Redundancy Removal and Alternating Projection Synthesis Method for Large-Scale Irregular Planar Arrays

Abstract

The present invention discloses a redundancy-removing alternating projection synthesis method for large-scale irregular planar arrays, which relates to the field of array synthesis and solves the problem of unsatisfactory synthesis efficiency in beam synthesis of large-scale irregular planar arrays. The present invention includes: under the alternating projection framework, giving a definition formula for the residual pattern of a large-scale irregular planar array; under the alternating projection framework, based on the obtained residual pattern, giving a least-squares solution for the excitation and removing redundant computational amounts; under the alternating projection framework, based on the redundancy-removing least-squares excitation, giving an iterative process for the synthesis of a large-scale irregular planar array. This method can be applied to planar arrays with arbitrary layouts and has high synthesis efficiency, especially for large-scale arrays (the number of elements is not less than 1000).

Description

Technical Field

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

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

[0003] Chinese Patent No. 202110251847.7 discloses a conformal array pattern synthesis method based on a solution space pruning particle swarm algorithm, which prunes the solution space of the particle swarm algorithm to reduce the computational amount of the algorithm and effectively avoids 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 No. 201510362211.4 discloses a cascaded optimization method for pattern synthesis of large planar array antennas. The method combines the iterative Fourier transform method and intelligent optimization algorithms to jointly optimize the array pattern, and takes into account the mutual coupling effect between antenna elements. This method can efficiently synthesize large-scale planar arrays with more than 1000 elements. However, due to the dependence of the Fourier transform on a uniform grid, this method is only applicable to uniformly arranged arrays and cannot be used for the synthesis of large-scale irregular planar arrays either.

[0005] Chinese Patent No. 202310774989.0 discloses an accurate vector beamforming method for large-scale irregular conformal arrays. The method uses an alternating projection framework to express the synthesis problem and provides a means to correct the co-polarization and cross-polarization components of the vector pattern. This method can relatively efficiently synthesize large-scale irregular conformal arrays. However, the least squares solution of the excitation used in its iterative process still has redundant computational amounts and can be further improved to achieve the synthesis of larger-scale irregular arrays with limited computational resources. Summary of the Invention

[0006] To solve the above-mentioned technical bottlenecks, that is, the problem of unsatisfactory synthesis efficiency in the synthesis of large-scale irregular planar arrays, based on an efficient and flexible alternating projection framework, the present invention improves the traditional alternating projection method to further improve the synthesis efficiency, and proposes a redundant-free alternating projection synthesis method applicable to large-scale irregular planar arrays.

[0007] The present invention is realized 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 the residual pattern.

[0010] Step 2: Based on the obtained residual pattern, find the redundant-free least squares solution of the excitation.

[0011] Step 3: Based on the obtained excitation, find the new generation of reference pattern and residual pattern.

[0012] Step 4: Repeat Steps 2 and 3 until the iteration termination condition 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 element pattern is considered in the synthesis process, the influence of element mutual coupling and platform effect is taken into account, which improves the accuracy of the array pattern synthesized by this method.

[0015] b) The present invention has good versatility. Due to the use of the alternating projection framework, this method does not depend on the array layout type and is applicable to any irregular planar array.

[0016] c) The present invention has high computational efficiency. Since redundant computational amounts are removed in obtaining the excitation least-squares solution, the computational efficiency is significantly improved. In the embodiment, for the synthesis of a large-scale irregular planar array of 1000 elements, the efficiency of this method is doubled 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, form a part of this application, and do not limit the embodiments of the present invention. In the drawings:

[0018] Figure 1 is the overall flow block diagram of the redundancy-removing alternating projection method of the present invention;

[0019] Figure 2 is the schematic diagram of the array layout of a large-scale irregular planar array of 1000 elements in the embodiment of the present invention;

[0020] Figure 3 is the array radiation pattern synthesized by the redundancy-removing alternating projection method in the embodiment of the present invention;

[0021] Figure 4 is the change curve of the number of sampling points not meeting the requirements during the iteration process in the embodiment of the present invention. Detailed Embodiments

[0022] Before describing any embodiment of the present invention in detail, it should be understood that the application of the present invention is not limited to the details of the structures shown in the following description or the drawings. The present invention may adopt other embodiments and may be implemented or executed in various ways. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative improvements fall within the scope of protection of the present invention.

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

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

[0025] Considering an N-element large-scale irregular planar array antenna, the array radiation pattern in the global coordinate system can be expressed as

[0026]

[0027] wherein, β is the wave number in free space, θm and are the elevation angle and azimuth angle in the observation direction, respectively, 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 element pattern of the nth array element, and n = 1, …, N. E n (u, v) can be obtained by actual measurement or full-wave simulation, which includes the influence of element mutual coupling and platform effect.

[0028] Given the array beam synthesis specifications, including: ① in the sidelobe region (u m , v m ) ∈ Ω SL , the sidelobe level is lower than Γ SL ; ② in the null region (u m , v m ) ∈ Ω Null , the null level is lower than Γ Null . Γ SL and Γ Null can be combined into a function Γ(u m , v m ) that varies with the sampling points. Then, in the framework of the alternating projection method, the reference pattern can be described as

[0029]

[0030] where ξ is an overpressure factor used to improve the convergence rate, F F (u m , v m ) is the current pattern, Ω C is the region where the pattern does not meet the desired requirements, which contains K sampling points. Define the residual pattern as ε(u m , v m ) = F R (u m , v m ) - F F (u m , v m ), combined with equation (2), ε(u m , v m ) can be expressed as

[0031]

[0032] 2) Based on the obtained residual pattern, find the de-redundant least-squares solution 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 direction pattern, a vector f similar to equation (4b) can be defined R . Combining with the least squares method, the least squares solution of the excitation can be obtained

[0038]

[0039] Let's assume B = (A H A) -1 A H , ε = {ε(u1,v1), ε(u2,v2),…, ε(u M ,v M )} T . Combining with the definition of the reference direction pattern in equation (2), equation (5) can be expanded as

[0040]

[0041] The above equation is the redundancy-removed least squares solution of the excitation, and this solution introduces the inheritance property for the current excitation w F . Among them, ε C , A C and B C are respectively 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 all (u m ,v m ) ∈ Ω C, can be directly obtained by extracting the corresponding elements in ε, A, and B respectively. By comparing Equation (5) and Equation (6), for the least squares solution after redundancy removal, compared with the original least squares solution, the computational complexity changes from N×M complex multiplications to N×K complex multiplications. Since in general, the number of sampling points K in the non-satisfying region does not satisfy being much smaller than the total number of sampling points M, the computational complexity is greatly reduced.

[0045] 3) Based on the obtained excitation, find the new generation of reference pattern and residual pattern.

[0046] According to the least squares solution after redundancy removal of the obtained excitation, find the new generation of the current pattern, that is, f F = Aw LS . According to the preset beam synthesis index, re-evaluate the region Ω where the pattern does not meet the requirements C . Based on the framework of the alternating projection method, according to Equation (2) and Equation (3), further find the new generation of reference pattern f R and residual pattern ε.

[0047] 4) Repeat steps 2 and 3, continuously update the current excitation and pattern until the iteration termination condition is met.

[0048] The iteration process starts with an initial current excitation , and according to steps 2 and 3, continuously update and , where the superscript q represents the iteration order. Preset the maximum number of iterations Q. When the obtained current pattern meets all the preset beam synthesis indexes (i.e., K = 0) or the iteration order reaches the maximum value (i.e., q = Q), jump out of the iteration loop and output the current excitation and the corresponding pattern to complete the pattern synthesis of the large-scale irregular planar array.

[0049] Example:

[0050] To verify the proposed redundancy removal alternating projection synthesis method, consider synthesizing a large-scale irregular planar array with 1000 elements, and the array layout is as shown in Figure 2 . Assume that the array operates at 1 GHz, and all elements are ideal point sources, that is, for m = 1, …, M, there is E n (u m , v m ) = 1. The preset array beam synthesis indexes are: in the sidelobe region of , the sidelobe level is lower than -35 dB; in the null region of 0.4 ≤ u ≤ 0.7 and -0.1 ≤ v ≤ 0.1, the null level is lower than -50 dB. In the proposed redundancy removal alternating projection synthesis method, set the maximum number of iterations to 500 times, the overvoltage factor to -5 dB, and the total number of sampling points to M = 106491 (according to obtained by uniform sampling, where λ is the operating wavelength, L is the array aperture, and 114.6°λ / L is the estimated elevation beamwidth; this sampling interval means that each elevation main beam contains 15 sampling points). Using the proposed method, the iteration process reaches the termination condition at 330 times, and the current pattern obtained at this time satisfies all beam synthesis indexes, such as Figure 3 shown. If the original least squares solution rather than the de-redundant least squares solution is used in the iteration process, that is, using the traditional alternating projection method, the obtained pattern is Figure 3 exactly the same. However, in terms of the synthesis time, the de-redundant alternating projection method only needs 40.16 seconds, while the traditional alternating projection method needs 84.39 seconds, and the synthesis efficiency is doubled (all synthesis programs are run on the same ordinary desktop computer). This efficiency improvement can be explained by Figure 4 which shows the change curve of the number of sampling points not meeting the requirements during the iteration process. It can be seen that only after dozens of iterations, the number of points not meeting the requirements drops to a very low level, much smaller than the total number of sampling points. Therefore, using the proposed method will eliminate a large amount of redundant computational load.

Claims

1. A method for removing redundant alternating projections from large-scale irregular planar arrays, characterized in that: The steps include: Step 1: Given the beam synthesis index, define the reference pattern and residual pattern; In step 1, based on the framework of the alternating projection method, the reference direction map is: The residual direction map is: Among them, (u m ,v m ) is the observation direction; θ m and are the elevation angle and azimuth angle in the observation direction, respectively, and m = 1,…,M; M is the total number of sampling points; ξ is the overvoltage factor used to improve the convergence speed, Γ(u m ,v m ) is the threshold function of the sidelobe or null area changing with the observation direction, 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; Step 2: Based on the obtained residual pattern, find the least square solution of excitation redundancy removal; the expression of the least square solution of excitation redundancy removal is: 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 is the vector formed by the residual pattern defined in the region where the requirement is not met; Step 3, based on the de-redundant least squares solution of the obtained excitation, a new generation of reference directional patterns and residual directional patterns are obtained; Step 4: Repeat steps 2 and 3 until the condition for exiting the iteration is met.

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