CN117078863A - Rapid beam forming method of heterogeneous array antenna - Google Patents
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Abstract
The invention discloses a rapid beam forming method of a heterogeneous array antenna. The method is based on multi-scale iterative chirp Z transformation and comprises the following steps: aiming at a heterogeneous array formed by a plurality of subarrays with different array elements, K subarrays in a working state are obtained at a certain frequency; obtaining a directional diagram of each working subarray and a total directional diagram of the heterogeneous array by using multi-scale CZT; correcting the total pattern according to the requirement; independently acting the correction value on the kth subarray, and updating excitation of the subarray by using multi-scale inv-CZT; obtaining a directional diagram of the subarray and a total directional diagram of the heterogeneous array at the moment by using multi-scale CZT; repeating the correction and transformation processes until the K sub-arrays are excited and the directional diagram is updated once or the directional diagram meets the expected requirement; and iteratively executing the multi-scale correction and transformation operation until the direction diagram meets the requirement or reaches the set iteration upper limit. The method can realize the shaping requirements of various patterns of the heterogeneous array, and simultaneously maintain high precision and efficiency.
Description
Technical Field
The invention belongs to the technical field of array antenna pattern synthesis, and particularly relates to a rapid beam forming method of a heterogeneous array antenna.
Background
The array antenna has extremely important application value in electronic countermeasure, high-resolution imaging and multifunctional integrated systems. The heterogeneous array is an effective array form which can solve the problem that the aperture of the traditional large-scale phased array antenna is mutually restricted with the ultra-wideband and high efficiency, and simultaneously gives consideration to the requirement of the ultra-wideband system on the number of the high-frequency grating lobes and the compression channels. Thus, research into heterogeneous arrays is of great value.
Since the heterogeneous array is composed of antenna elements of different structures, the directional patterns thereof cannot be directly obtained by using the directional pattern product theorem, which makes the beamforming problem of the heterogeneous array more complex than that of the conventional homogeneous array. At present, the heterogeneous array antenna belongs to the newer research field, and few reports about the research of a beam forming method thereof are provided. The conformal array cannot use the pattern product theorem because the cell orientations are different. This makes the conformal array beamforming problem similar to that of heterogeneous arrays. Therefore, the conformal array beam forming method has great reference significance for the heterogeneous array beam forming problem.
The existing conformal array beam forming technology mainly comprises an analysis method, a numerical iteration method, a random optimization method and the like. The analysis method has high calculation efficiency, but cannot be used for the beam forming problem of complex shapes. The numerical iteration method of the conformal array is such as an alternate projection method, the calculation complexity is low, and cross polarization, excitation dynamic range ratio and near field amplitude optimization can be considered in the synthesis process; the iterative convex optimization method has the advantages of higher solving speed, stable solving result and better than other optimization methods, has certain advantages for the optimization design of medium or large-scale arrays, and cannot be directly used for non-convex problems. The random optimization method such as genetic algorithm, particle swarm optimization algorithm and the like are widely applied to conformal array beam forming, and the method has the main advantages of being capable of flexibly setting objective functions and constraint conditions and good in problem applicability. However, for large arrays, the random optimization method is very computationally inefficient, and for high dimensional problems with many optimization variables, it is difficult to obtain satisfactory results.
Although the above methods for conformal array antenna beamforming are suitably adapted to be applied to heterogeneous array antenna problems, these methods generally do not allow for rapid beamforming synthesis for large-scale arrays. For uniformly spaced planar arrays, the iterative fast fourier transform method (fast Fourier transform, FFT) is a well-known low complexity digital beamforming method that can be adapted for large-scale arrays. Instead of using a non-uniform FFT (nununiform FFT), the iterative FFT method can be generalized to the synthesis of non-uniformly spaced arrays. Chinese patent 201811042658.3 discloses a planar array sparse method based on the Chirp-Z transform (CZT), wherein the excitation of the array elements can be optimized by iterative CZT, for arrays of tens of thousands of elements, the integration time is only on the order of hundred seconds. For heterogeneous arrays, because the cell patterns and the spacing are different, it is difficult to directly establish the relationship between the array excitation distribution and the array patterns, and both the above two methods cannot be directly used. If the subarrays formed by different units are considered to be respectively subjected to a beam forming process, in the process of exciting the directional diagram, the total directional diagram of the array is the result of the combined action of all subarrays, for an iterative FFT method, the positions of sampling points are constrained by the spacing of array elements, and the problem that the positions of the sampling points are different due to the different spacing of the array elements of different subarrays is also required to be eliminated by an interpolation method, a certain error is introduced in the process, and the beam forming precision is reduced; in the process of calculating the pattern-excitation, there is no clear correspondence between the correction of the total pattern and the correction of each subarray pattern, so the method cannot be directly used for heterogeneous array beamforming. There is still a gap in research for the rapid synthesis of heterogeneous arrays.
In order to solve the technical problems faced by the background technology, the invention provides a rapid beamforming method suitable for a heterogeneous array.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a rapid beam forming method of an ultra-wideband heterogeneous array. The method is suitable for ultra-wideband heterogeneous arrays formed by regularly combining a plurality of uniformly-spaced arrays or uniformly-spaced radiation base units, and realizes accurate beam forming requirements on the premise of keeping high comprehensive efficiency.
In order to achieve the technical purpose, the invention comprises the following steps:
step 1: judging the working state of each subarray at a certain working frequency f aiming at a heterogeneous array formed by a plurality of uniformly-spaced subarrays with different array elements, obtaining K subarrays in the working state and numbering the K subarrays;
step 2: respectively obtaining the patterns of K subarrays in a working state and the total patterns of the heterogeneous arrays by using a multi-scale CZT method;
step 3: correcting the total pattern according to the pattern performance requirement to obtain a corrected total pattern;
step 4: independently acting the correction value of the direction diagram on the direction diagram of the kth subarray, and obtaining the corrected excitation distribution of the subarray by using multi-scale inv-CZT;
step 5: obtaining a directional diagram of one-time iterative updating of the subarray and a total directional diagram of the heterogeneous array at the moment by using multi-scale CZT;
step 6: the correction and transformation processes are respectively carried out on the other subarrays until all K subarray excitation and directional patterns are updated once or the directional patterns meet the expected requirements, and one iteration is completed;
step 7: and iteratively executing the multi-scale correction and transformation operation on the heterogeneous array until the array pattern meets the requirement or reaches the upper limit of the set iteration times, and completing the pattern shaping.
Further, the heterogeneous array in step 1 is formed by different subarrays, the units in each subarray are identical and are uniformly arranged, and for the array elements of the different subarrays, the working frequency, the pattern, the arrangement spacing and the like of the array elements may be different, and at the frequency f, K subarrays work simultaneously, and the numbers of the subarrays are k=1, 2, … and K.
Further, in step 2, assuming that the heterogeneous array is located in the xoy plane, the total pattern may be expressed as an accumulated form of K sub-array patterns that work simultaneously
Wherein,N (k) representing the total number of cells of the kth subarray, +.>Representing the excitation of the nth element in the kth subarray, β=2pi f/c representing the wavenumber of the free space operating at frequency point f, +.>Indicating the position of the nth cell in the kth subarray,/->An active cell pattern representing an nth cell in a kth sub-array operating at a frequency point f.
Further, in step 2, for the K sub-arrays in the working state, the K sub-arrays are respectively supplemented into uniform planar arrays by using virtual units, excitation corresponding to the virtual array elements is 0, and initial excitation corresponding to the actual array elements can be selected according to the shaping requirement; for different subarray patterns, the same observation point sampling mode is adopted in order to enable the subarray patterns to be directly overlapped
And rapidly calculating each subarray pattern through two-dimensional CZT, and superposing to obtain the total pattern of the heterogeneous array at the moment.
Further, in step 3, the correction of the total pattern corrects the amplitude of the value that does not satisfy the requirement to the desired value, and the phase remains unchanged, which may be expressed as:
wherein ζ is E [0,1]]Is an overvoltage factor for accelerating the lowering of the implemented sidelobe level Γ U For the upper boundary of the desired pattern, Γ L Is the lower bound of the desired pattern.
Further, in step 4, a multi-scale inv-CZT method is proposed, wherein the correction to the total pattern is first applied to the kth working subarray, i.e.
And obtaining the directional diagram of the corrected subarray k, and obtaining the excitation of the subarray through an inv-CZT process.
Further, in step 5, the subarray k is supplemented to be a uniform planar array by using a virtual array element, wherein the virtual array element excitation is 0, the actual array element excitation is the result obtained by the calculation in step 4, the directional diagram corresponding to the subarray k at the moment is rapidly calculated by a CZT method, and the directional diagram is added with the directional diagrams of the rest working subarrays obtained by the calculation in step 2 to obtain the total directional diagram of the heterogeneous array.
Further, in step 6, it is determined whether k=k or whether the pattern satisfies the desired requirement, if not, k=k+1 is set, and steps 3 to 5 are repeated; if yes, finishing a beam forming iteration process, and performing step 7.
Further, in step 7, the maximum iteration number Q may be preset, when the updated achievable heterogeneous array pattern meets the target requirement or the iteration number reaches the upper limit, the synthesis is completed, otherwise, the process returns to step 3, and the next beamforming iteration is performed.
The beneficial effects brought by adopting the technical scheme are that:
according to the invention, the heterogeneous array is divided into different subarrays, and a multi-scale iterative CZT method is provided, and multi-scale CZT is adopted for each subarray, so that the direction diagram of each subarray and the total direction diagram of the heterogeneous array under the same sampling point can be rapidly calculated; the corresponding excitation distribution of each subarray can be calculated by using the heterogeneous array directional diagram by adopting the multiscale inv-CZT; and introducing multi-scale CZT and inv-CZT into an alternate projection frame, and accelerating through FFT (fast Fourier transform) to realize the rapid beamforming of the heterogeneous array antenna.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions of the prior art, the drawings which are used in the description of the embodiments or the prior art will be briefly described, it being obvious that the drawings in the description below are only some embodiments of the invention, and that other drawings can be obtained according to these drawings without inventive faculty for a person skilled in the art.
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of a heterogeneous array model according to the present invention;
FIG. 3 is a schematic diagram of the virtual array element point padding of the present invention;
FIG. 4 is a flow chart of the CZT and inv-CZT method of the present invention, (a) CZT, (b) inv-CZT;
FIG. 5 is a three-dimensional directional diagram of low side lobe forming of a focused beam in an embodiment of the inventionA cross-sectional pattern;
FIG. 6 is a three-dimensional pattern of low side lobe forming of a flat-top beam in an embodiment of the inventionA cross-sectional view.
Detailed Description
The following description of the present invention is provided in detail with reference to the accompanying drawings and specific embodiments so that those skilled in the art may better understand the present invention and implement it, but the examples are not meant to limit the invention. The invention is capable of other embodiments and of being practiced or of being carried out in various ways. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive improvements, are intended to fall within the scope of the invention.
As shown in fig. 1, the present invention includes the steps of:
step 1: for a heterogeneous array formed by different uniform subarrays, the working state of each subarray at a certain working frequency f is judged, and K subarrays in the working state are obtained and numbered.
Referring to the heterogeneous array layout shown in fig. 2, at a certain frequency f, subarrays 1,2, 3 operate simultaneously, numbered k=1, respectively. Due to the heterogeneous array total pattern F at that frequency tol As the result of the combined action of the subarrays, the traditional CZT method is only applicable to the planar array with uniform intervals, so how to lead F on the premise that the subarrays respectively and rapidly carry out wave beam forming tol Meeting expectations is a problem that needs to be addressed by this study. The invention provides a multi-scale iterative CZT method, which is specifically described as steps 2-7.
Step 2: and respectively obtaining the patterns of the K subarrays in the working state and the total patterns of the heterogeneous arrays by using a multi-scale CZT method.
Taking subarray 1 as an example, in order to apply two-dimensional CZT to array pattern beamforming, virtual units which are the same as subarray 1 array elements are adopted according to the intervalThe subarray 1 is supplemented with a uniform planar array a as shown in fig. 3. The array factor pattern of array a is represented as a two-dimensional form represented by u, v:
where, β=2pi/λ is the wave constant in space, λ is the wavelength,represents the number of array elements of array A along the x-axis, ">Represents the array element number g of the array A along the y-axis direction (1) (f, u, v) represents a cell pattern of 1 array element of the subarray,/o>Represents array A array element (n) x ，n y ) When the excitation corresponding to the virtual array element is 0, the above expression is the pattern expression of the subarray 1, is beam pointing.
When neglecting inter-cell coupling and array edge effect, let
In this case, formula (1) may be expressed as
Defining two sequences
The two-dimensional convolution between the two sequences in equation (5) can yield the sequence y (s u ，s v )
The equation (6) satisfies a linear convolution form, and according to a convolution theorem, the calculation process can be accelerated by an FFT algorithm, so that quick convolution is realized. The fast convolution is derived from the circular convolution, which is also called circular convolution, and the condition that the circular convolution is equal to the linear convolution result and no aliasing occurs is that the number of points of the circular convolution is larger than the length of the linear convolution output sequence, so that two T's are obtained after the sequence h and the sequence b are subjected to point-filling and point-filling u ×T v Sequence h' (t u ，t v ) And b' (t) u ，t v ). At this time, equation (6) may be calculated by FFT to obtain y'. Formula (4) may be represented as
The process of rapid calculation from array excitation to array pattern can be achieved by the CZT method, the specific flow is shown in fig. 4 (a).
Step 3: and correcting the total pattern according to the pattern performance requirement to obtain a corrected total pattern.
The correction method adopted is to correct the amplitude of the value which does not meet the requirement to the expected value, and the phase is kept unchanged, and can be expressed as:
wherein ζ ε [0,1] is an overpressure factor, and is used to accelerate and reduce the level of the side lobe, so as to reduce the number of iterations required for completing synthesis.
Step 4: and (3) independently acting the correction value of the direction diagram on the direction diagram of the kth subarray, and obtaining the corrected excitation distribution of the subarray by using the multiscale inv-CZT.
The method comprises the steps of firstly, independently reflecting correction of a total directional diagram to the subarray 1, keeping the subarray 2 and the subarray 3 unchanged, and obtaining the following components:
for equation (9), the excitation corresponding to the subarray 1 at this time is obtained by using a multiscale inv-CZT method. The inv-CZT is the inverse process of formulas (6) and (7), and the specific flow is shown in FIG. 4 (b).
Step 5: and obtaining a directional diagram of one iteration update of the subarray and a total directional diagram of the heterogeneous array at the moment by using the multi-scale CZT.
Step 6: and (3) respectively carrying out the correction and transformation processes on the rest subarrays until all K subarray excitation and directional patterns are updated once or the directional patterns meet the expected requirements, and completing one iteration.
And (3) for the heterogeneous array shown in fig. 2, repeating the steps 3-5 until all three subarrays complete one excitation and updating of the directional diagram, or the total directional diagram of the heterogeneous array meets the expected requirement, and completing one iteration at the moment to obtain the directional diagram of the heterogeneous array.
Step 7: and iteratively executing the multi-scale correction and transformation operation on the heterogeneous array until the array pattern meets the requirement or reaches the upper limit of the set iteration times, and completing the pattern shaping.
Judging whether the heterogeneous array pattern obtained in the step 6 meets the requirement or not, or if the heterogeneous array pattern meets the upper limit of the set iteration times, finishing the pattern shaping if the heterogeneous array pattern meets the upper limit of the set iteration times, and returning to the step 3 if the heterogeneous array pattern does not meet the upper limit of the set iteration times, and carrying out the next iteration.
The specific implementation mode of the rapid beam forming method of the ultra-wideband heterogeneous array provided by the invention can be further given by the following simulation examples and results:
in this simulation example, taking the array shown in FIG. 2 as an example, the number of 1 array elements of the subarray is N (1) =108; the number of subarray 2 array elements is N (2) =108; the number of subarray 3 array elements is N (3 ) =144. Wherein the array element pattern of the subarray 3 is approximately represented by formula (10):
at a certain frequency f, subarrays 1,2 and 3 work simultaneously, wherein the array element spacing of subarray 3 is as followsThe subarray 2 array elements are formed by combining subarray 3 array elements according to 2 multiplied by 2, and the array element distance is +.>The subarray 1 array element is formed by combining subarray 3 array elements according to 4 multiplied by 4, and the distance between the array elements is equal to the sound +.>At this time, the proposed multi-scale iterative CZT method is used to perform focused beam low side lobe shaping and flat top beam low side lobe shaping on the heterogeneous array respectively. Wherein the set sampling point number is T u ＝T v =512; upper iteration limit q=500; the desired side lobe level set in the focused beam low side lobe is no more than-25 dB, the overpressure factor is ζ=0.708; and the side lobe level is set to be not more than-20 dB in the low side lobe forming of the flat-top beam, the overvoltage factor is xi=0.562, and the main lobe width is 26 degrees. The focused beam low side lobe shaping result is shown in fig. 5, wherein the dotted line is the prescribed side lobe upper boundary; flat-top beam low side lobe shaping is shown in fig. 6, where the red dashed line is a defined shaping boundary. It can be seen that the integrated patterns can meet the desired shaping requirements. In the aspect of comprehensive efficiency, for a 360-element heterogeneous array, the operation time for realizing the low-sidelobe focused beam is only 6.30 seconds, and the operation time for realizing the low-sidelobe flat-top beam is only 9.68 seconds, which reflects that the method can realize accurate and efficient heterogeneous array beam forming.
Claims (10)
1. The rapid beam forming method of the heterogeneous array antenna is characterized by comprising the following steps of:
step 1: judging the working state of each subarray at a certain working frequency f aiming at a heterogeneous array formed by a plurality of uniformly-spaced subarrays with different array elements, obtaining K subarrays in the working state and numbering the K subarrays;
step 2: respectively using multi-scale CZT to obtain the patterns of K subarrays in a working state and the total patterns of the heterogeneous arrays;
step 3: correcting the total pattern according to the pattern performance requirement to obtain a corrected total pattern;
step 4: independently acting the correction value of the direction diagram on the direction diagram of the kth subarray, and obtaining the corrected excitation distribution of the subarray by using multi-scale inv-CZT;
step 5: obtaining a directional diagram of one-time iterative updating of the subarray and a total directional diagram of the heterogeneous array at the moment by using multi-scale CZT;
step 6: the correction and transformation processes are respectively carried out on the other subarrays until all K subarray excitation and directional patterns are updated once or the directional patterns meet the expected requirements, and one iteration is completed;
step 7: and iteratively executing the multi-scale correction and transformation operation on the heterogeneous array until the array pattern meets the requirement or reaches the upper limit of the set iteration times, and completing the pattern shaping.
2. The method for fast beamforming of a heterogeneous array antenna according to claim 1, wherein: the heterogeneous array antenna is an array formed by antenna units with different structures, and the method provides a multi-scale iterative CZT method to solve the problem that the traditional iterative FFT method and the iterative CZT method cannot be applied due to different unit patterns and arrangement intervals in heterogeneous array beamforming, so that the heterogeneous array rapid beamforming is realized.
3. The method for fast beamforming of a heterogeneous array antenna according to claim 1, wherein: the heterogeneous array in the step 1 is composed of different subarrays, units in each subarray are identical and are uniformly distributed, the working frequency, the directional diagram, the distribution spacing and the like of the array elements of the different subarrays are possibly different, and under the frequency f, K subarrays work simultaneously and are numbered as k=1, 2, … and K.
4. The method for fast beamforming of a heterogeneous array antenna according to claim 1, wherein: in step 2, assuming that the heterogeneous array is located in the xoy plane, its total pattern can be expressed as an accumulated form of K sub-array patterns operating simultaneously
Wherein,N (k) representing the total number of cells of the kth subarray, +.>Representing the excitation of the nth element in the kth subarray, β=2pi f/c representing the wavenumber of the free space operating at frequency point f, +.>Indicating the position of the nth cell in the kth subarray,/->An active cell pattern representing an nth cell in a kth sub-array operating at a frequency point f.
5. The method for fast beamforming of a heterogeneous array antenna according to claim 1, wherein: in the step 2, for K sub-arrays in a working state, the K sub-arrays are respectively supplemented into uniform plane arrays by using virtual units, the excitation corresponding to the virtual array elements is 0, and the initial excitation corresponding to the actual array elements can be selected according to the shaping requirement; for different subarray patterns, the same observation point sampling mode is adopted in order to enable the subarray patterns to be directly overlapped
And rapidly calculating each subarray pattern through two-dimensional CZT, and superposing to obtain the total pattern of the heterogeneous array at the moment.
6. The method for fast beamforming of a heterogeneous array antenna according to claim 1, wherein: in step 3, the correction of the total pattern corrects the amplitude of the value that does not satisfy the requirement to the desired value, and the phase remains unchanged, which can be expressed as:
wherein ζ is E [0,1]]Is an overvoltage factor for accelerating the lowering of the implemented sidelobe level Γ U For the upper boundary of the desired pattern, Γ L Is the lower bound of the desired pattern.
7. The method for fast beamforming of a heterogeneous array antenna according to claim 1, wherein: in step 4, a multi-scale inv-CZT method is proposed, in which the correction to the total pattern is first applied to the kth working subarray, i.e.
And obtaining the directional diagram of the corrected subarray k, and obtaining the excitation of the subarray through an inv-CZT process.
8. The method for fast beamforming of a heterogeneous array antenna according to claim 1, wherein: in step 5, the subarray k is supplemented to be a uniform planar array by using a virtual array element, wherein the virtual array element excitation is 0, the actual array element excitation is the result obtained by the calculation in step 4, the directional diagram corresponding to the subarray k at the moment is rapidly calculated by a CZT method, and the directional diagram is added with the directional diagrams of the rest working subarrays obtained by the calculation in step 2 to obtain the total directional diagram of the heterogeneous array.
9. The method for fast beamforming of an ultra-wideband heterogeneous array antenna according to claim 1, wherein: in step 6, judging whether k=k or whether the pattern meets the expected requirement, if not, making k=k+1, and repeating the steps 3-5; if yes, finishing a beam forming iteration process, and performing step 7.
10. The method for fast beamforming of a heterogeneous array antenna according to claim 1, wherein: in step 7, the maximum iteration number Q may be preset, when the updated achievable heterogeneous array pattern meets the target requirement or the iteration number reaches the upper limit, the synthesis is completed, otherwise, the step 3 is returned to for the next beamforming iteration.
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