Fractal-based joint spatial-polarization domain interference suppression method

Abstract

The application provides a fractal dimension-based joint space-polarization domain interference suppression method, which comprises the following steps: a signal model of a rectangular reconfigurable planar array joint space-polarization domain processing is established, the characteristics of fractal dimension are derived, the rectangular array is decomposed into two orthogonal dimensions, and two-stage interference suppression is performed on the equivalent linear array, the polarization information of the signal is introduced, the one-dimensional linear array is subjected to joint space-polarization domain beamforming, and the other one-dimensional linear array is subjected to space domain beamforming. The method comprises two-stage processing: the first stage is performed in the non-azimuth dimension, the joint space-polarization domain constraint of the beam pointing of the beam pattern is performed, the main lobe interference suppression in the non-azimuth dimension is completed, and the second stage is performed in the azimuth dimension, and static sum and difference beamforming is performed. The application avoids the problem that the expected signal is cancelled when the coming directions of the interference signal and the expected signal are the same in pure space domain beamforming, the fractal dimension processing ensures better linear degree of a single pulse curve, and higher azimuth performance is obtained.

Description

Technical Field

[0001] This application relates to the field of radar information technology, and in particular to a fractal-dimensional joint spatial-polarization domain interference suppression method. Background Technology

[0002] Currently, countering defensive and accompanying jamming within the main lobe of radar is a key focus of anti-jamming methods. Since both types of jamming enter from the main lobe, traditional adaptive beamforming disrupts the linearity of the monopulse angle discrimination curve, reducing the accuracy and reliability of angle measurement. Accompanying jamming is spatially similar to the target signal, while defensive jamming is spatially aligned with it. Therefore, while adaptive beamforming suppresses jamming, it also suppresses the target signal, resulting in a lower signal-to-noise ratio (SNR) after beamforming and deteriorating monopulse angle measurement performance.

[0003] Recent anti-jamming technologies primarily suppress interference by comprehensively utilizing the different characteristics of the interfering and target signals in the spatial, temporal, and frequency domains. Since single-domain anti-jamming methods utilize limited information, multi-domain joint anti-jamming methods have been proposed to improve performance. For example, spatial-temporal joint adaptive processing is performed on top of spatial filtering, increasing the degrees of freedom by utilizing spatial and temporal information without increasing the number of array elements, thus simultaneously suppressing multiple main lobe interferences. However, both spatial and spatial-temporal joint processing have problems: when the desired signal and the interfering signal travel in the same direction, a null is formed in the receiver pattern along the direction of the desired signal, suppressing both signals simultaneously.

[0004] The polarization information of a signal source is another important characteristic that can represent electromagnetic waves, in addition to spatial, temporal, and frequency domain information. Utilizing signal polarization can introduce a new dimension to anti-interference methods. A polarization sensitive array (PSA), as an array capable of acquiring signal source polarization information, can simultaneously provide spatial phase information and polarization component information, achieving joint spatial-polarization domain anti-interference. Common methods that incorporate signal polarization information into traditional space-time adaptive methods, such as the joint spatial-polarization domain anti-interference method based on the Linearly Constrained Minimum Variance (LCMV) criterion, effectively suppress interference signals, but their angle measurement performance degrades due to distortion of the single-pulse angle discrimination curve. Summary of the Invention

[0005] This application provides a fractal-dimensional spatial-polarization domain joint interference suppression method, which can be used to solve the technical problem of poor angle measurement performance of traditional space-time adaptive methods.

[0006] A fractal-dimensional spatial-polarization domain joint interference suppression method is proposed, which includes:

[0007] Step 1: Decompose the rectangular polarimetric reconfigurable planar array into two dimensions: azimuth dimension (u-dimensional) and elevation dimension (v-dimensional). Establish a signal model for joint processing of the spatial domain and polarization domain, and derive its characteristic of split-dimensional processing.

[0008] Step two: When measuring the elevation angle, the beam pattern is subjected to joint spatial-polarization domain constraints in the azimuth dimension to suppress the main lobe interference in the non-angle measurement dimension. By introducing polarization information, when the desired signal and the interference signal have the same or similar direction of arrival, nulls are formed in the polarization domain to suppress interference of other polarization forms, thus obtaining the azimuth beamforming output. Then, spatial static synthesis is performed in the elevation dimension to obtain the sum and difference beam data output of the entire array when measuring the elevation angle.

[0009] Step 3: When measuring angles in the azimuth dimension, the beam pattern is subjected to joint spatial-polarization domain constraints in the elevation dimension to suppress the main lobe interference in the non-angle measurement dimension. By introducing polarization information, when the desired signal and the interference signal have the same or similar direction of arrival, nulls are formed in the polarization domain to effectively suppress interference of other polarization forms, thus obtaining the elevation beamforming output. Then, spatial static synthesis is performed in the azimuth dimension to ensure that the slope of the single-pulse angle discrimination curve is not distorted, thus obtaining the sum and difference beam data output of the entire array when measuring angles in the azimuth dimension.

[0010] This invention avoids the problem of desired signal cancellation caused by interference signals and desired signals coming from similar or close directions during pure spatial beamforming by combining the spatial domain and polarization domain.

[0011] This invention suppresses interference in the non-angle measurement dimension by performing fractal processing on the rectangular array, while only static synthesis is performed in the angle measurement dimension. Therefore, it ensures better linearity of the single pulse curve in the angle measurement dimension and obtains higher angle measurement performance. Attached Figure Description

[0012] Figure 1 A uniform area array model diagram composed of polarimetric reconfigurable array elements provided in an embodiment of this application;

[0013] Figure 2 A flowchart illustrating the method provided in this application embodiment;

[0014] Figure 3 The elevation and beam pattern provided in the embodiments of this application;

[0015] Figure 4 The elevation dimension difference beam pattern provided in the embodiments of this application;

[0016] Figure 5 The azimuth dimension and beam pattern provided in the embodiments of this application;

[0017] Figure 6 The azimuth dimension beam pattern provided in the embodiments of this application;

[0018] Figure 7 The single-pulse angle discrimination curves of the spatial-polarization domain joint interference suppression method based on fractal dimension provided in the embodiments of this application are shown in the figure; wherein, (a) is the pitch angle discrimination curve; and (b) is the azimuth angle discrimination curve.

[0019] Figure 8 The single-pulse angle discrimination curves of the spatial-polarization domain joint anti-interference method based on the LCMV criterion provided in the embodiments of this application are shown in the figure; wherein, (a) is the pitch angle discrimination curve; and (b) is the azimuth angle discrimination curve.

[0020] Figure 9 The diagram shows the single-pulse angle measurement results provided in the embodiments of this application; where (a) is a diagram of the spatial-polarization domain joint interference suppression method based on fractal dimension; and (b) is a diagram of the spatial-polarization domain joint anti-interference method based on the LCMV criterion. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0022] The embodiments of this application will now be described in conjunction with the accompanying drawings.

[0023] Step 1: Decompose the rectangular polarimetric reconfigurable planar array into two dimensions: azimuth dimension (u-dimensional) and elevation dimension (v-dimensional). Establish a signal model for joint spatial-polarization domain processing and derive its characteristic of multidimensional processing.

[0024] A uniform surface array consisting of M×N polarimetric reconfigurable array elements, such as Figure 1 As shown, the element spacing is d; each element consists of a pair of crossed dipoles, which are placed orthogonally at the same point in space, respectively receiving electric field components parallel to the dipoles, corresponding to two mutually orthogonal signal receiving channels, the horizontal H channel and the vertical V channel.

[0025] A fully polarized electromagnetic wave signal along the direction vector Incident to Figure 1 In the rectangular coordinate system shown; for the scenario of two-dimensional DOA estimation, θ∈[0,π / 2] is the off-axis angle, representing the angle between the unit direction vector and the +z direction; The rotation angle represents the angle between the projection of the incident signal onto the xoy plane and the +x direction; the direction vector... The projections onto the x-axis and y-axis are as follows:

[0026]

[0027] The spatial steering vector of the array signal is then expressed as:

[0028]

[0029] In the formula, (x m,n u+y m,n v) represents the coordinates of the matrix element in the m-th row and n-th column, and the superscript T indicates the transpose operation;

[0030] Consider L fully polarized incident signals, where P are desired signals and Q are interference signals. Their polarization vectors are expressed as:

[0031]

[0032] In the formula, (γ,η) represents the polarization parameter, γ∈[0,π / 2] is the polarization auxiliary angle, tanγ represents the ratio of the electric field amplitude in the +y direction to the electric field amplitude in the +x direction; η=φ y -φ x η∈[0,2π] is the polarization phase difference, where η represents the difference between the electric field phase in the +y direction and the electric field phase in the +x direction. E represents the off-axis angle, rotation angle, polarization auxiliary angle, and polarization phase difference of the l-th signal; x (l) and E y (l) represent the horizontal and vertical polarization components of the l-th signal, respectively;

[0033] Combining equations (2) and (3), the joint spatial-polarization domain steering vector for array reception is obtained as follows:

[0034]

[0035] in, For Kronecker product;

[0036] Therefore, the received signal model of the array is represented as:

[0037] X(t)=a s,p S(t)+n(t)(5)where, S(t)=[s1(t),s2(t),...,s L [(t)] represents L incident signal vectors, and n(t) represents an additive white Gaussian noise vector;

[0038] The horizontally and vertically polarized signals received by the m-th row element of the polarization-reconfigurable array can be written as:

[0039]

[0040] The signals received by the nth array element under horizontal and vertical polarization can be written as:

[0041]

[0042] in, The horizontally polarized signal received by the array element in the m-th row and n-th column. For the vertically polarized signal received by the array element in the m-th row and n-th column, r Rm Let r be a 2N×1 dimensional column vector. Cn It is a 2M×1 dimensional column vector;

[0043] The spatial steering vectors of the equivalent linear arrays in azimuth (u) and elevation (v) dimensions are respectively and

[0044]

[0045] The joint steering vector of the u-dimensional and v-dimensional spatial-polarization domains is:

[0046]

[0047] At this point, the joint steering vector of the entire array in the spatial and polarimetric domains is decomposed into the form of the Kronecker product of the steering vectors in two dimensions. When spatial-polarimetric joint beamforming is performed in the v dimension and spatial beamforming is performed in the u dimension, the joint steering vector of the entire array is written as:

[0048]

[0049] in, Let be the spatial guiding vector of the u-dimensional equivalent linear array. It is the joint steering vector of the v-dimensional spatial domain and polarization domain;

[0050] When u-dimensional spatial-polarization domain joint beamforming is performed and v-dimensional spatial beamforming is performed, the full array joint steering vector is written as:

[0051]

[0052] in, Let be the spatial guiding vector of the v-dimensional equivalent linear array. It is the joint steering vector of the u-dimensional spatial domain and polarization domain. and The only difference is the order, while they are physically equal. That is, the spatial-polarization domain joint beamforming of a rectangular planar array can be decomposed into spatial beamforming and spatial-polarization domain joint beamforming in two dimensions respectively.

[0053] Similarly, the total array weights are expressed as the Kronecker product of the weights of two one-dimensional linear arrays. When v-dimensional beamforming is performed for joint spatial-polarization domain beamforming and u-dimensional beamforming is performed for spatial domain beamforming, the total array joint weight vector is written as:

[0054]

[0055] When u-dimensional spatial-polarization domain joint beamforming is performed and v-dimensional spatial beamforming is performed, the full array joint steering vector is written as:

[0056]

[0057] in, and These are the weights for beamforming in the u-dimensional and v-dimensional spatial domains, respectively. and These are the joint beamforming weights for the u-dimensional and v-dimensional spatial-polarization domains, respectively.

[0058] The basic process of the proposed fractal-dimensional spatial-polarization domain joint interference suppression method is as follows: Figure 2 As shown.

[0059] Step two: When measuring the elevation angle, the beam pattern in the azimuth dimension is subjected to joint spatial-polarization domain constraints on the beam pointing, thus completing the suppression of main lobe interference in the non-angle measurement dimension. By introducing polarization information, when the desired signal and the interference signal have the same or similar direction of arrival, nulls are formed in the polarization domain to effectively suppress interference of other polarization forms, thereby obtaining the azimuth beamforming output. Then, spatial static synthesis is performed in the elevation dimension to ensure that the slope of the single-pulse angle discrimination curve is not distorted, thus obtaining the sum and difference beam data output of the entire array when measuring the elevation angle.

[0060] Step 2-1: Perform joint spatial-polarization domain constraints on the beam pointing of the beam pattern in the azimuth dimension to complete the suppression of main lobe interference in the non-angle measurement dimension;

[0061] Performing joint spatial-polarization domain anti-interference along the m-th row of the polarimetric reconfigurable array, the adaptive beam output is obtained as follows:

[0062]

[0063] In the formula, Let r be the 2N-dimensional optimal weight vector corresponding to the m-th row element. Rm ∈C 2N×1 For the horizontally and vertically polarized signals received by the m-th row element of the polarization-reconfigurable array;

[0064] Joint spatial-polarization domain constraints on beam pointing for beam pattern: Based on the minimum mean square error criterion, the optimal weight vector in the spatial-polarization domain is determined. The optimization model is written as:

[0065]

[0066] in, The azimuth spatial domain-polarization domain joint steering vector for the beam pointing direction; The sampling covariance matrix is ​​the number of K sampling snapshots corresponding to the m-th row element:

[0067]

[0068] Where, r Rm (k) represents the horizontal and vertical polarization signals received by the m-th row element of the polarization reconfigurable array during the k-th sampling snapshot;

[0069] Using the Lagrange multiplier method, the u-dimensional weight vector is obtained.

[0070]

[0071] After performing joint spatial-polarization domain anti-interference on each row of the array, the obtained u-dimensional beamforming data is written as follows:

[0072] y R =[y R1 ,…y RM ] T (19)

[0073] Step 2-2: Perform static spatial synthesis in the elevation dimension to obtain the sum and difference beam data output results of the entire array when measuring the elevation dimension.

[0074] Performing v-dimensional static sum and difference beamforming on equation (16), the v-dimensional angle measurement sum and difference beamforming results are as follows:

[0075]

[0076] In the formula, and These are the static sum and difference weights in the v-dimensional spatial domain, respectively.

[0077] After the joint beamforming of the spatial and polarization domains, the radiation pattern of the elevation and difference beam is written as follows:

[0078]

[0079] in, The radiation pattern after spatial-polarization domain joint beamforming of the azimuth-equivalent linear array. and The radiation patterns after static beamforming in the airspace using an equivalent linear array in the elevation dimension are shown respectively.

[0080] The expression for the pitch dimension sum difference single-pulse ratio is written as:

[0081]

[0082] Where, m E (v) represents the sum and difference single pulse ratio of the pitch-dimensional equivalent linear array.

[0083] The pitch dimension single-pulse angle measurement can be completed using equation (22). As can be seen from equation (22), when measuring pitch dimension angle, after the fractal spatial-polarization domain joint beamforming, the pitch dimension sum and difference single-pulse ratio of the rectangular polarization reconfigurable planar array is equal to the static sum and difference single-pulse ratio of the equivalent linear array in the pitch dimension. Therefore, this method ensures better linearity of the single-pulse curve while resisting interference, and obtains higher angle measurement performance.

[0084] Step 3: When measuring angles in the azimuth dimension, the beam pattern is subjected to joint spatial-polarization domain constraints in the elevation dimension to suppress the main lobe interference in the non-angle measurement dimension. By introducing polarization information, when the desired signal and the interference signal have the same or similar direction of arrival, nulls are formed in the polarization domain to effectively suppress interference of other polarization forms, thus obtaining the elevation beamforming output. Then, spatial static synthesis is performed in the azimuth dimension to ensure that the slope of the single-pulse angle discrimination curve is not distorted, thus obtaining the sum and difference beam data output of the entire array when measuring angles in the azimuth dimension.

[0085] Example

[0086] This embodiment uses a uniform array composed of polarimetric reconfigurable array elements as an example to simulate and verify the interference suppression and single-pulse angle measurement performance of the method under the simultaneous presence of a self-defense interference and a follower interference. The simulation parameters and interference scenarios are shown in Table 1. In the scenarios, both interferences are main lobe interferences, and the interference-to-noise ratio (IRR) and signal-to-noise ratio (SNR) are taken at the array element level. For ease of plotting and analysis, without affecting generality, the polarization auxiliary angles of the two interferences are uniformly set to 45°, and the rotation angles of the desired signal and the two interferences are uniformly set to 45°.

[0087] Table 1 Simulation Parameters

[0088]

[0089] Figure 3 The elevation and beamforming results for angle measurement in the elevation dimension are presented. The method of this invention employs a two-stage processing approach: spatial-polarization domain joint beamforming to suppress interference in the azimuth dimension, and static beamforming and beamforming in the elevation dimension. Figure 4 The elevation difference beamforming results for angle measurement in the elevation dimension are presented. Interference suppression is achieved through joint spatial-polarization beamforming in the azimuth dimension, while static difference beamforming is performed in the elevation dimension. For ease of analysis, the joint spatial-polarization pattern needs to be fixed during plotting. and η.

[0090] in Figure 3 (a) is fixed γ = 45°, i.e., the elevation dimension and beam pattern under the interference polarization parameters, shows that the pattern forms nulls at both interference locations. The zero-depression depth is -87.98 dB. The zero-depression depth is -81.88 dB; Figure 3 (b) is fixed γ = 80°, which is the elevation and beam pattern under the polarization parameters of the signal. It can be seen that the pattern does not form a null at the signal position, that is, the signal is not canceled.

[0091] Figure 5 The azimuth and beamforming results for angle measurement in the azimuth dimension are presented. The method of this invention employs a two-stage processing approach: joint spatial-polarization domain beamforming to suppress interference in the elevation dimension, and static beamforming in the azimuth dimension. Figure 6 The azimuth difference beamforming results for angle measurement in the azimuth dimension are presented. Interference suppression is achieved through joint spatial-polarization beamforming in the elevation dimension, while static difference beamforming is performed in the azimuth dimension. For ease of analysis, the joint spatial-polarization pattern needs to be fixed during plotting. and η.

[0092] in Figure 5 (a) is fixed γ = 45°, i.e., the azimuth dimension and beam pattern under the polarization parameters of the interference, show that the beam pattern forms nulls at both interference locations. The zero-depression depth is -88.01 dB. The zero-depression depth is -81.83 dB; Figure 5 (b) is fixed γ = 80°, which is the azimuth and beam pattern under the polarization parameters of the signal. It can be seen that the pattern does not form nulls at the signal position, that is, the signal is not canceled.

[0093] Simulations were performed on the signal-to-interference-plus-noise ratio (SNR) before and after anti-interference, and the results are shown in Table 2. It can be seen that the SNR is improved after using the two-stage joint beamforming anti-interference method of this invention. This indicates that the method can ensure that the desired signal is not suppressed while suppressing interference, thus achieving higher angle measurement accuracy.

[0094] Table 2 Signal-to-Interference Ratio Before and After Interference Suppression

[0095]

[0096] The single-pulse angle detection curve was simulated, and the performance of the method of this invention and the spatial-polarization domain joint anti-interference method based on the LCMV criterion were compared. Figure 7The results of single-pulse angle discrimination curves in elevation and azimuth dimensions after two-stage beamforming using a fractal-based spatial-polarization domain joint interference suppression method are presented. Figure 7 (a) and Figure 7 (b) It can be seen that, since the method performs joint processing of the spatial and polarization domains in the fractal dimension, the interference of the two main lobes is jointly suppressed in the spatial-polarization domain in the non-angle measurement dimension, which ensures that the single-pulse angle discrimination curve in the angle measurement dimension is consistent with the static angle discrimination curve and ensures that its slope is not distorted. Figure 8 The results of the single-pulse angle discrimination curves in the elevation and azimuth dimensions after beamforming using the spatial-polarization domain joint anti-interference method based on the LCMV criterion are presented. It can be seen that the single-pulse angle discrimination curves are distorted due to the influence of main lobe interference.

[0097] Monte Carlo simulation was used to analyze the single-pulse angle measurement performance of the two methods after anti-interference, with the number of simulations set to L=1000. Figure 9 The distribution diagrams of single-pulse angle measurement results in the u and v dimensions are presented for two methods: the method of this invention and the spatial-polarization domain joint anti-interference method based on the LCMV criterion. Because the method of this invention uses joint spatial-polarization domain processing, when the interference and the desired signal have similar or identical spatial directions, nulls are generated in the polarization domain for suppression, ensuring that the desired signal is not affected. Simultaneously, due to the fractal dimension processing, main lobe interference is suppressed in the non-angle measurement dimension, ensuring that the slope of the angle discrimination curve is not distorted. Therefore, the single-pulse angle measurement results show no deviation, and the dispersion area is very small. The spatial-polarization domain joint anti-interference method based on the LCMV criterion, when suppressing interference from both main lobes, causes distortion of the single-pulse angle discrimination curve, leading to deterioration of single-pulse angle measurement performance and a larger angle measurement deviation.

[0098] The embodiments described above do not constitute a limitation on the scope of protection of this application.

Claims

1. A fractal-dimensional spatial-polarization domain joint interference suppression method, characterized in that, The method includes: Step 1: Decompose the rectangular polarimetric reconfigurable planar array into its azimuth dimension. Wei, and the upward and downward Wei, that is We establish a signal model for joint spatial-polarization domain processing using two dimensions, and derive its characteristic of fractal-dimensional processing. Step two: When measuring the elevation angle, the beam pattern in the azimuth dimension is subjected to joint spatial-polarization domain constraints on the beam pointing, thus completing the suppression of main lobe interference in the non-angle measurement dimension. By introducing polarization information, when the desired signal and the interference signal have the same or similar direction of arrival, nulls are formed in the polarization domain for interference with a different polarization form than the desired signal, thereby suppressing it and obtaining the azimuth beamforming output. Then, spatial static synthesis is performed in the elevation dimension to obtain the sum and difference beam data output of the entire array when measuring the elevation angle. Step 3: When measuring angles in the azimuth dimension, the beam pattern is subjected to joint spatial-polarization domain constraints in the elevation dimension to suppress the main lobe interference in the non-angle measurement dimension. By introducing polarization information, when the desired signal and the interference signal have the same or similar direction of arrival, nulls are formed in the polarization domain for interference with a polarization form different from that of the desired signal, thus effectively suppressing it and obtaining the elevation beamforming output. Then, spatial static synthesis is performed in the azimuth dimension to ensure that the slope of the single-pulse angle discrimination curve is not distorted, and the sum and difference beam data output of the entire array is obtained when measuring angles in the azimuth dimension. Step 1: Decompose the rectangular polarimetric reconfigurable planar array into its azimuth dimension. Wei, and the upward and downward Wei, that is We establish a signal model for joint spatial-polarization domain processing using two dimensions, and derive its fractal-dimensional processing characteristics; including: Depend on A uniform surface array composed of polarimetric reconfigurable array elements, with an element spacing of... Each array element consists of a pair of crossed dipoles, which are placed orthogonally at a common point in space. Each dipole receives an electric field component parallel to the dipole, corresponding to two mutually orthogonal signal receiving channels, horizontally... Channels and verticals aisle; A fully polarized electromagnetic wave signal along the direction vector Incident on a Cartesian coordinate system; for a two-dimensional DOA estimation scenario, The off-axis angle represents the angle between the unit direction vector and the angle between the two axes. The angle between directions; Let be the rotation angle, representing the projection of the incident signal onto the xoy plane and... Angle between directions; direction vector exist shaft and The projections of the axes are as follows: (1)； The spatial steering vector of the array signal is then expressed as: (2)； In the formula, Indicates the first line, number Array element coordinates, with the superscript T indicating the transpose operation; consider A fully polarized signal is incident, in which One is the expected signal. One is an interference signal, and its polarization vector is represented as: (3)； In the formula, Indicates the polarization parameter, For polarization auxiliary angle, It indicates Directional electric field amplitude and The ratio of the amplitude of the directional electric field; , For polarization phase difference, It indicates Directional electric field phase and The difference in phase of the directional electric field. Indicates the first The off-axis angle, rotation angle, polarization auxiliary angle, and polarization phase difference of each signal; and They represent the first The horizontal and vertical polarization components of the signal; Combining equations (2) and (3), the joint spatial-polarization domain steering vector for array reception is obtained as follows: (4)； in,' 'For Kronecker product; Therefore, the received signal model of the array is represented as: (5)； in, for An incident signal vector, It is an additive white Gaussian noise vector; Polarizable reconfigurable array The horizontally and vertically polarized signals received by the array elements are written as follows: (6)； Array number The horizontally and vertically polarized signals received by the array elements are written as follows: (7)； in, For the first Line 1 The horizontally polarized signal received by the array elements For the first Line 1 The vertically polarized signal received by the array elements for 3D column vector, for 3D column vector; The spatial steering vectors of the equivalent linear arrays in azimuth (u) and elevation (v) dimensions are respectively and : (8)； (9)； The joint steering vector of the u-dimensional and v-dimensional spatial-polarization domains is: (10)； At this point, the joint spatial-polarization domain steering vector of the entire array is decomposed into the form of the Kronecker product of the two-dimensional steering vectors. Dimensional joint beamforming of spatial and polarization domains The joint steering vector of the entire array during spatial beamforming is written as: (11)； in, Let be the spatial guiding vector of the u-dimensional equivalent linear array. It is the joint steering vector of the v-dimensional spatial domain and polarization domain; when Dimensional joint beamforming of spatial and polarization domains The joint steering vector of the entire array during spatial beamforming is written as: (12)； in, Let be the spatial guiding vector of the v-dimensional equivalent linear array. It is the joint steering vector of the u-dimensional spatial domain and polarization domain; The total array weights are represented as the Kronecker product of the weights of two one-dimensional linear arrays, when Dimensional joint beamforming of spatial and polarization domains The joint weight vector of the entire array during spatial beamforming is written as: (13)； when Dimensional joint beamforming of spatial and polarization domains The joint steering vector of the entire array during spatial beamforming is written as: (14)； in, and These are the weights for beamforming in the u-dimensional and v-dimensional spatial domains, respectively. and These are the joint beamforming weights for the u-dimensional and v-dimensional spatial-polarization domains, respectively.

2. The method according to claim 1, characterized in that, Step two: During elevation angle measurement, the beam pattern is subjected to joint spatial-polarization domain constraints in the azimuth dimension to suppress main lobe interference in non-angle measurement dimensions. By introducing polarization information, when the desired signal and the interference signal have the same or similar direction of arrival, nulls are formed in the polarization domain to suppress interference from other polarization forms, thus obtaining the azimuth beamforming output. Then, spatial static synthesis is performed in the elevation dimension to ensure that the slope of the single-pulse angle discrimination curve is not distorted, obtaining the sum and difference beam data output of the entire array during elevation angle measurement, including: Step 2-1: Perform joint spatial-polarization domain constraints on the beam pointing of the beam pattern in the azimuth dimension to complete the suppression of main lobe interference in the non-angle measurement dimension; Step 2-2: Perform static spatial synthesis in the elevation dimension to obtain the sum and difference beam data output results of the entire array when measuring the elevation dimension angle.

3. The method according to claim 2, characterized in that, Step 2-1: Perform joint spatial-polarization domain constraints on the beam pattern in the azimuth dimension to suppress main lobe interference in the non-angular dimension; including: Along the polarization reconfigurable array The combined spatial-polarization domain anti-interference method is used to obtain the adaptive beam output result: (15)； In the formula, For the first The corresponding array element 3D optimal weight vector For polarization reconfigurable arrays Signals received by the array elements under horizontal and vertical polarization; Joint spatial-polarization domain constraints on beam pointing for beam pattern: Based on the minimum mean square error criterion, the optimal weight vector in the spatial-polarization domain is determined. The optimization model is written as: (16)； in, The azimuth spatial domain-polarization domain joint steering vector for the beam pointing direction; For the first The corresponding array element The sampling covariance matrix of each sample snapshot: (17)； in, For the first In the next sample snapshot, the polarization reconfigurable array... Signals received by the array elements under horizontal and vertical polarization; Using the Lagrange multiplier method, we obtain Rights Protection Vector : (18)； After performing joint spatial-polarization domain anti-interference on each row of the array, the obtained The beamforming data of the dimension is written as (19)。 4. The method according to claim 2, characterized in that, Step 2-2: Perform static spatial synthesis in the elevation dimension to obtain the sum and difference beam data output results of the entire array when measuring the elevation dimension. include: Perform on equation (16) 3D static sum-difference beamforming, to obtain The results of the angular sum and difference beamforming are as follows: (20)； In the formula, and They are respectively Spatial static sum and difference weights; After the joint beamforming of the spatial and polarization domains, the radiation pattern of the elevation and difference beam is written as follows: (21)； in, The radiation pattern after spatial-polarization domain joint beamforming of the azimuth-equivalent linear array. and The radiation patterns after static beamforming in the airspace using an equivalent linear array in the elevation dimension are shown respectively. The expression for the pitch dimension sum difference single-pulse ratio is written as: (22)； in, This represents the sum and difference single pulse ratio of the pitch-dimensional equivalent linear array.

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