Fast synthesis and beam forming method for arbitrary polarization reconfigurable array

Abstract

The invention discloses a fast synthesis and beam forming method for an arbitrary polarization reconfigurable array. The fast synthesis and beam forming method can be widely applied to a low-cost large-scale phased array. According to the invention, the polarization states of the antenna units and the array beamforming algorithm are switched through the radio frequency switch, and beamforming of any polarization state can be realized under the condition that each antenna unit only uses one radio frequency channel. In the design process, firstly, polarization state arrangement is solved with the information entropy of the polarization reconfigurable array as an optimization target, an optimal array topological structure is obtained, and then the excitation amplitude and the excitation phase are solved with the expected polarization state and the expected scanning angle. The maximum innovation of the invention lies in that under the condition that each antenna unit only uses one radio frequency link, the wide-angle scanning capability of any polarization beam is realized through the irregular distribution of the polarization state.

Description

Technical Field

[0001] This invention relates to antenna and electromagnetic wave applications, and is a method for rapid synthesis and beamforming of polarization reconfigurable arrays. It can be widely used in phased array scenarios that require rapid polarization switching and wide-angle scanning capabilities, such as electronic reconnaissance, weather radar, satellite communication, and mobile communication. Background Technology

[0002] Traditional polarization reconfigurable arrays rely on dual-polarization units switching between different polarization states to improve system adaptability. However, traditional solutions suffer from high hardware costs, as each dual-polarization unit requires two independent transmit / receive (T / R) modules, with T / R module costs typically accounting for more than half of the total system cost. Other solutions, such as irregular arrays, reduce the number of T / R components by grouping subarrays, but experience significant gain degradation at large scan angles; sparse or sparsely distributed arrays reduce costs by removing units at intervals, but also exhibit significant gain degradation at wide-angle scans. Patent CN111106442A achieves right-hand circular polarization, horizontal linear polarization, and left-hand circular polarization based on a leaky antenna structure, but it is difficult to achieve arbitrary polarization. Patent CN112952405A designs a reconfigurable array that can be arbitrarily polarized based on a rotating subarray. However, since the number of elements for horizontal and vertical polarization is equal, when the required polarization is horizontal or vertical, the polarization elements orthogonal to the desired polarization need to be set to zero to reduce the cross-polarization ratio. However, this also leads to a 3dB antenna gain loss.

[0003] Reconfigurable array architectures based on RF switches or PIN diodes offer a novel solution to this problem, achieving dynamic polarization switching by loading active devices such as PIN diodes into each element. Patent CN117673768A constructs a small-scale reconfigurable array based on PIN diodes and a reconfigurable feed network, enabling arbitrary polarization reconfiguration. However, this array is difficult to scale up, failing to meet the application requirements of large-scale arbitrary polarization reconfigurable arrays. In fact, array beamforming based on PIN diodes and array-level beamforming can achieve arbitrary polarization reconfiguration, but while it allows dynamic polarization switching, it introduces circuit complexity and reliability issues. More importantly, each polarization switch requires resolving the polarization distribution state, and the complexity of this integer programming problem increases exponentially with aperture. When the aperture increases to hundreds of wavelengths and the number of array elements reaches tens of thousands, solving the array polarization distribution in real time for each new beam is equivalent to solving an exponentially growing integer programming problem. Existing approximation algorithms based on sparse arrays or representative beam libraries still struggle to provide feasible solutions within seconds.

[0004] Therefore, this patent proposes a fast synthesis and beamforming method for arbitrarily polarized reconfigurable arrays. It explicitly correlates polarization distribution with array scanning performance using a maximum entropy model, constructing row and column entropy metrics. Maximizing array information entropy minimizes sidelobe power without sacrificing main lobe gain. The problem is also transformed into mixed-integer linear programming. Experiments show that the optimal polarization state for a 16×16 polarized reconfigurable array can be solved within 9 seconds, and for a 100×100 ultra-large-scale array, it takes approximately 45 seconds, representing a speedup of one to two orders of magnitude compared to existing methods. Summary of the Invention

[0005] In view of the above technical background, the present invention provides a fast synthesis method for arbitrary polarization reconfigurable arrays. The purpose of the present invention is to quickly solve for the polarization state distribution of arbitrary polarization reconfigurable arrays compared with existing optimization techniques and architectures.

[0006] This invention has the following contents:

[0007] To maximize the scanning gain of a polarimetric reconfigurable array and minimize sidelobes and cross-polarization levels, the beamforming algorithm design requires simultaneously solving for the polarization state distribution and the excitation amplitude and phase of each element. The polarization state distribution is an integer variable, while the excitation amplitude and phase are complex variables. Solving for both simultaneously presents a non-convex programming problem, resulting in long solution times and significant memory consumption, limiting its applicability to small-scale arrays. For very large-scale arrays, memory consumption and solution time increase exponentially. Therefore, the optimization method proposed in this patent consists of two steps: the first step optimizes the array polarization state distribution variables using an integer programming model, with maximum entropy as the optimization objective; the second step, based on the obtained array arrangement, optimizes the excitation amplitude and phase using existing beamforming algorithms, ultimately achieving suppression of sidelobes and cross-polarization levels.

[0008] For phased array architectures based on reconfigurable elements (such as...) Figure 1 As shown, each RF link connects the horizontal and vertical polarization ports of the antenna element through an RF switch. The arrangement of each element in the array remains uniform. The arbitrary polarization beam of the array is achieved by switching the RF switch and optimizing the excitation amplitude and phase of each port.

[0009] Consider an M×N planar regular array, where the array elements are spaced along the x-axis and y-axis as follows: and Each element in the array has two polarization states, and the radiation pattern corresponding to the d-th polarization state is as follows: , No. The excitation amplitude and excitation phase of each unit are respectively and Therefore, the far-field pattern of this array for

[0010] (1)

[0011] in Represents the free space wavenumber. Where λ is the wavelength corresponding to the operating frequency, and D represents the total number of polarization states. Indicates the first The polarization state selection of each unit, if Indicates the first Each element chooses the d-th polarization state if Indicates the first The unit did not choose the d-th polarization state. and Let represent the elevation angle and azimuth angle in standard spherical coordinates, respectively. Each antenna element can only choose one polarization state at any given time; therefore, the following constraint exists:

[0012] (2)

[0013] Simultaneously, regarding the polarization state Optimizing the excitation amplitude and phase is quite difficult, so we first optimize the polarization state distribution, and then optimize the excitation amplitude and phase after the polarization state distribution is determined.

[0014] Any polarization and the corresponding cross-polarization Both can be decomposed into horizontal polarization components and vertical polarization components:

[0015] (3)

[0016] in and These represent the horizontal and vertical polarization components of any given polarization, respectively. This indicates the direction of linear polarization, with values ​​ranging from 0° to 360°. The relative phase difference between horizontal and vertical polarizations ranges from 0° to 360°. Therefore, by defining (γ, η), any polarization state obtained by combining horizontal and vertical polarizations can be represented, for example... Indicates horizontal polarization. Indicates vertical polarization. and These represent left-handed and right-handed circular polarization, respectively.

[0017] To ensure the highest radiated power in the main polarization direction of the far-field pattern, while minimizing the cross-polarization level, it is necessary to limit the number of each polarization state in the array:

[0018] (4)

[0019] in This represents the number of the d-th polarization state in the array. Given a polarization state (γ, η), the ratio of the number of the d-th polarization state to the total number of elements in the array can be calculated using the above formula. When D=2, that is, d=1 corresponds to horizontal polarization, and d=2 corresponds to vertical polarization. For example, if the desired polarization state is left-handed or right-handed circular polarization, the above formula can be used to obtain... However, the above formula only calculates the number of units for each polarization state. The next step is to optimize the arrangement of each state.

[0020] To minimize sidelobes and cross-polarization in polarimetric reconfigurable arrays, besides optimizing excitation amplitude and phase, polarization state arrangement is also a crucial optimization variable. Regularly arranged cells are more prone to periodic superposition in undesirable far-field directions, which is the core reason for the higher sidelobes and cross-polarization in regular arrays. Therefore, for polarimetric reconfigurable arrays, ensuring that each polarization state is randomly distributed within the array is crucial for suppressing sidelobes and cross-polarization in the overall radiation pattern. For a regularly arranged array with equal spacing, the information entropy model of a polarimetric reconfigurable array is defined as follows:

[0021] (5)

[0022] in and For integer variables, when When, it means that there are k polarization states of type d in the m-th row. Let $k$ represent the number of $d$ polarization states in the $n$-th column. Information entropy is defined by finding the number of polarization states in each row and column of the regular array. The more disordered the distribution of the $d$-th polarization state in the entire array, the more evenly it appears in each row and column, and the greater the corresponding information entropy. The overall information entropy reaches its maximum when the distribution of each polarization state in the array is highly disordered. Therefore, the optimization model for a polarimetric reconfigurable array based on maximizing information entropy is:

[0023] (6a)

[0024] (6b)

[0025] (6c)

[0026] (6d)

[0027] (6e)

[0028] (6f)

[0029] This model is an integer linear optimization model, which can actually be solved quickly for large-scale arrays using commercial solvers. After solving the model, the polarization state distribution is obtained. The next step is to use convex optimization algorithms to optimize the excitation amplitude and phase distribution in the array to achieve a low sidelobe pattern, i.e., to find a solution that satisfies the following problem.

[0030] (7a)

[0031] (7b)

[0032] in Indicates the desired direction Principal polarization far-field value, This represents the sidelobe region of the main polarization far-field pattern. For the preset sidelobe level, This represents the far-field radiation pattern of cross-polarization. The preset cross-polarization level, This indicates finding the 2-norm of a matrix. This indicates finding the real part of a complex number. This indicates finding the imaginary part of a complex number.

[0033] The innovation of this invention lies in the development of an arrangement algorithm for arbitrarily polarized reconfigurable arrays, characterized by wide-angle scanning, low sidelobes, and low cross-polarization. Compared with existing technologies, this invention has the following advantages:

[0034] 1. Adopting a polarization-reconfigurable unit form, each unit uses only one TR component, which reduces the number of TR components by half compared to the traditional dual-polarization array. Through array beamforming method, arbitrary polarization reconfigurability is achieved, while still ensuring that the antenna array has the characteristics of low sidelobes and wide-angle scanning, which greatly saves costs and reduces power supply complexity.

[0035] 2. An optimization method based on information entropy was adopted to achieve a fast solution for the polarization state distribution. Experiments show that the optimal polarization state solution for a 16×16 polarization reconfigurable array can be completed within 9 seconds, and the solution for a 100×100 ultra-large-scale array takes about 45 seconds, which is an order of magnitude faster than existing methods. Attached Figure Description

[0036] Figure 1 This is a diagram of the array structure for a polarization reconfigurable array.

[0037] Figure 2 The worst-case topology of the polarization reconfigurable array in Example 1 is (M×N=16×16).

[0038] Figure 3 For example, the worst-case polarization reconfigurable array in Example 1 is scanned to... The main polarization pattern and the cross polarization pattern when the polarization is left-handed circular polarization.

[0039] Figure 4 The example is a suboptimal topology of a polarization reconfigurable array (M×N=16×16).

[0040] Figure 5 For example, in the suboptimal array of the polarization reconfigurable array in Example 1, when scanning to... The main polarization pattern and the cross polarization pattern when the polarization is left-handed circular polarization.

[0041] Figure 6 The optimal topology of the polarization reconfigurable array in Example 1 is (M×N=16×16).

[0042] Figure 7 For example, the optimal array of the polarization reconfigurable array in Example 1 is scanned to... The main polarization pattern and the cross polarization pattern when the polarization is left-handed circular polarization. Detailed Implementation

[0043] Consider a polarimetric reconfigurable array with a size of M×N=16×16 and an array spacing of... , Each antenna element can freely switch between horizontal and vertical polarization beams via an RF switch, and each antenna element has only one RF channel. The first step involves solving the model (6) using a commercial solver based on the desired polarization state to obtain the topology of the polarization-reconfigurable array. The second step involves solving the model (7) using a commercial solver based on the fixed polarization state and preset scanning angle, sidelobes, and cross-polarization levels to obtain the excitation amplitude and excitation phase of the polarization-reconfigurable array.

[0044] To compare the superiority of the proposed algorithm, for left-hand circular polarization, the worst, second-best, and best topologies of the polarization-reconfigurable array were obtained, such as... Figure 2 , 4 As shown in Figure 6, the three arrays scanned... When the polarization is left-handed circular polarization, the corresponding principal polarization and cross polarization patterns are as follows: Figure 3 , 5As shown in Figure 7, observation reveals that the horizontal and vertical polarization units in the worst-case polarization reconfigurable array are uniformly arranged, with a maximum sidelobe of -12dB and a maximum cross-polarization level of -10dB. The suboptimal array has a maximum sidelobe of -20dB and a maximum cross-polarization level of -19dB. The optimal array has a maximum sidelobe of -22dB and a maximum cross-polarization level of -25dB. Therefore, the optimal array is significantly better than the other two arrays in terms of sidelobe and cross-polarization suppression. This example only shows the radiation pattern of left-hand circular polarization. In fact, through polarization switching and array beamforming, the above method can achieve arbitrary polarization states while possessing wide-angle scanning capability with low sidelobe and low cross-polarization. The above experiments are based only on a 16×16 polarimetric reconfigurable array, with an optimal polarization state solution time of approximately 8.5 seconds. The solution time for a large-scale array with a size of 32×32 is approximately 15 seconds, and the solution time for a very large-scale array with a size of 100×100 is approximately 45 seconds.

[0045] The above description is provided to those skilled in the art regarding the invention and its embodiments. This description should be considered illustrative rather than limiting. Those skilled in the art can implement the invention based on the ideas in the claims and specific problems, and can naturally make a series of modifications to the embodiments described above. All of these should be considered within the scope of this invention.

Claims

1. A fast synthesis and beamforming method for arbitrary polarization reconfigurable arrays, characterized in that, By switching the polarization state of the antenna elements with RF switches and using the array beamforming algorithm, beamforming of arbitrary polarization states can be achieved with only one RF channel per antenna element. In the design process, the polarization state arrangement is first solved with the information entropy of the polarization reconfigurable array as the optimization objective to obtain the optimal array topology. Then, the excitation amplitude and excitation phase are solved with the desired polarization state and scanning angle.

2. The method for optimizing polarization state distribution in a polarization-reconfigurable array according to claim 1, characterized in that, The optimization method is as follows: ； ； in and These represent the number of rows and columns of the rectangular planar array, respectively. and They represent the first row and number In the column, D represents the total number of polarization states, and d represents the d-th polarization state. A binary variable representing the first integer. The polarization state selection of each unit, if Indicates the first Each element chooses the d-th polarization state if Indicates the first The unit did not choose the d-th polarization state. This represents the number of cells required for the d-th polarization state in the array. and For integer binary variables, when When, it means that there are k polarization states of type d in the m-th row. When, it means that there are k possible polarization states of the dth type in the nth column, where K is the maximum possible number of polarization states in each row or column. It refers to the complete set.

3. The beamforming optimization method in a polarization-reconfigurable array according to claim 1, characterized in that, The specific optimization algorithm for the convex optimization synthesis pattern is as follows: ； ； in and The first The excitation amplitude and excitation phase of each unit Indicates the desired direction Principal polarization far-field value, This represents the sidelobe region of the main polarization far-field pattern. For the preset sidelobe level, This represents the far-field radiation pattern of cross-polarization. The preset cross-polarization level, This indicates finding the 2-norm of a matrix. This indicates finding the real part of a complex number. This indicates finding the imaginary part of a complex number. and These represent the pitch and azimuth angles in the standard spherical coordinate system, respectively.

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