Redundancy elimination alternate projection comprehensive method for large-scale irregular planar array

Abstract

The invention discloses a redundancy elimination alternate projection synthesis method for a large-scale irregular planar array, relates to the field of array synthesis, and solves the problem of non-ideal synthesis efficiency in large-scale irregular planar array beam synthesis. The method comprises the following steps: giving a definition formula of a residual directional diagram of a large-scale irregular planar array under an alternating projection framework; under an alternating projection framework, based on the obtained residual directional diagram, giving out a least square solution of excitation, and removing redundant calculation amount; under an alternative projection framework, based on redundancy-removed least square excitation, an iteration process for large-scale irregular planar array synthesis is given. The method can be suitable for a planar array with any layout, and has very high comprehensive efficiency, especially for a large-scale array (the number of units is not less than 1000).

Description

Technical Field

[0001] The invention relates to the field of array synthesis, and in particular to a redundancy-removing alternating projection synthesis method for a large-scale irregular planar array. Background Art

[0002] Nowadays, with the rapid development of electronic information, the array synthesis technology of large-scale irregular planar arrays has attracted increasing attention. The application background of this technology covers many key fields, including 5G communications, Internet of Things, satellite communications, aerospace, radar systems, etc. These fields have an urgent need for high-performance, customizable antenna systems. Therefore, large-scale irregular planar arrays came into being. A larger array size means that the antenna system can provide stronger gain, wider coverage and stronger signal strength, which is especially important for applications that require long-distance communication, wide-area coverage or improved signal quality. The irregular array layout provides antenna engineers with a new design dimension, which can not only achieve better radiation performance than the regular layout, but also better adapt to various carrier shapes and maximize the use of limited space. For a given array layout, array synthesis technology can achieve a variety of array beams by optimizing the amplitude and phase of unit excitation to meet different performance and application requirements. Although the large-scale and irregular characteristics bring broad design freedom to array synthesis technology, they also bring many difficulties, mainly including: 1) As the number of array elements increases, the variables to be optimized also increase, resulting in an exponential increase in the computational complexity of the optimization problem, so a more efficient algorithm is needed to achieve large-scale array synthesis; 2) The irregular layout makes the classical synthesis methods used for regular layout no longer applicable, such as Taylor synthesis method, Fourier transform method, etc., so new array synthesis methods need to be developed. In summary, in-depth research on array synthesis technology is urgently needed to overcome these challenges.

[0003] Chinese patent 202110251847.7 discloses a conformal array pattern synthesis method based on a particle swarm algorithm with solution space clipping, which clips the solution space of the particle swarm algorithm to reduce the amount of algorithm calculation and effectively avoid the local convergence problem of the particle swarm algorithm. This method can be effectively used for the synthesis of irregular conformal arrays. However, due to the low computational efficiency of the particle swarm algorithm, this method is only applicable to small-scale arrays and cannot be used for the synthesis of large-scale irregular planar arrays.

[0004] Chinese patent 201510362211.4 discloses a method for comprehensive cascade optimization of large-scale planar array antenna patterns, which uses iterative Fourier transform method and intelligent optimization algorithm to jointly optimize array patterns, and takes into account the mutual coupling effect between antenna units. This method can efficiently synthesize large-scale planar arrays with more than 1000 units. However, since Fourier transform depends on uniform grids, this method is only applicable to uniformly laid out arrays and cannot be used for the synthesis of large-scale irregular planar arrays.

[0005] Chinese patent 202310774989.0 discloses a precise vector beamforming method for large-scale irregular conformal arrays, which uses an alternating projection framework to express the synthesis problem and provides a means to correct the main polarization and cross-polarization components of the vector pattern. This method can efficiently synthesize large-scale irregular conformal arrays. However, the excited least squares solution used in its iterative process still has redundant calculations, which can be further improved to achieve the synthesis of larger-scale irregular arrays with limited computing resources. Summary of the invention

[0006] In order to solve the above-mentioned technical bottleneck, namely, the problem of unsatisfactory comprehensive efficiency in the synthesis of large-scale irregular planar arrays, the present invention improves the traditional alternating projection method based on an efficient and flexible alternating projection framework, further improves the comprehensive efficiency, and proposes a de-redundant alternating projection synthesis method suitable for large-scale irregular planar arrays.

[0007] The present invention is achieved through the following technical solutions:

[0008] The method steps of the present invention are as follows:

[0009] Step 1: Given the beam synthesis index, define the reference pattern and residual pattern;

[0010] Step 2, based on the obtained residual pattern, find the least square solution of excitation redundancy removal;

[0011] Step 3, based on the obtained excitation, a new generation of reference directional pattern and residual directional pattern is obtained;

[0012] Step 4: Repeat steps 2 and 3 until the condition for exiting the iteration is met.

[0013] The present invention has the following advantages and beneficial effects:

[0014] a) The calculation accuracy of the present invention is high. Since the active unit directional pattern is considered in the synthesis process, the influence of unit mutual coupling and platform effect is taken into account, which improves the accuracy of the array directional pattern synthesized by the method.

[0015] b) The present invention has good versatility. Due to the use of an alternating projection framework, the method is independent of the array layout type and is applicable to any irregular planar array.

[0016] c) The present invention has high computational efficiency, and since redundant computation is removed in obtaining the least square solution of the excitation, the computational efficiency is significantly improved. In an embodiment, for a large-scale irregular planar array of 1000 yuan, the efficiency of the present method is increased by 1 times compared with the traditional alternating projection method. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0018] Figure 1 It is an overall flow chart of the redundant alternate projection method of the present invention;

[0019] Figure 2 Schematic diagram of the array layout of a 1000-element large-scale irregular planar array in an embodiment of the present invention;

[0020] Figure 3 The array pattern obtained by the redundant alternating projection method in the embodiment of the present invention;

[0021] Figure 4 This is a curve showing the variation of the number of sampling points that do not meet the requirements during the iteration process in the embodiment of the present invention. DETAILED DESCRIPTION

[0022] Before any embodiment of the present invention is described in detail, it should be understood that the application of the present invention is not limited to the details of the structure shown in the following description or the accompanying drawings. The present invention may adopt other embodiments and may be implemented or executed in various ways. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative improvements are within the scope of protection of the present invention.

[0023] like Figure 1 As shown, the present invention comprises the following steps:

[0024] 1) Given the beam synthesis index of a large-scale irregular planar array pattern, the reference pattern and the residual pattern are defined.

[0025] Considering a large-scale irregular planar array antenna with N elements, the array pattern can be expressed as

[0026]

[0027] in, β is the wave number in free space, θm and are the elevation angle and azimuth angle in the observation direction, and m = 1,…,M. (x n ,y n ) is the position of the nth array element, w n is the excitation weight of the nth array element, E n (u,v) is the active unit pattern of the nth array element, and n = 1,…,N. n (u,v) can be obtained using actual measurement or full-wave simulation, which includes the influence of unit mutual coupling and platform effect.

[0028] Given the comprehensive index of array beam, including: ① In the side lobe area (u m ,v m )∈Ω SL , the sidelobe level is lower than Γ SL ;②In the zero-sink area (u m ,v m )∈Ω Null , the zero-fall level is lower than Γ Null Γ SL and Γ Null can be combined into a function Γ(u m ,v m ). Then, in the framework of the alternating projection method, the reference pattern can be described as

[0029]

[0030] Where ξ is the overvoltage factor used to improve the convergence speed, F F (u m ,v m ) is the current directional diagram, Ω C is the area where the directional map does not meet the expected requirements, which contains K sampling points. The residual directional map is defined as ε(u m ,v m )=F R (u m ,v m )-F F (u m ,v m ), combined with formula (2), ε(u m ,v m ) can be expressed as

[0031]

[0032] 2) Based on the obtained residual pattern, find the least squares solution for de-redundancy of the excitation.

[0033] Define the following matrices and vectors:

[0034]

[0035] f F ={F F (u1,v1),F F (u2,v2),...,F F (u M ,v M )} T (4b)

[0036]

[0037] Obviously, there is f F =Aw F For the reference pattern, a vector f similar to that in (4b) can be defined R . Combined with the least squares method, the least squares solution of the excitation can be obtained

[0038]

[0039] Let B = (A H A) -1 A H , ε={ε(u1,v1),ε(u2,v2),…,ε(u M ,v M )} T Combined with the definition of the reference pattern in equation (2), equation (5) can be expanded to

[0040]

[0041] The above formula is the least square solution to the redundancy of the excitation, which introduces the current excitation w F The inheritance of . Among them, ε C , A C and B C They are defined as

[0042] ε C ={ε(u1,v1),ε(u2,v2),…,ε(u K ,v K )} T (7a)

[0043]

[0044] The domains of these vectors and matrices are (u m ,v m )∈Ω C, which can be directly obtained by extracting the corresponding elements in ε, A, and B, respectively. By comparing equations (5) and (6), the amount of calculation of the redundant least squares solution is reduced from N×M complex multiplications to N×K complex multiplications compared to the original least squares solution. Since in general, the number of sampling points K in the unsatisfied area is much smaller than the total number of sampling points M, the amount of calculation is greatly reduced.

[0045] 3) Based on the obtained excitation, a new generation of reference directional patterns and residual directional patterns are obtained.

[0046] According to the least square solution of the obtained excitation, the new generation of current directional diagram is obtained, that is, f F =Aw LS According to the preset beam comprehensive index, re-evaluate the area where the pattern does not meet the requirements Ω C Based on the framework of the alternating projection method, according to equations (2) and (3), the new generation of reference pattern f is obtained. R and the residual direction map ε.

[0047] 4) Repeat steps 2 and 3, and continue to update the current excitation and direction map until the conditions for exiting the iteration are met.

[0048] The iteration process starts with an initial current stimulus Start by following steps 2 and 3. and Update, the superscript q indicates the iteration order. The maximum number of iterations is preset to Q. When the current pattern meets all the preset beam comprehensive indicators (i.e. K = 0) or the iteration order reaches the maximum value (i.e. q = Q), the iteration loop is exited and the current excitation is output. And the corresponding direction diagram Complete the synthesis of large-scale irregular planar array patterns.

[0049] Example:

[0050] To verify the proposed redundant alternating projection synthesis method, consider synthesizing a large-scale irregular planar array with 1000 units. The array layout is as follows: Figure 2 Assume that the array operates at 1 GHz and all units are ideal point sources, that is, for m = 1, ..., M, E n (u m ,v m )=1. The preset array beam comprehensive index is: In the sidelobe region, the sidelobe level is lower than -35dB; in the null region of 0.4≤u≤0.7 and -0.1≤v≤0.1, the null level is lower than -50dB. In the proposed de-redundant alternating projection synthesis method, the maximum number of iterations is set to 500 times, the overvoltage factor is -5dB, and the total number of sampling points is M = 106491 (according to uniform sampling, where λ is the operating wavelength, L is the array aperture, and 114.6°λ / L is an estimate Profile beamwidth; this sampling interval means that each The main beam of the profile contains 15 sampling points). Using the proposed method, the iterative process reaches the exit condition after 330 times. At this time, the current directivity pattern obtained satisfies all beam comprehensive indicators, such as Figure 3 If the original least squares solution is used in the iteration process instead of the redundant least squares solution, that is, the traditional alternating projection method is used, the resulting directional pattern is similar to Figure 3 However, in terms of integration time, the redundant alternate projection method only takes 40.16 seconds, while the traditional alternate projection method takes 84.39 seconds, which doubles the overall efficiency (all integrated programs are run on the same ordinary desktop computer). This efficiency improvement can be attributed to Figure 4 Explanation, which shows the curve of the number of sampling points that do not meet the requirements during the iteration process. It can be seen that after only dozens of iterations, the number of points that do not meet the requirements drops to a very low level, which is much smaller than the total number of sampling points. Therefore, the use of the proposed method will eliminate a large amount of redundant calculations.

Claims

1. Redundant alternating projection synthesis method for large-scale irregular planar arrays, It is characterized in that The steps include: Step 1: Given the beam synthesis index, define the reference pattern and residual pattern; Step 2, based on the obtained residual pattern, find the least square solution of excitation redundancy removal; Step 3, based on the obtained excitation, a new generation of reference directional pattern and residual directional pattern is obtained; Step 4: Repeat steps 2 and 3 until the condition for exiting the iteration is met.

2. The method for removing redundant alternating projections of a large-scale irregular planar array according to claim 1, It is characterized in that In step 1, based on the framework of the alternating projection method, the concept and definition of the residual direction map are introduced; for the observation direction (u m ,v m ), the expression of the residual pattern is: Among them, Γ(u m ,v m ) is the threshold function for the change of the observed direction in the side lobe or null region, F F (u m ,v m ) is the current direction diagram, Ω C It is the area where the directional diagram does not meet the requirements.

3. The method for removing redundant alternating projections of a large-scale irregular planar array according to claim 1, It is characterized in that In step 2, the expression of the least squares solution of the excitation redundancy removal is: w LS =w F +B C ε C Among them, w LS and w F are the vectors composed of the redundant least squares excitation and the current excitation, B C is the transformation matrix defined in the region where the requirements are not met, ε C It is the vector formed by the residual pattern defined in the area where the requirements are not met.

4. The method for removing redundant alternating projections of a large-scale irregular planar array according to claim 1, It is characterized in that In step 2, the expression of the redundant least squares excitation intuitively proves the introduction of the inheritance of the current excitation, so that the amount of calculation involved is changed from N×M complex multiplications to N×K complex multiplications, where N is the number of array elements, M is the total number of sampling points, and K is the number of sampling points that do not meet the requirements; usually K<<M, so the proposed method can greatly reduce the computational overhead in the alternating projection iteration process.

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