An analytical method for mainlobe shaping of conformal array based on multi-beam aperture projection

Abstract

The present invention discloses an analytical method for conformal array main lobe shaping based on multi-beam aperture projection, comprising the following steps: for a three-dimensional conformal array, select K observation points in the desired shaping area, corresponding to different beam directions; establish a reference plane perpendicular to the kth desired beam; select effective radiating array elements under the beam direction; calculate the projection position and projection area of ​​the effective radiating array elements on the reference plane; calculate the projection array excitation by an analytical method; calculate the conformal array excitation; repeat the above projection array position, excitation and conformal array excitation calculation process for different observation points until the excitations corresponding to all the desired beams are obtained; perform weighted superposition on the obtained multiple groups of excitations to achieve beam shaping. The method proposes a method for quickly and effectively calculating the projection area under beam scanning, which is combined with weighted beam superposition, breaking through the applicability limitations of traditional analytical methods, and generalizing the aperture projection method to three-dimensional conformal array beam scanning and shaping problems.

Description

Technical Field

[0001] The present invention relates to the field of array antennas, and in particular to a conformal array main lobe shaping analysis method based on multi-beam aperture projection. Background Art

[0002] With the development of a new generation of high-speed platforms, conformal phased array antennas have received more and more attention, and how to achieve conformal array beamforming has also become a research hotspot. The beamforming technologies that have been developed so far, including analytical methods, alternating projection methods, convex optimization methods or semi-positive definite programming, random optimization methods, etc., are mainly aimed at linear and planar regular arrays, and rarely consider complex conformal arrays with different unit patterns. Methods with good versatility, such as random optimization, convex optimization, and alternating projection, can be used for beamforming of conformal arrays. However, the computational complexity of the random optimization algorithm is extremely large and is not suitable for beamforming of large-scale arrays; the convex optimization method cannot currently achieve the control of arbitrary main lobe shapes of the beam; semi-positive definite programming has a large computational complexity; the alternating projection method relies heavily on the selection of the initial solution and requires multiple iterations, which increases the calculation time.

[0003] Traditional analytical methods such as Taylor synthesis and Chebyshev synthesis cannot handle conformal array problems that consider unit radiation patterns, and cannot achieve arbitrary beamforming. Chinese Patent 202110927133.3 discloses a Taylor weight optimization method based on a circular conformal array. The Taylor technology is applied to the excitation optimization of conformal arrays, which can achieve high gain in the main lobe direction and deep zero-depression in the interference direction, and can also achieve multi-beamforming. However, this method is not suitable for the shaping of the main lobe of an arbitrary conformal array beam, and there is currently no analytical beamforming method suitable for arbitrary conformal arrays.

[0004] The aperture projection method is a method of projecting the elements on the conformal array onto an equivalent plane orthogonal to the main beam direction, synthesizing the directional pattern on this equivalent aperture plane, and then converting the obtained excitation distribution into the conformal array excitation distribution. This method converts the three-dimensional array synthesis into a two-dimensional array synthesis problem, and is often used in combination with numerical optimization methods. At present, most of the research on the aperture projection method stays on the focused beam synthesis problem of the fan array, and there is no research on the beam scanning and shaping of the three-dimensional conformal array. At present, there are the following problems in the beam shaping of the three-dimensional conformal array: First, the projection array of the three-dimensional conformal array is a non-uniform plane array, the number of adjacent elements of each array element is not equal, and the position relationship is complex, and the projection area is difficult to calculate by the array element position analysis; when the array performs beam scanning, there is a problem that some array elements are physically blocked along the main beam direction. At this time, the number of effective array elements and the equivalent aperture of the array will change, so the projection array needs to change with the beam scanning angle. For different scanning angles, the effective array elements and their projection areas are different. In this case, no research has given a clear method on how to quickly calculate the projection array element positions and corresponding projection areas corresponding to different scanning directions and how to achieve beamforming.

[0005] In order to solve the technical problems faced by the above-mentioned background technology, the present invention proposes a new beamforming method suitable for a three-dimensional conformal array. Summary of the invention

[0006] In view of the above problems, the present invention aims to propose a conformal array main lobe shaping analysis method based on multi-beam aperture projection. The method is applicable to three-dimensional conformal arrays and can achieve the required beamforming while maintaining a high overall efficiency.

[0007] In order to achieve the above technical objectives, the present invention comprises the following steps:

[0008] Step 1: For a given N-element 3D conformal array, according to the desired pattern shaping requirements, select K observation points in the shaping main lobe area, corresponding to the desired beam pointing of K focused beams;

[0009] Step 2: For the kth (k=0, 1, ..., K-1) desired focused beam pointing Establish a reference plane k perpendicular to it;

[0010] Step 3: Direct the beam according to your needs and the orientation of each array element, select the effective radiation array element m that is not blocked under the direction of the beam, m∈[1,N];

[0011] Step 4: Get the projection position and projection area of ​​the array element m on the kth reference plane;

[0012] Step 5: According to the projection array aperture and the expected directivity pattern requirements, the excitation distribution of the projection array is obtained by analytical method;

[0013] Step 6: Make the far-field radiation intensities of the corresponding array elements of the conformal array and the projection array in the desired beam direction equal to obtain the conformal array excitation distribution;

[0014] Step 7: Determine whether the excitation distributions corresponding to all K focused beams with different directions are obtained. If so, proceed to the next step. If not, repeat the above projection array position, excitation and conformal array excitation calculation process to obtain the corresponding conformal array excitation distribution.

[0015] Step 8: Perform weighted superposition on the multiple groups of excitations obtained to obtain a conformal array excitation distribution that meets the shaping requirements, and the synthesis is completed.

[0016] Further, in step 1, for a given N-element three-dimensional conformal array, a desired pattern requirement is given, including a desired main lobe pointing direction, a side lobe level, or an upper and lower boundary of the desired pattern. The expected requirement is that if it is focused beam low sidelobe synthesis or focused beam scanning, the number of sampling points K = 1; if it is main lobe shaping, the weighted beam superposition method is used to select K observation points approximately at 3dB intervals in the lower boundary area of ​​the shaped main lobe. The angle corresponding to each observation point is the desired beam direction of the different focused beams used for superposition. Through this method, any main beam shaping can be achieved in theory.

[0017] Furthermore, in step 2, the normal of the reference plane is the desired beam direction The reference plane equation is established as

[0018] u k x+v k y+w k z=0 (1)

[0019] in, w k = cosθ k .

[0020] Furthermore, the array element selection in step 3 is based on the kth beam pointing With array element orientation Is the angle between them greater than 90°? When the angle is greater than 90°, the array element does not participate in the pattern synthesis due to physical occlusion. Therefore, the role of this type of array element is not considered in the projection array. The array element number participating in the pattern synthesis is recorded as m, m∈[1,N], which can be expressed as a set:

[0021]

[0022] in, is the orientation vector of array element n; is the desired beam pointing vector; w n = cosθ n .

[0023] Furthermore, in step 4, the geometric position of the screened array element m is projected onto the kth reference plane to obtain the projection position corresponding to the array element m. The calculation method is

[0024]

[0025]

[0026] Where (x′ m ,y′ m ,z′ m ) is the transition coordinate. Since the projection array is a non-uniform plane array and the projection array changes with the scanning angle, the projection area of ​​each array element is difficult to be obtained through geometric analysis. Currently, no research has specifically given a method for calculating the projection area of ​​a two-dimensional projection array. The present invention proposes a method for quickly and automatically calculating the projection area. First, the obtained projection array is divided into a triangular mesh. Each triangle vertex has an array element. The area of ​​each triangular mesh is calculated. The array element m corresponds to the projection area S m That is, it is 1 / 3 of the area of ​​all triangular meshes with the array element as the vertex. The sum of the projected areas of all array elements is equal to the size of the projection array aperture.

[0027] Furthermore, in step 5, according to the projection array aperture and the expected directional pattern requirements, a suitable planar array analytical method is selected to obtain the excitation distribution of the projection array. The present invention adopts the Taylor synthesis method. First, the corresponding Taylor distribution is approximately selected according to the aperture size of the projection array and the expected sidelobe level. Then, the Taylor distribution is sampled according to the position of the projection array element. The Taylor sampling value T corresponding to each array element is m The projection area S calculated in step 4 m The excitation amplitude of the projection array is obtained by multiplying them, and the phase is matched according to the desired beam direction to obtain the projection array excitation distribution

[0028]

[0029] in, β is the free space propagation constant.

[0030] Furthermore, in step 6, according to the far-field radiation intensity of the corresponding array elements of the conformal array and the projection array in the desired beam direction is equal, we get

[0031]

[0032] The excitation of other array elements that do not participate in the pattern synthesis is 0, that is,

[0033]

[0034] Thus, the excitation sequence corresponding to the conformal array element can be obtained

[0035]

[0036] Furthermore, in step 7, determine whether k=K-1. If not, set k=k+1 and repeat steps 3 to 6; if yes, execute step 8.

[0037] Furthermore, the weighted overlay expression in step 8 is

[0038]

[0039] where σ k is the weighting coefficient corresponding to the kth superposition beam, and the upper boundary is shaped by the desired pattern Decide: Depend on It is obtained by weighting according to the normalized weight of the corresponding focused beam radiation power pattern.

[0040] The beneficial effects brought by adopting the above technical solution are:

[0041] a) The present invention combines the planar array analytical synthesis method with the aperture projection method, which is a three-dimensional conformal analytical beamforming method with low computational complexity and high comprehensive efficiency.

[0042] b) The present invention does not specify the position of array elements and is applicable to conformal arrays of arbitrary layout.

[0043] c) The present invention can realize the control and scanning of the main lobe shape of the radiation pattern, and at the same time can achieve the desired side lobe level performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0045] Figure 1 is a flow chart of the method of the present invention;

[0046] Figure 2is a schematic diagram of a conformal array model of the present invention;

[0047] Figure 3 A schematic diagram of selecting observation points within the main lobe range for beamforming problems according to the present invention;

[0048] Figure 4 The projection plane and projection array of the present invention are shown in FIG. );

[0049] Figure 5 This is a schematic diagram of the triangulation of the projection array of the present invention;

[0050] Figure 6 The three-dimensional radiation pattern of the low sidelobe focused beam of the integrated conformal array in the embodiment of the present invention and Cross-sectional directional diagram;

[0051] Figure 7 The three-dimensional scanning pattern of the low sidelobe focused beam (20°, 0°) of the integrated conformal array in the embodiment of the present invention and Cross-sectional directional diagram;

[0052] Figure 8 The corresponding superposition beam pointing of the conformal array low sidelobe flat-top beamforming in the embodiment of the present invention;

[0053] Fig. 9 The three-dimensional radiation pattern of the low sidelobe flat-top beamforming of the integrated conformal array in the embodiment of the present invention and Cross-sectional orientation diagram. DETAILED DESCRIPTION

[0054] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0055] Step 1: For a given N-element 3D conformal array, according to the desired pattern shaping requirements, select K observation points in the shaped main lobe area, corresponding to the desired beam pointing of the K focused beams.

[0056] For a given N-element three-dimensional conformal array, Figure 2 Taking the spherical cap array shown in the figure as an example, the position of each array element is x=[x0,x1,…,x N-1 ] T , y=[y0,y1,…,y N-1 ] T 、z=[z0,z1,…,z N-1 ] T , the unit directivity diagram of array element n is The far-field radiation pattern of the array is:

[0057]

[0058] in β = 2π / λ, λ is the wavelength of the antenna; w n is the excitation of array element n; w=cosθ.

[0059] For the array, given the desired pattern requirements, including the desired main lobe pointing, side lobe level, or the upper and lower boundaries of the desired pattern The expected requirement is that if it is a focused beam low sidelobe or focused beam scanning, the number of sampling points K = 1; if it is a main lobe shaping, the weighted beam superposition method is used to select K observation points approximately at 3dB intervals in the lower boundary area of ​​the shaped main lobe. K-1, such as Figure 3 The angle corresponding to each observation point is the expected beam direction of the different focused beams used for superposition, and the weighting coefficient corresponding to each focused beam is the sampling of the expected upper bound. By using this method, any main beam forming can be achieved in theory.

[0060] Step 2: For the kth (k=0, 1, ..., K-1) desired focused beam pointing A reference plane k is established perpendicular to it.

[0061] The normal to the reference plane is the desired beam direction The reference plane equation is established as

[0062] u k x+v k y+w k z=0 (2)

[0063] in, w k = cosθ k .

[0064] Step 3: Direct the beam according to your needs And the orientation of each array element, select the effective radiation array element m that is not blocked under the direction of the beam, m∈[1,N].

[0065] The array element selection is based on the kth desired beam pointing With array element orientation Is the angle between them greater than 90°? When the angle is greater than 90°, the array element does not participate in the pattern synthesis due to physical occlusion. Therefore, the role of this type of array element is not considered in the projection array. The array element number participating in the pattern synthesis is recorded as m, m∈[1,N], which can be expressed as a set:

[0066]

[0067] in, is the orientation vector of array element n; is the desired beam pointing vector;

[0068] w n = cosθ n .

[0069] Step 4: Get the projection position and projection area of ​​array element m on the kth reference plane.

[0070] The geometric position of the screened array element m is projected onto the kth reference plane to obtain the projection array layout located on the reference plane, as shown in Figure 4 As shown. The projection position corresponding to the array element m is The calculation method is

[0071]

[0072]

[0073] Where (x′ m ,y′ m ,z′ m ) is the transition coordinate. Since the projection array is a non-uniform plane array, and the projection array layout changes with the scanning angle, the projection area of ​​each array element is difficult to be obtained through geometric analysis. Currently, no research has specifically given a method for calculating the projection area of ​​a two-dimensional projection array. The present invention proposes a method for quickly calculating the projection area. First, the obtained projection array is triangulated, such as Figure 5 As shown, each triangle vertex has an array element. The area of ​​each triangle mesh is calculated. The array element m corresponds to the projected area S. m That is, it is 1 / 3 of the area of ​​all triangular meshes with the array element as the vertex. The sum of the projected areas of all array elements is equal to the size of the projection array aperture.

[0074] Step 5: According to the projection array aperture and the expected directivity pattern requirements, the excitation distribution of the projection array is obtained by analytical methods.

[0075] According to the projection array aperture and the expected directional pattern requirements, a suitable planar array analytical method is selected to obtain the excitation distribution of the projection array. The present invention adopts the Taylor synthesis method. First, according to the aperture shape and size of the projection array and the expected sidelobe level, the corresponding rectangular aperture or circular aperture Taylor distribution is approximately selected. Secondly, according to the position of the projection array element, the Taylor distribution is sampled. The Taylor sampling value T corresponding to each array element is m The projection area S calculated in step 4 m The excitation amplitude of the projection array is obtained by multiplying them, and the phase is matched according to the desired beam direction to obtain the projection array excitation distribution

[0076]

[0077] The corresponding projected plane array pattern can be expressed as

[0078]

[0079] Step 6: Make the far-field radiation intensities of the corresponding array elements of the conformal array and the projection array in the desired beam direction equal to obtain the conformal array excitation distribution.

[0080] make In the direction, the far-field intensity of the conformal array element m is equal to that of the corresponding projection array element m, that is,

[0081]

[0082]

[0083] It can be obtained that when the desired beam pointing is When , the excitation corresponding to the mth element of the conformal array is

[0084]

[0085] For other array elements that do not participate in the synthesis of the directional pattern, that is, The array element is set to 0, and the conformal array excitation sequence is obtained.

[0086]

[0087]

[0088] Step 7: Determine whether the excitation distributions corresponding to all K focused beams with different directions are obtained. If so, execute the next step. If not, repeat the above projection and excitation calculation process to obtain the corresponding conformal array excitation distribution.

[0089] Determine whether k=K-1. If not, set k=k+1 and repeat steps 3 to 6 to obtain multiple groups of corresponding different beam directions. Corresponding conformal array excitation distribution If yes, go to step 8.

[0090] Step 8: Perform weighted superposition on the multiple groups of excitations obtained to obtain a conformal array excitation distribution that meets the shaping requirements, and the synthesis is completed.

[0091] The obtained K groups of scanning focusing beam excitations are weighted superimposed, as shown in formula (13), and the excitation distribution corresponding to the shaped direction pattern can be obtained.

[0092]

[0093] where σ k is the weighting coefficient corresponding to the kth superposition beam, and the upper boundary is shaped by the desired pattern Decide: Depend on It is obtained by weighting according to the normalized weight of the corresponding focused beam radiation power pattern. After obtaining the excitation distribution, the pattern of the conformal array at this time can be calculated according to formula (1).

[0094] The specific implementation of the conformal array main lobe shaping analytical method based on multi-beam aperture projection proposed in the present invention can be further given by the following simulation examples and results:

[0095] In this simulation example, the Figure 2 The array model shown in the figure has the number of array elements in each layer as N = [1, 6, 12, 18, 24, 28, 32, 36, 38, 40, 40]; the array element spacing is d = 0.55λ; the spherical crown array radius is R = 3.50λ; the orientation is The conformal array unit of is approximately expressed by equation (14):

[0096]

[0097] The direction diagrams of other units are obtained by rotating the coordinates of this unit.

[0098] Since the conformal array is a spherical crown array, the projection array can be approximated as a circular aperture array, so the circular aperture Taylor distribution is selected. The radius of the circular aperture Taylor distribution is determined by the maximum distance between the projection array and the origin, and the number of zero points can be adjusted. The sidelobe level is the expected sidelobe level of the conformal array pattern. To verify the applicability of the method of the present invention, three types of beamforming patterns are considered. The first is low sidelobe focused beamforming. Let the expected beam pointing be The expected sidelobe level is PSLL = -25dB. The comprehensive results are as follows Figure 6 As shown in the results, the proposed method can achieve the low sidelobe synthesis of the spherical crown array focused beam. The main beam of the synthesized directional pattern is accurately pointed. The sidelobe is -25.59dB.

[0099] The second is a low sidelobe focused beam scanning pattern. Let the desired beam pointing be The expected sidelobe level is PSLL = -25dB. The comprehensive results are as follows Figure 7As shown. The main beams of the conformal array pattern and the projection array pattern obtained by synthesis are accurately pointed, among which the maximum sidelobe level of the conformal array pattern is -24.38dB. The synthesis process for a focused beam takes about 15.87s, of which the time required for unit rotation and array manifold calculation is 15.83s, the time required for projection array calculation is 0.0019s, and the time required for excitation calculation and pattern synthesis is only 0.0411s.

[0100] The third type is the flat-top beamforming pattern. Let the main beam range of the desired lower boundary in the θ direction be The expected sidelobe level is PSLL = -25dB; the superimposed beam pointing is as follows Figure 8 As shown in ; the beam superposition weighting coefficient is the corresponding pattern normalization coefficient. The comprehensive result is as follows Fig. 9 As shown. From the results, it can be obtained that the main beam of the conformal array pattern and the projection array pattern meet the expected shaping requirements, and the maximum sidelobe level of the conformal array pattern is -25.0dB, which meets the expected requirements. For all required scanning directions, the time required for the calculation process of the corresponding aperture projection array layout and excitation, and the conformal array pattern calculation process is only 2.05s. It can be seen that for these three different pattern conditions, the pattern synthesized by the method of the present invention meets the requirements, and verifies the effectiveness of the present invention for conformal array beamforming.

Claims

1. A conformal array main lobe shaping analytical method based on multi-beam aperture projection, characterized in that The following steps are involved: Step 1: For a given N-element 3D conformal array, according to the desired pattern shaping requirements, select K observation points in the shaping main lobe area, corresponding to the desired beam pointing of K focused beams; Step 2: For the kth desired focused beam pointing Wherein, k = 0, 1, ..., K-1, and a reference plane k perpendicular thereto is established; Step 3: Direct the beam according to your needs and the orientation of each array element, select the effective radiation array element m that is not blocked under the direction of the beam, m∈[1,N]; Step 4: Get the projection position and projection area of ​​array element m on the kth reference plane; Step 5: According to the projection array aperture and the expected directivity pattern requirements, the excitation distribution of the projection array is obtained by analytical method; Step 6: Make the far-field radiation intensities of the corresponding array elements of the conformal array and the projection array in the desired beam direction equal to obtain the conformal array excitation distribution; Step 7: Determine whether the excitation distributions corresponding to all K focused beams with different directions are obtained. If so, proceed to the next step. If not, repeat the above projection array position, excitation and conformal array excitation calculation process to obtain the corresponding conformal array excitation distribution. Step 8: Perform weighted superposition on the multiple groups of excitations obtained to obtain a conformal array excitation distribution that meets the shaping requirements, and the synthesis is completed.

2. According to claim 1, a conformal array main lobe shaping analysis method based on multi-beam aperture projection is characterized by: In step 1, for a given N-element three-dimensional conformal array, the desired pattern requirements are given, including the desired main lobe pointing, side lobe level, or the upper and lower boundaries of the desired pattern. The expected requirement is that if it is focused beam low sidelobe synthesis or focused beam scanning, the number of sampling points K = 1; if it is main lobe shaping, the weighted beam superposition method is used to select K observation points approximately at 3dB intervals in the lower boundary area of ​​the shaped main lobe. The angle corresponding to each observation point is the desired beam direction of the different focused beams used for superposition.

3. The method for analyzing conformal array main lobe shaping based on multi-beam aperture projection according to claim 1, characterized in that: In step 3, the array element selection is based on the kth beam pointing With array element orientation Is the angle between them greater than 90°? When the angle is greater than 90°, the array element does not participate in the pattern synthesis due to physical occlusion. Therefore, the role of the occluded array element is not considered in the projection array. The array element number participating in the pattern synthesis is recorded as m, m∈[1,N], which can be expressed as a set: in, is the orientation vector of array element n; is the desired beam pointing vector; w n = cosθ n , w k = cosθ k .

4. The method for analyzing conformal array main lobe shaping based on multi-beam aperture projection according to claim 1, characterized in that: Step 4: Project the geometric position of the selected array element m onto the kth reference plane to obtain the projection position corresponding to the array element m. The calculation method is Where (x′ m ,y′ m ,z′ m ) is the transition coordinate, and the obtained projection array is divided into triangular meshes. Each triangle vertex has an array element. The area of ​​each triangular mesh is calculated. The array element m corresponds to the projection area S m That is, it is 1 / 3 of the area of ​​all triangular meshes with the array element as the vertex. The sum of the projected areas of all array elements is equal to the size of the projection array aperture.

5. The method for analyzing conformal array main lobe shaping based on multi-beam aperture projection according to claim 1, characterized in that: In step 6, the far-field radiation intensity of the corresponding array elements of the conformal array and the projection array in the desired beam direction is equal, and we get The excitation of other array elements that do not participate in the pattern synthesis is 0, that is, Thus, the excitation sequence corresponding to the conformal array element can be obtained 6. The method for analyzing conformal array main lobe shaping based on multi-beam aperture projection according to claim 5, characterized in that: The weighted overlay expression in step 8 is where σ k is the weighting coefficient corresponding to the kth superposition beam, and the upper boundary is shaped by the desired pattern Decide: Depend on It is obtained by weighting according to the normalized weight of the corresponding focused beam radiation power pattern.

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