference beamforming is a traditional monopulse direction finding method, widely studied due to its computational simplicity. Sum-difference beamforming under strong interference environments has been a research hotspot in this field. Can Hao et al., in their paper "Monopulse Estimation with Multipoint Constrained Adaptation in Mainlobe Jamming," proposed a multi-point constrained adaptive monopulse angle finding method that can maintain the angle discrimination curve characteristics well while suppressing main lobe interference. However, this method is only applicable to one-dimensional linear arrays, which has significant limitations. Cao Yunhe et al., in their paper "Subarray-level Adaptive Sum-difference Beamforming Method Based on Feature Space," addressed the problem of sum-difference beam pattern distortion caused by traditional anti-interference algorithms by proposing an adaptive sum-difference beamforming algorithm based on feature space subarrays. This algorithm can solve the direction finding problem of uniform arrays under strong interference environments, but it has a high computational cost and can only be used for regular arrays.

[0004] In summary, sum-difference beamforming algorithms typically employ a half-array method for direction finding and are only applicable to uniform linear and uniform area arrays. In contrast, direction finding algorithms for irregular arrays are generally more complex. Xie Yuanju, in his dissertation "Research and Implementation of Non-Uniform Array Direction Finding Technology," used the MUSIC and ESPRIT algorithms for direction finding of irregular arrays, but the direction search increased the computational load, and phase ambiguity also existed. Guo Lin et al., in "Implementation of Two-Dimensional Direction Finding Technology Based on Non-Uniform Arrays," studied a frequency domain joint algorithm based on spectrum detection and spatial spectrum estimation for L-shaped arrays. This algorithm is used for robust two-dimensional high-precision frequency and direction finding, but it can only perform direction finding for specific arrays. Summary of the Invention

[0005] This invention addresses the limitation of existing sum-difference beamforming algorithms in directly performing direction finding and tracking of irregular arrays by proposing a sum-difference beamforming direction finding method based on adaptive digital beamforming.

[0006] This invention is achieved through the following technical solution:

[0007] A sum-difference beam direction finding and tracking method based on adaptive digital beamforming includes:

[0008] S1. Place the irregular antenna array in the xy coordinate system, divide the irregular antenna array into two subarrays with the x-axis as the boundary, and divide the irregular antenna array into two subarrays with the y-axis as the boundary, resulting in a total of four subarrays.

[0009] S2, adaptive digital beamforming is performed on the received signals of the four subarrays to form four anti-interference beams;

[0010] S3, perform sum and difference beam direction finding based on four anti-interference beams to obtain the direction finding results;

[0011] S4 uses the direction finding results of S3 as the prior direction to perform phase and amplitude compensation on the four anti-interference beams and update the four anti-interference beams.

[0012] S5: Determine whether the deviation angle between the two most recent direction finding results is less than the set threshold. If it is less than the set threshold, the iteration ends and the most recent direction finding result is output as the final direction finding result. Otherwise, return to S3.

[0013] Preferably, S2 specifically includes:

[0014] S21, calculate the autocorrelation matrix of the received signals of the four subarrays respectively;

[0015] S22, the MVDR beamforming weighting coefficients of the four subarrays are calculated using the received signals, autocorrelation matrix and prior direction steering vector of the four subarrays respectively.

[0016] S23 utilizes the received signals from the four subarrays and the MVDR beamforming weighting coefficients to perform adaptive digital beamforming, forming four anti-interference beams.

[0017] Furthermore, in S21, the specific calculation method is as follows:

[0018]

[0019]

[0020] Among them, R i Let x be the autocorrelation matrix of the received signal of subarray i. i (n) represents the received signal of subarray i. Let the dimension of submatrix i be M i ×1 guiding vector, M i Let θ be the number of antenna elements in subarray i. s , Let θ be the angle between the direction of the incoming target signal and the y-axis and x-axis, respectively, and let s(n) be the known target signal. j (n) represents the interference signals; there are J interference signals in total, θ j , v represents the elevation angle of the direction of arrival of the interfering signal, the azimuth angle of the direction of arrival of the interfering signal, and the steering vector of the interfering signal in subarray i, respectively. i (n) represents the noise in subarray i, () H The representative vector is the conjugate transpose, and N is the number of sampling snapshots.

[0021] Furthermore, in S22, the specific calculation method is as follows:

[0022]

[0023] Among them, w i Let be the MVDR beamforming weighting coefficients of subarray i, () -1 Represents the inversion of a matrix, θ0, These are the prior elevation angle and prior azimuth angle of the target signal, respectively.

[0024] Furthermore, in S23, the method for adaptive digital beamforming is as follows:

[0025]

[0026] Furthermore, in S23, after adaptive digital beamforming, the method further includes: pulse compression of the signal obtained from adaptive digital beamforming to obtain four anti-interference beams; the pulse compression method specifically includes:

[0027] z i (n)=s H (n)y i (n), i = 1, 2, 3, 4;

[0028] Among them, s H (n)=[s(n),s(n-1),...,s(n-N+1)] T N is the number of pulse compression points, y i (n)=[y i (n),y i (n-1),...,y i (n-N+1)] T .

[0029] Preferably, S3 specifically includes:

[0030] S31, calculate the sum beam and difference beam in the elevation dimension based on the two anti-interference beams corresponding to the two subarrays divided by the x-axis, and calculate the elevation angle based on the sum beam and difference beam in the elevation dimension.

[0031] S32, calculate the sum beam and difference beam in the azimuth dimension based on the two anti-interference beams corresponding to the two subarrays divided by the y-axis, and calculate the azimuth angle based on the sum beam and difference beam in the azimuth dimension.

[0032] S33, the direction finding results are obtained based on the elevation angle and azimuth angle.

[0033] Furthermore, for the k-th sum-difference beam direction finding, k=0, in S31, the specific calculation method is as follows:

[0034]

[0035]

[0036] Where λ represents the wavelength of the target signal, d1 represents the distance between the reference phase centers of the two subarrays divided by the x-axis, θ0 represents the prior elevation angle of the target signal, and z1(n) and z2(n) are the anti-jamming beams of the two subarrays divided by the x-axis, respectively.

[0037] For the k-th sum-difference beam direction finding, k=0, in S32, the specific calculation method is as follows:

[0038]

[0039]

[0040] Where λ represents the wavelength of the target signal, d2 represents the distance between the reference phase centers of the two subarrays divided by the y-axis, θ0 represents the prior elevation angle of the target signal, and z3(n) and z4(n) are the anti-jamming beams of the two subarrays divided by the y-axis, respectively.

[0041] Furthermore, S4 specifically refers to: Let the direction finding result obtained in the k-th iteration be... If k≥0, phase and amplitude compensation is performed on the four anti-interference beams, specifically as follows:

[0042]

[0043] Among them, w i Let i be the MVDR beamforming weighting coefficients for subarray i. For subarray i in the direction The guide vector in S3 and z i(n), i = 1, 2, 3, 4 are respectively replaced with and i = 1, 2, 3, 4.

[0044] Preferably, in S5, the two direction finding results and The deviation angle is defined as:

[0045]

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] This invention provides an anti-interference sum-difference beamforming direction finding and tracking method for irregular antenna arrays. The method first divides the irregular antenna array into four subarrays (upper, lower, left, and right) bounded by the x-axis and y-axis. Each subarray undergoes spatial anti-interference treatment using adaptive digital beamforming, enabling the array to have adaptive anti-interference capabilities and improving subsequent direction finding accuracy. Then, the prior direction of the sum-difference beamforming algorithm is iteratively changed, and the phase and amplitude of the synthesized anti-interference beams from each subarray are compensated. The target signal direction is then iteratively solved using the sum-difference beamforming algorithm until the algorithm converges to a preset threshold range. This method provides more accurate signal direction estimation upon convergence, thus solving the problem of high-precision direction finding and tracking of irregular arrays in strong interference environments. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a flowchart of the sum and difference beam direction finding and tracking method based on adaptive digital beamforming according to the present invention.

[0050] Figure 2 This is a schematic diagram of the subarray division of the antenna array in this invention.

[0051] Figure 3 The figure shows the simulation results of this invention. Detailed Implementation

[0052] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0053] It should be noted that the process equipment or apparatus not specifically mentioned in the following embodiments are all conventional equipment or apparatus in the art.

[0054] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products, or apparatuses. Furthermore, unless otherwise stated, the numbering of each method step is merely a convenient tool for identifying each method step, and not intended to limit the order of the method steps or define the scope of the invention. Changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0055] The overall concept of this invention is as follows: Figure 1 As shown, firstly, an irregular antenna array is used to receive signals. The irregular antenna array is placed in an xy coordinate system, and divided into two subarrays along the x-axis and two subarrays along the y-axis, resulting in a total of four subarrays. These subarrays can overlap. Reference phase points are selected for each of the four subarrays, where the phase is 0. The line connecting the reference phase points of the two subarrays divided along the x-axis is parallel to the y-axis, and the line connecting the reference phase points of the two subarrays divided along the y-axis is parallel to the x-axis. The autocorrelation matrix of the received signals from the four subarrays is calculated. Using the received signals from the four subarrays, the autocorrelation matrix, and the prior direction steering vector... Calculate the MVDR beamforming weight coefficients, and use the MVDR beamforming weight coefficients of the four subarrays to perform adaptive digital beamforming on the received signals of the four subarrays to form four anti-interference beams. Perform iterative sum-difference beam direction finding, using the previous direction finding result as the prior direction, and perform phase and amplitude compensation on the four anti-interference beams, and perform sum-difference beam direction finding again. Determine whether the deviation angle of the two most recent direction finding results is less than the set threshold. If it is less than the set threshold, the iteration ends, and the most recent measured direction is output as the final direction finding result. Otherwise, iterate the sum-difference beam direction finding again until the deviation angle of the two most recent direction finding results is less than the set threshold.

[0056] This invention relates to a sum-difference beam direction finding method based on adaptive digital beamforming, specifically including the following steps:

[0057] Step 1: Place the irregular antenna array in the xy coordinate system, with the center of the irregular antenna array coinciding with the dot. Divide the irregular antenna array into two subarrays using the x-axis as the boundary and into two subarrays using the y-axis as the boundary, resulting in a total of four subarrays. The antenna elements of each subarray may partially overlap. The received signals of the four subarrays at time n are as follows:

[0058]

[0059] in, Let the dimension of submatrix i be M i ×1 guiding vector, M i Let θ be the number of antenna elements in subarray i, and the line connecting the reference phase centers of two subarrays divided by the x-axis is parallel to the y-axis; the line connecting the reference phase centers of two subarrays divided by the y-axis is parallel to the x-axis, θ s , Let θ be the angles (elevation and azimuth) between the direction of the incoming target signal and the y-axis and x-axis, respectively, and s(n) be the known target signal. j (n) represents the interference signals; there are J interference signals in total, θ j , v represents the elevation angle of the direction of arrival of the interfering signal, the azimuth angle of the direction of arrival of the interfering signal, and the steering vector of the interfering signal in subarray i, respectively. i (n) represents the noise in subarray i.

[0060] Step 2 involves performing MVDR beamforming on the received signals from the four subarrays, including the following steps:

[0061] Step 2.1, calculate the autocorrelation matrix of the received signals of the four subarrays:

[0062]

[0063] in,() H The representative vector is the conjugate transpose, and N is the number of sampling snapshots, which can be predetermined according to actual needs;

[0064] Step 2.2, calculate the MVDR beamforming weighting coefficients for the four subarrays:

[0065]

[0066] in,() -1 Represents the inversion of a matrix, θ0, These are the prior elevation angle and prior azimuth angle of the target signal, respectively;

[0067] Step 2.3: Perform MVDR beamforming on the received signals of the four subarrays:

[0068]

[0069] Step 2.4: Perform pulse compression on the signal obtained in Step 2.3.

[0070] z i (n)=s H (n)y i (n), i = 1, 2, 3, 4;

[0071] Among them, s H (n)=[s(n),s(n-1),...,s(n-N+1)] T N is the number of pulse compression points, y i (n)=[y i (n),y i (n-1),...,y i (n-N+1)] T ;

[0072] Step 3: Use the signal obtained in step 2.4 to perform sum-difference beam direction finding. The elevation and azimuth angles need to be estimated separately, including the following steps:

[0073] Step 3.1, using the signal obtained in step 2.4 to estimate the tracking pitch angle, includes the following steps:

[0074] Step 3.1.1: Calculate the sum beam in the elevation dimension and the difference beam output signal in the elevation dimension:

[0075]

[0076] Where λ represents the wavelength of the target signal, d1 represents the distance between the reference phase centers of the upper and lower subarrays, θ0 represents the prior elevation angle of the target signal, and z1(n) and z2(n) are the output signals of the two subarrays divided by the x-axis after MVDR beamforming and pulse compression.

[0077] Step 3.1.2, calculate the pitch angle estimation result:

[0078]

[0079] Where || represents the modulus of the complex number;

[0080] Step 3.2, using the signal and difference beam output signal obtained in 2.4 to estimate the tracking azimuth angle, includes the following steps:

[0081] Step 3.2.1, calculate the sum beam and difference beam in the azimuth dimension:

[0082]

[0083] Where d2 represents the distance between the reference phase centers of the two subarrays, with the y-axis as the boundary. The a priori azimuth angle representing the target signal, z3(n) and z4(n) are the output signals of the two subarrays divided by the y-axis after MVDR beamforming and pulse compression, respectively;

[0084] Step 3.2.2, calculate the azimuth estimation result:

[0085]

[0086] Where λ represents the wavelength of the target signal, d2 represents the distance between the reference phase centers of the two subarrays divided by the y-axis, θ0 represents the prior elevation angle of the target signal, and z3(n) and z4(n) are the anti-jamming beams of the two subarrays divided by the y-axis, respectively.

[0087] Step 4: Iteratively solve for the target signal direction using the sum-difference beamforming algorithm, where the direction obtained in the k-th iteration (k≥0) is... Phase and amplitude compensation is performed on the output signals of each subarray in step 2.4, specifically as follows:

[0088]

[0089] in, For the i-th subarray in the direction The guide vector, in step 3 and z i (n), i = 1, 2, 3, 4 are respectively replaced with and z ik (n), i = 1, 2, 3, 4, repeat step 3 to obtain the direction finding result of the (k+1)th time.

[0090] Step 5: Determine the results of the two most recent direction finding attempts. and If the deviation angle is less than a set threshold, the iteration is considered sufficient, and the last direction finding result is output as the final direction finding result; otherwise, steps 4 and 5 are repeated until the deviation angle of the two most recent direction finding results is less than the set threshold. and The deviation angle is defined as:

[0091]

[0092] The algorithm ends here.

[0093] Simulation Examples

[0094] In the simulation, the array used was a 16-element uniform circular array, with the array radius set to four times the signal wavelength. For example... Figure 2 As shown, the beamforms are arranged on the xoy plane, divided into upper and lower subarrays by the x-axis and left and right subarrays by the y-axis. The elevation and azimuth angles are defined as the angles between the incoming wave direction and the positive y-axis and x-axis directions. The size of each of the four subarrays (upper, lower, left, and right) is 8, and their phase reference centers are all set to the geometric centers of the subarrays. The prior direction of the target signal is set to (90°, 90°), the true incoming direction of the target signal is set to (92°, 91°), and the incoming direction of the interference signal is set to (100°, 100°). The signal-to-noise ratio (SNR) is set to -10dB, the signal-to-interference ratio (SINR) is set to -30dB, and the transmitted signal is a known linear frequency modulated (LFM) signal. A 500-point pulse compression is applied to the beamformed signal. 10,000 experiments are conducted, and the CCDF curves showing the deviation angles between the direction-finding results and the true signal angles after 10,000 experiments are shown below. Figure 3 As shown.

[0095] In the simulation, the deviation between the original prior direction and the desired signal direction was 2.24°. The algorithm proposed in this invention, after 10,000 experiments, showed a maximum deviation of only 0.59° from the true direction in terms of direction finding results. Furthermore, it had a 99.9% probability of achieving a deviation angle less than 0.51° and a 99% probability of achieving a deviation angle less than 0.41°. In summary, this invention can achieve adaptive anti-interference and high-precision direction finding and tracking of irregular arrays under strong interference environments.

Claims

1. A sum-difference beam direction finding and tracking method based on adaptive digital beamforming, characterized in that, include: S1. Place the irregular antenna array in the xy coordinate system, divide the irregular antenna array into two subarrays with the x-axis as the boundary, and divide the irregular antenna array into two subarrays with the y-axis as the boundary, resulting in a total of four subarrays. S2, adaptive digital beamforming is performed on the received signals of the four subarrays to form four anti-interference beams; S3, perform sum and difference beam direction finding based on four anti-interference beams to obtain the direction finding results; S4 uses the direction finding results of S3 as the prior direction to perform phase and amplitude compensation on the four anti-interference beams and update the four anti-interference beams. S5: Determine whether the deviation angle between the two most recent direction finding results is less than the set threshold. If it is less than the set threshold, the iteration ends and the most recent direction finding result is output as the final direction finding result. Otherwise, return to S3.

2. The sum and difference beam direction finding and tracking method based on adaptive digital beamforming according to claim 1, characterized in that, S2 specifically includes: S21, calculate the autocorrelation matrix of the received signals of the four subarrays respectively; S22, the MVDR beamforming weighting coefficients of the four subarrays are calculated using the received signals, autocorrelation matrix and prior direction steering vector of the four subarrays respectively. S23 utilizes the received signals from the four subarrays and the MVDR beamforming weighting coefficients to perform adaptive digital beamforming, forming four anti-interference beams.

3. The sum and difference beam direction finding and tracking method based on adaptive digital beamforming according to claim 2, characterized in that, In S21, the specific calculation method is as follows: ， ， in, For the sub-array The autocorrelation matrix of the received signal, For the sub-array The received signal, For the sub-array The dimension is The guiding vector, For the sub-array The number of antenna array elements, These are the angles between the direction of the incoming target signal and the y-axis and x-axis, respectively. Given a known target signal, As interference signals, there are a total of An interference, , These represent the elevation angle of the direction of arrival of the interfering signal, the azimuth angle of the direction of arrival of the interfering signal, and the position of the interfering signal in the subarray. The guiding vector in For the sub-array Noise in This represents the conjugate transpose of a vector. This represents the number of snapshots taken.

4. The sum and difference beam direction finding and tracking method based on adaptive digital beamforming according to claim 3, characterized in that, In S22, the specific calculation method is as follows: ， in, For the sub-array MVDR beamforming weighting coefficients Represents finding the inversion of a matrix. These are the prior elevation angle and prior azimuth angle of the target signal, respectively.

5. The sum and difference beam direction finding and tracking method based on adaptive digital beamforming according to claim 4, characterized in that, In S23, the adaptive digital beamforming method is as follows: 。 6. The sum and difference beam direction finding and tracking method based on adaptive digital beamforming according to claim 5, characterized in that, In step S23, after adaptive digital beamforming, the method further includes: pulse compression of the signal obtained from adaptive digital beamforming to obtain four anti-interference beams; the pulse compression method specifically includes: ； in, , This represents the number of pulse compression points. .

7. The sum and difference beam direction finding and tracking method based on adaptive digital beamforming according to claim 6, characterized in that, S3 specifically includes: S31, calculate the sum beam and difference beam in the elevation dimension based on the two anti-interference beams corresponding to the two subarrays divided by the x-axis, and calculate the elevation angle based on the sum beam and difference beam in the elevation dimension. S32, calculate the sum beam and difference beam in the azimuth dimension based on the two anti-interference beams corresponding to the two subarrays divided by the y-axis, and calculate the azimuth angle based on the sum beam and difference beam in the azimuth dimension. S33, the direction finding results are obtained based on the elevation angle and azimuth angle.

8. The sum and difference beam direction finding and tracking method based on adaptive digital beamforming according to claim 7, characterized in that, For the Subsum and difference beam direction finding In S31, the specific calculation method is as follows: ， ， in, Represents the wavelength of the target signal. This represents the distance between the reference phase centers of two subarrays, bounded by the x-axis. The prior pitch angle representing the target signal. These are the anti-interference beams of two subarrays divided by the x-axis; For the Subsum and difference beam direction finding In S32, the specific calculation method is as follows: ， ， in, Represents the wavelength of the target signal. This represents the distance between the reference phase centers of the two subarrays, divided by the y-axis. The prior pitch angle representing the target signal. These are the anti-jamming beams of two subarrays divided by the y-axis.

9. The sum and difference beam direction finding and tracking method based on adaptive digital beamforming according to claim 8, characterized in that, S4 specifically refers to: Let the... The direction finding results obtained this time are , Phase and amplitude compensation is performed on the four anti-interference beams, specifically as follows: ， in, For the sub-array MVDR beamforming weighting coefficients For the sub-array In direction The guide vector in S3 and Replace with and .

10. The sum and difference beam direction finding and tracking method based on adaptive digital beamforming according to claim 9, characterized in that, In S5, the results of the two direction finding operations and deviation angle Defined as: 。

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