CN117078863A - Rapid beam forming method of heterogeneous array antenna - Google Patents

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

A fast beamforming method for heterogeneous array antennas

Technical field

The invention belongs to the technical field of array antenna pattern synthesis, and specifically relates to a fast beam forming method for heterogeneous array antennas.

Background technique

Array antennas have extremely important application value in electronic countermeasures, high-resolution imaging and multi-functional integrated systems. Heterogeneous array is an effective array that can solve the mutual constraints between traditional large-scale phased array antenna aperture and ultra-wideband and high efficiency, and at the same time take into account the requirements of ultra-wideband systems for suppressing high-frequency grating lobes and compressing the number of channels. form. Therefore, research on heterogeneous arrays is extremely valuable.

Since the heterogeneous array is composed of antenna units with different structures, its pattern cannot be obtained directly using the pattern product theorem, which makes the beamforming problem of the heterogeneous array more complex than that of a conventional uniform array. At present, heterogeneous array antennas are a relatively new research field, and there are very few reports on their beamforming methods. Since the units in the conformal array have different orientations, the pattern product theorem cannot be used. This makes the beamforming problem of conformal arrays similar to that of heterogeneous arrays. Therefore, the conformal array beamforming method has great reference significance for the heterogeneous array beamforming problem.

Currently, the existing conformal array beamforming technologies mainly include analytical methods, numerical iterative methods, stochastic optimization methods, etc. Among them, the analytical method has high computational efficiency, but it cannot be used for complex-shaped beamforming problems. Numerical iteration methods for conformal arrays, such as the alternating projection method, have low computational complexity, and the optimization of cross-polarization, excitation dynamic range ratio and near-field amplitude can be considered during the synthesis process; the iterative convex optimization method has a faster solution speed and The solution results are stable and better than other optimization methods. It has certain advantages for the optimal design of medium or large arrays, but it cannot be used directly for non-convex problems. Stochastic optimization methods such as genetic algorithm and particle swarm optimization algorithm have been widely used in conformal array beamforming. The main advantage is that the objective function and constraint conditions can be flexibly set, and it has good problem applicability. However, for large arrays, the computational efficiency of stochastic optimization methods is very low, and it is difficult to obtain satisfactory results for high-dimensional problems with many optimization variables.

Although the above methods for conformal array antenna beamforming can be applied to heterogeneous array antenna problems with appropriate modifications, these methods generally cannot achieve fast beamforming synthesis of large-scale arrays. For uniformly spaced planar arrays, the iterative fast Fourier transform (FFT) method is a recognized low-complexity numerical beamforming method that can be applied to large-scale arrays. By replacing FFT with nonuniform FFT (NUFFT), the iterative FFT method can be extended to the synthesis of non-uniform spacing arrays. Chinese patent 201811042658.3 discloses a planar array sparse method based on Chirp-Z transform (CZT), in which array element excitation can be optimized through iterative CZT. For arrays of tens of thousands of elements, the synthesis time is only on the order of hundreds of seconds. For heterogeneous arrays, due to the different unit patterns and spacing, it is difficult to directly establish the relationship between the array excitation distribution and the array pattern. Neither of the above two methods can be used directly. If we consider the beamforming process for subarrays composed of different units, in the "excitation-direction pattern" process, the total pattern of the array is the result of the joint action of each subarray. For the iterative FFT method, the position of the sampling point is affected by the array element. For spacing constraints, it is also necessary to eliminate the problem of different sampling point positions caused by different spacing between different sub-array elements through interpolation. This process will introduce a certain error and reduce the beamforming accuracy; and in the "pattern-excitation" calculation process, There is currently no clear correspondence between the correction of the overall pattern and the correction of each sub-array pattern, so the above method cannot be directly used for heterogeneous array beamforming. There are still research gaps for rapid synthesis methods for heterogeneous arrays.

In order to solve the technical problems faced by the above background technology, the present invention proposes a fast beamforming method suitable for heterogeneous arrays.

Contents of the invention

In response to the above problems, the purpose of the present invention is to propose a fast beamforming method for ultra-wideband heterogeneous arrays. This method is suitable for ultra-wideband heterogeneous arrays composed of multiple uniformly spaced arrays or regularly combined by uniformly spaced radiation basic units. It can achieve accurate beamforming requirements while maintaining high overall efficiency.

In order to achieve the above technical objectives, the present invention includes the following steps:

Step 1: For a heterogeneous array composed of multiple uniformly spaced sub-arrays with different array elements, determine the working status of each sub-array at a certain operating frequency f, obtain K sub-arrays in working status and number them;

Step 2: Use the multi-scale CZT method to obtain the pattern of K sub-arrays in working condition and the total pattern of the heterogeneous array;

Step 3: According to the pattern performance requirements, correct the general direction pattern to obtain the corrected general direction pattern;

Step 4: Apply the correction value of the pattern to the pattern of the k-th subarray alone, and use multi-scale inv-CZT to obtain the corrected excitation distribution of the subarray;

Step 5: Use multi-scale CZT to obtain the pattern of one iteration update of the sub-array, as well as the total pattern of the heterogeneous array at this time;

Step 6: Carry out the above "correction + transformation" process for the remaining sub-arrays respectively until all K sub-array excitations and patterns are updated or the patterns meet the expected requirements, and one iteration is completed;

Step 7: Iteratively perform the above-mentioned "multi-scale correction + transformation" operation on the heterogeneous array until the array pattern meets the requirements or reaches the upper limit of the set number of iterations, and the pattern shaping is completed.

Furthermore, the heterogeneous array in step 1 is composed of different sub-arrays, and the units in each sub-array are the same and evenly arranged. The operating frequencies, patterns, arrangement spacing, etc. of the array elements in different sub-arrays may be different. , at frequency f, there are K sub-arrays working simultaneously, which are numbered k=1, 2,...,K.

Further, in step 2, assuming that the heterogeneous array is located in the xoy plane, its total pattern can be expressed as the accumulation of K sub-array patterns that work simultaneously.

in, N ^(k) represents the total number of units in the k-th subarray,/> represents the excitation of the n-th unit in the k-th sub-array, β=2πf/c represents the wave number of the free space operating at frequency point f,/> Represents the position of the n-th unit in the k-th subarray,/> Represents the active unit pattern of the n-th unit in the k-th sub-array operating at frequency point f.

Further, in step 2, for the K sub-arrays in the working state, virtual units are used to supplement them into uniform planar arrays. The corresponding excitations of the virtual array elements are 0, and the initial excitations corresponding to the actual array elements can be based on the shaping requirements. Selection; for different sub-array patterns, in order to allow them to be directly superimposed, the same observation point sampling method is used

The pattern of each sub-array is quickly calculated through two-dimensional CZT, and the total pattern of the heterogeneous array at this time is obtained by superposition.

Further, in step 3, the overall direction pattern is corrected by correcting the amplitude of the value that does not meet the requirements to the expected value, while the phase remains unchanged, which can be expressed as:

Among them, ξ∈[0, 1] is the overvoltage factor, which is used to accelerate the reduction of the achieved side lobe level, Γ _U is the upper bound of the desired pattern, and Γ _L is the lower bound of the desired pattern.

Furthermore, in step 4, a multi-scale inv-CZT method is proposed. First, all corrections to the general pattern are applied to the k-th working subarray, that is,

The pattern of the corrected subarray k is obtained, and the excitation of the subarray is obtained through the inv-CZT process.

Further, in step 5, virtual array elements are used to supplement the sub-array k into a uniform plane array, in which the virtual array element excitation is 0 and the actual array element excitation is the result calculated in step 4. The sub-array k is quickly calculated by the CZT method. The pattern corresponding to array k is added to the patterns of the remaining working sub-arrays calculated in step 2 to obtain the total pattern of the heterogeneous array.

Further, in step 6, determine whether k=K is satisfied at this time or whether the pattern meets the expected requirements. If not, set k=k+1 and repeat steps 3-5; if yes, complete the beam once. For the shaping iterative process, proceed to step 7.

Further, in step 7, the maximum number of iterations Q can be preset. When the updated achievable heterogeneous array pattern meets the target requirements or the number of iterations reaches the upper limit, the synthesis is completed. Otherwise, return to step 3 for the next beamforming. Iterate.

Beneficial effects brought about by adopting the above technical solutions:

The present invention proposes a multi-scale iterative CZT method by dividing the heterogeneous array into different sub-arrays. Using multi-scale CZT for each sub-array, the pattern of each sub-array and the total heterogeneous array at the same sampling point can be quickly calculated. Directional pattern; using multi-scale inv-CZT, it is possible to calculate the corresponding excitation distribution of each sub-array from the heterogeneous array pattern; introducing multi-scale CZT and inv-CZT into the alternating projection framework, and through FFT acceleration, the rapid development of heterogeneous array antennas can be achieved Beamforming.

Description of the drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without exerting any creative effort.

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

Figure 2 is a schematic diagram of the heterogeneous array model of the present invention;

Figure 3 is a schematic diagram of the virtual array element filling points of the present invention;

Figure 4 is a flow chart of the CZT and inv-CZT methods of the present invention, (a) CZT, (b) inv-CZT;

Figure 5 is a three-dimensional pattern of low side lobe shaping of the focused beam in the embodiment of the present invention. Sectional orientation diagram;

Figure 6 is a three-dimensional pattern of flat-top beam low sidelobe shaping in the embodiment of the present invention. Sectional orientation diagram.

Detailed ways

The technical solutions of the present invention will be described in further detail below with reference to the accompanying drawings and specific examples, so that those skilled in the art can better understand the present invention and implement it, but the examples are not intended to limit the present invention. The invention is capable of other embodiments and of being practiced or carried out in various ways. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative improvements shall fall within the scope of protection of the present invention.

As shown in Figure 1, the present invention includes the following steps:

Step 1: For a heterogeneous array composed of different uniform sub-arrays, determine the working status of each sub-array at a certain working frequency f, obtain K sub-arrays in working status and number them.

Referring to the heterogeneous array layout shown in Figure 2, at a certain frequency f, sub-array 1, sub-array 2, and sub-array 3 work simultaneously, and their numbers are k=1 respectively. Since the total pattern F _tol of the heterogeneous array at this frequency is the result of the joint action of the sub-arrays, and the traditional CZT method is only suitable for uniformly spaced planar arrays, how to make F tol on the premise that each of the sub-arrays performs fast beamforming? _tolMeeting expectations is the problem that this study needs to solve. The present invention proposes a multi-scale iterative CZT method, which is specifically described as steps 2-7.

Step 2: Use the multi-scale CZT method to obtain the pattern of K sub-arrays in working condition and the total pattern of the heterogeneous array.

Taking subarray 1 as an example, in order to apply two-dimensional CZT to array pattern beamforming, first use the same virtual unit as the array element of subarray 1 according to the spacing. Subarray 1 is supplemented into a uniform plane array A, as shown in Figure 3. Express the array factor pattern of array A as a two-dimensional form represented by u, v:

Among them, β=2π/λ is the wave constant in space, λ is the wavelength, Represents the number of array elements of array A along the x-axis direction,/> represents the number of array elements of array A along the y-axis direction, g ⁽¹⁾ (f, u, v) represents the unit square diagram of array element 1 of sub-array,/> Represents the excitation of the array element (n _x , _ny ) of array A. When the excitation corresponding to the virtual array element is 0, the above formula is the pattern expression of sub-array 1, To direct the beam.

When neglecting inter-unit coupling and array edge effects, let

At this time, equation (1) can be expressed as

Define two sequences

Calculate the two-dimensional convolution between the two sequences in equation (5), and you can get the sequence y(s ^u , s ^v )

Equation (6) satisfies the linear convolution form. According to the convolution theorem, the FFT algorithm can be used to accelerate its calculation process and achieve fast convolution. Fast convolution comes from circular convolution, also called circular convolution. The condition to ensure that the results of circular convolution and linear convolution are equal without aliasing is that the number of points of circular convolution is greater than the length of the linear convolution output sequence. , so it is necessary to perform complementation on the sequence h and the sequence b to obtain two T ^u ×T ^v sequences h′ (t ^u , t ^v ) and b′ (t ^u , t ^v ). At this time, equation (6) can be calculated by FFT to obtain y′. Formula (4) can be expressed as

The CZT method can realize the process of rapid calculation from array excitation to array pattern. The specific process is shown in Figure 4(a).

Step 3: According to the performance requirements of the direction pattern, correct the general direction pattern to obtain the corrected general direction pattern.

The correction method adopted is to correct the amplitude of the value that does not meet the requirements to the expected value, while the phase remains unchanged, which can be expressed as:

Among them, ξ∈[0, 1] is the overvoltage factor, which is used to accelerate the reduction of the achieved side lobe level, thereby reducing the number of iterations required to complete the synthesis.

Step 4: Apply the correction value of the pattern to the pattern of the k-th subarray alone, and use multi-scale inv-CZT to obtain the corrected excitation distribution of the subarray.

This method first embodies the correction of the general pattern in sub-array 1 alone, keeping sub-array 2 and sub-array 3 unchanged, and obtains:

For equation (9), the multi-scale inv-CZT method is used to obtain the excitation corresponding to subarray 1 at this time. inv-CZT is the reverse process of equations (6) and (7). The specific process is shown in Figure 4(b).

Step 5: Use multi-scale CZT to obtain the pattern of one iteration update of the subarray, as well as the total pattern of the heterogeneous array at this time.

Step 6: Carry out the above "correction + transformation" process for the remaining sub-arrays respectively until all K sub-array excitations and patterns are updated or the patterns meet the expected requirements, and one iteration is completed.

For the heterogeneous array shown in Figure 2, repeat steps 3-5 until all three sub-arrays have completed an update of the excitation and pattern, or the total pattern of the heterogeneous array meets the expected requirements. At this time, one iteration is completed and the heterogeneous array is obtained. Array pattern.

Step 7: Iteratively perform the above-mentioned "multi-scale correction + transformation" operation on the heterogeneous array until the array pattern meets the requirements or reaches the upper limit of the set number of iterations, and the pattern shaping is completed.

Determine whether the heterogeneous array pattern obtained in step 6 meets the requirements or reaches the upper limit of the set number of iterations. If so, the pattern shaping is completed. If not, return to step 3 for the next iteration.

The specific implementation of the fast beamforming method for ultra-wideband heterogeneous array proposed by the present invention can be further given through the following simulation examples and results:

In this simulation example, taking the array shown in Figure 2 as an example, the number of elements in sub-array 1 is N ⁽¹⁾ = 108; the number of elements in sub-array 2 is N ⁽²⁾ = 108; the number of elements in sub-array 3 is N(3 ⁾ =144. Among them, the array element pattern of sub-array 3 is approximately expressed by Equation (10):

At a certain frequency f, subarray 1, subarray 2, and subarray 3 work simultaneously, where the array element spacing of subarray 3 is The array elements of sub-array 2 are formed by combining the array elements of sub-array 3 according to 2×2, and the spacing between array elements is/> The 1st array element of the subarray is formed by combining the 3rd array elements of the subarray in a 4×4 manner. The spacing between the array elements is /> At this time, the proposed multi-scale iterative CZT method is used to perform focused beam low sidelobe shaping and flat-top beam low sidelobe shaping on the heterogeneous array. Among them, the set number of sampling points is ^Tu = T ^v = 512; the iteration upper limit Q = 500; the expected side lobe level set in the focused beam low side lobe is no more than -25dB, and the overvoltage factor is ξ = 0.708 ; In the flat-top beam low side-lobe shaping, set the side-lobe level to not exceed -20dB, the over-voltage factor to be ξ=0.562, and the main-lobe width to be 26°. The low side-lobe shaping results of the focused beam are shown in Figure 5, where the dotted line is the prescribed upper boundary of the side lobe; the low side-lobe shaping results of the flat-top beam are shown in Figure 6, where the red dotted line is the prescribed shaping boundary. It can be seen that the comprehensive direction maps can meet the desired shaping requirements. In terms of overall efficiency, for a 360-element heterogeneous array, the computing time to achieve a low side-lobe focused beam is only 6.30 seconds, and the computing time to achieve a low side-lobe flat-top beam is only 9.68 seconds, which reflects the The invented method can achieve accurate and efficient heterogeneous array beamforming.

Claims (10)

1. A fast beamforming method for heterogeneous array antennas, which is characterized by including the following steps: Step 1: For a heterogeneous array composed of multiple uniformly spaced sub-arrays with different array elements, determine the working status of each sub-array at a certain operating frequency f, obtain K sub-arrays in working status and number them; Step 2: Use multi-scale CZT to obtain the pattern of the K sub-arrays in working condition and the total pattern of the heterogeneous array; Step 3: According to the pattern performance requirements, correct the general direction pattern to obtain the corrected general direction pattern; Step 4: Apply the correction value of the pattern to the pattern of the k-th subarray alone, and use multi-scale inv-CZT to obtain the corrected excitation distribution of the subarray; Step 5: Use multi-scale CZT to obtain the pattern of one iteration update of the sub-array, as well as the total pattern of the heterogeneous array at this time; Step 6: Carry out the above "correction + transformation" process for the remaining sub-arrays respectively until all K sub-array excitations and patterns are updated or the patterns meet the expected requirements, and one iteration is completed; Step 7: Iteratively perform the above-mentioned "multi-scale correction + transformation" operation on the heterogeneous array until the array pattern meets the requirements or reaches the upper limit of the set number of iterations, and the pattern shaping is completed. 2. A fast beamforming method for heterogeneous array antennas according to claim 1, characterized in that: heterogeneous array antennas refer to arrays composed of antenna units with different structures. This method proposes a multi-scale iteration The CZT method is used to solve the problem that the traditional iterative FFT method and the iterative CZT method are not applicable due to different unit patterns and arrangement spacings in heterogeneous array beamforming, and achieve rapid beamforming of heterogeneous arrays. 3. A fast beamforming method for heterogeneous array antennas according to claim 1, characterized in that: the heterogeneous array in step 1 is composed of different sub-arrays, and the units in each sub-array are the same and evenly arranged. , for the array elements of different sub-arrays, their operating frequencies, patterns, arrangement spacing, etc. may be different. At the frequency f, there are K sub-arrays working at the same time, and they are numbered k=1, 2,...,K. 4. A fast beamforming method for heterogeneous array antennas according to claim 1, characterized in that: in step 2, assuming that the heterogeneous array is located in the xoy plane, its total pattern can be expressed as simultaneously working The form of K subarray pattern accumulation in, N ^(k) represents the total number of units in the k-th subarray,/> represents the excitation of the n-th unit in the k-th sub-array, β=2πf/c represents the wave number of the free space operating at frequency point f,/> Represents the position of the n-th unit in the k-th subarray,/> Represents the active unit pattern of the n-th unit in the k-th sub-array operating at frequency point f. 5. A fast beamforming method for heterogeneous array antennas according to claim 1, characterized in that: in step 2, for the K sub-arrays in the working state, virtual units are used to supplement them into uniform planes. array, the excitation corresponding to the virtual array element is 0, and the initial excitation corresponding to the actual array element can be selected according to the shaping requirements; for different sub-array patterns, in order to make them directly superimposed, the same observation point sampling method is used The pattern of each sub-array is quickly calculated through two-dimensional CZT, and the total pattern of the heterogeneous array at this time is obtained by superposition. 6. A fast beamforming method for heterogeneous array antennas according to claim 1, characterized in that: in step 3, the correction of the general pattern is to correct the amplitude of the value that does not meet the requirements to the expected value, The phase remains unchanged and can be expressed as: Among them, ξ∈[0,1] is the overvoltage factor, which is used to accelerate the reduction of the achieved side lobe level, Γ _U is the upper bound of the desired pattern, and Γ _L is the lower bound of the desired pattern. 7. A fast beamforming method for heterogeneous array antennas according to claim 1, characterized in that: in step 4, a multi-scale inv-CZT method is proposed, and first all corrections to the total pattern are Acts on the kth working subarray, that is The pattern of the corrected subarray k is obtained, and the excitation of the subarray is obtained through the inv-CZT process. 8. A fast beamforming method for heterogeneous array antennas according to claim 1, characterized in that: in step 5, virtual array elements are used to supplement the sub-array k into a uniform plane array, wherein the virtual array elements are excited is 0, and the actual array element excitation is the result calculated in step 4. The CZT method is used to quickly calculate the pattern corresponding to sub-array k at this time, and is added to the pattern of the remaining working sub-arrays calculated in step 2 to obtain the total heterogeneous array. direction map. 9. The ultra-wideband heterogeneous array antenna fast beamforming method according to claim 1, characterized in that: in step 6, it is judged whether k=K is satisfied at this time or whether the pattern meets the expected requirements, if not, Then let k=k+1 and repeat steps 3-5; if yes, complete a beamforming iteration process and proceed to step 7. 10. A fast beamforming method for heterogeneous array antennas according to claim 1, characterized in that: in step 7, the maximum number of iterations Q can be preset, and when the updated achievable heterogeneous array pattern satisfies When the target requirement or the number of iterations reaches the upper limit, the synthesis is completed; otherwise, return to step 3 for the next beamforming iteration.