Directional diagram synthesis method of multimode orbital angular momentum array antenna

Abstract

The invention provides a directional diagram synthesis method for a multimode orbital angular momentum array antenna, and relates to the technical field of multimode orbital angular momentum array antennae, and the method comprises the steps: constructing a concentric ring array, and determining a first array factor of the concentric ring array based on a radiation directional diagram function of multilayer nested concentric rings; applying a Bessel function theory to derive a second matrix factor in an integral form; obtaining a third array factor by using the central axis rotation symmetry of the concentric circular ring array and the angular symmetry of the array factors; equivalently converting the third array factor into a linear array model with a Bessel function factor, and exporting a corresponding equivalent linear array factor expression; by setting constraint conditions and using Matlab and a convex optimization solution program cvx for solution, the optimized excitation weight is applied to the first array factor to obtain a final required power directional diagram. The method has good adaptability to a large-scale array, simplifies a two-dimensional array to be synthesized into a one-dimensional problem, and has the advantages of being low in calculation complexity and high in speed.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-mode orbital angular momentum array antennas, and in particular to a directional pattern synthesis method of a multi-mode orbital angular momentum array antenna. Background Art

[0002] Orbital angular momentum (OAM) is an inherent property of electromagnetic waves. Modulating information in this dimension can further improve spectrum utilization and communication capacity. Therefore, it has become a research hotspot in the fields of radar detection and communication. Uniform circular array (UCA) is a common solution for generating OAM beams in radio frequency. It only needs to add corresponding phase shifts to each antenna element to achieve OAM beams of different modes. However, the OAM beams generated by UCA generally have higher sidelobe levels and a divergence angle that expands as the number of OAM modes increases, which greatly limits its practical application.

[0003] In recent years, Chinese and foreign scholars have done a lot of research on array synthesis for generating OAM beams. Some scholars use the weighted effect of multi-layer ring arrays to adjust different modal OAM beams to the same divergence angle, and based on this, proposed a two-dimensional imaging method of vortex electromagnetic waves based on uniform concentric circular array (UCCA) antennas, which effectively improved the imaging effect. Kou Na and other scholars proposed an improved Bayliss synthesis method to extend the difference beam synthesis of linear arrays to UCCA, but with the increase in the number of OAM modes, the beam divergence angle and beam width gradually increase. To solve this problem, some scholars have used Fourier-Bessel expansion functions to realize OAM beam synthesis, controlling the main beam divergence angle while suppressing the sidelobe level. Using the above method, the array structure also needs to be adjusted accordingly, which increases the difficulty of design and processing. Uniformly spaced arrays have better versatility, and various optimization methods, such as fruit fly optimization algorithms and genetic algorithms, are used to optimize the aperture field distribution of uniform arrays to achieve sidelobe suppression or beam direction adjustment, but they often consume a lot of computing time and resources. The introduction of the multipole moment expansion method can increase the optimization speed and realize multi-mode OAM beam multiplexing, but the sidelobe suppression effect is limited. Summary of the invention

[0004] The purpose of the present invention is to provide a method for synthesizing the directional patterns of a multi-mode orbital angular momentum array antenna to improve the above-mentioned problem. In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is as follows:

[0005] The present application provides a method for synthesizing a directional pattern of a multi-mode orbital angular momentum array antenna, comprising:

[0006] Construct a concentric ring array, ignore the mutual coupling effect between units, and determine the first array factor of the concentric ring array based on the radiation pattern function of multi-layer nested concentric rings;

[0007] According to the first array factor, the array factor when the number of array elements in the circular array reaches a certain threshold is converted into an integral form, and the second array factor of its integral form is derived by applying the Bessel function theory;

[0008] By using the rotational symmetry of the central axis of the concentric ring array and the angular symmetry of the array factor, an observation plane with an azimuth angle of 0 is selected as the first condition, and the first condition is input into the second array factor to obtain a simplified third array factor;

[0009] By comparing and analyzing the similarity between the third array factor and the preset linear array factor, the third array factor is equivalently converted into a linear array model with Bessel function factors, and the corresponding equivalent linear array factor expression is derived;

[0010] Construct a convex optimization problem based on Bessel functions, apply equivalent linear array factor expressions and excitation weights to form power patterns, set constraints and use Matlab and the convex optimization solver cv x Solve, and then determine the optimized excitation weights, and apply the optimized excitation weights to the first array factor to obtain the final required power pattern.

[0011] Preferably, the calculation formula of the radiation pattern function of the multi-layer nested concentric rings in the first array factor of the concentric ring array determined based on the radiation pattern function of the multi-layer nested concentric rings is as follows:

[0012]

[0013] In the formula, is the directional pattern function, M is the number of circular sub-arrays, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, lφ mn The excitation phase introduced to generate the l-mode OAM beam, n is the number of array elements, m is the number of layers on the ring, a m is the radius of the mth ring, the pitch angle θ∈[0,π / 2], the azimuth angle Wave number k = 2π / λ, λ 为波 Length, φ mn =2π(n-1) / N m is the azimuth angle of the nth array element in the mth ring layer, j is an imaginary unit, and exp(*) is an exponential function.

[0014] Preferably, the radiation pattern function based on the multi-layer nested concentric rings determines the first array factor of the concentric ring array, wherein the calculation process of the first array factor is as follows:

[0015] A phase difference is introduced by exciting each array element, and each ring is fed with equal amplitude to ensure that the orbital angular momentum beam or array factor maintains azimuth symmetry, thereby generating an orbital angular momentum beam with an l-order mode.

[0016] Preferably, the array factor when the number of array elements in the circular array reaches a certain threshold is converted into an integral form, and the Bessel function theory is applied to derive the second array factor of the integral form, which includes:

[0017] When the number of array elements on the ring reaches a certain threshold, that is, the array element spacing is less than or equal to half the wavelength, the azimuth angle of the nth array element in the mth layer is regarded as a continuous variable, and then the calculation formula of the first array factor of the l-order mode is converted into an integral form, and the second array factor approximated by the Bessel function is derived.

[0018] Preferably, the calculation formula for obtaining the simplified third matrix factor is as follows:

[0019]

[0020] In the formula, F l (θ,0) is the third matrix factor, M is the number of circular sub-matrices, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, a m is the radius of the mth ring, the pitch angle θ∈[0,π / 2], the wave number k = 2 π / λ , λ is the wavelength, j is the imaginary unit, l is the mode number, J l (*) is the l-th order Bessel function.

[0021] Preferably, the corresponding equivalent linear array factor expression is derived, wherein the calculation process of the equivalent linear array factor expression comprises:

[0022] The third array factor of the concentric ring array is based on its equidistant array element arrangement, which is equivalent to a linear array model of M Bessel function factor array elements, and the circumference of the largest radius ring is used as the normalization benchmark.

[0023] Preferably, the construction is based on a convex optimization problem of a Bessel function, wherein the calculation formula of the convex optimization problem is:

[0024] min w -ε

[0025] st|wfl (θ) T |≥ε,θ∈Θ ML

[0026] |wf l (θ) T |≤ρε,θ∈Θ SL

[0027] |wf l (θ) T |==0,θ∈Θ NULL

[0028] |w|≤1.

[0029] Where min is the mathematical symbol for the minimum value, ε is the radiation intensity in the direction corresponding to the OAM divergence angle, and Θ is ML is the main beam pointing angle (also the divergence angle of the OAM beam), Θ SL is the sidelobe beam pointing angle, Θ NULL is the first zero point angle, ρ is the desired sidelobe level, w is the excitation weight and also the variable of the optimization problem, st is the abbreviation of the constraint condition, and f l (θ) is the beam pointing θ The matrix factor matrix of the direction, T is the matrix transpose symbol.

[0030] Preferably, the problem is solved by setting constraints and using Matlab and convex optimization solver cvX, wherein setting constraints includes:

[0031] The power pattern is obtained by taking the vector product of the excitation weight and the array factor of the beam pointing direction:

[0032] P l (θ)=wf l (θ) T

[0033]

[0034] Where P l (θ) is the power pattern, f l (θ) is the beam pointing θ The array factor matrix of the direction, J l (*) is the l-th order Bessel function, a1, a2, ..., a M is the radius of the ring, w is the weight of the array excitation, f l (θ) is the beam pointing θ The power directional map is used to establish the power constraint of the convex optimization problem.

[0035] The desired power constraint condition is set according to the power pattern so that the function of the power pattern is smaller or larger than the power value determined by the requirements of the direction corresponding to the OAM divergence angle and the sidelobe level.

[0036] Preferably, the optimized incentive weights are determined by setting constraint conditions and using Matlab and convex optimization solver cvx to solve the problem, which includes:

[0037] The convex optimization problem is implemented and described by programming language, and the program cvx is called to solve it, and then the optimal solution is obtained. Under the approximate condition that the number of circular array elements tends to be infinite, the optimal solution is inconsistent with the sidelobe level or zero point position in actual application.

[0038] The beneficial effects of the present invention are:

[0039] The present invention provides a method for synthesizing the directional patterns of a multi-mode orbital angular momentum array antenna. The method converts a two-dimensional OAM array with angular symmetry characteristics into a one-dimensional uniform linear array, utilizes the convexity of the equivalent array element directional pattern in the form of a Bessel function, adopts a convex optimization algorithm to obtain the global optimal solution of the array feeding weight under the constraint condition, realizes multi-mode beam zero point control and sidelobe level suppression, and theoretical analysis and simulation experiments also prove the effectiveness of the method. The present invention has good adaptability to large-scale arrays, simplifies the synthesis of two-dimensional arrays into a one-dimensional problem, and has the advantages of low computational complexity and high speed.

[0040] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or be understood by implementing the embodiments of the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0042] Figure 1 It is a schematic diagram of the flow of a method for synthesizing a directional pattern of a multi-mode orbital angular momentum array antenna according to an embodiment of the present invention;

[0043] Figure 2 It is a schematic diagram of an M-layer concentric annular array of a directional pattern synthesis method of a multi-mode orbital angular momentum array antenna described in an embodiment of the present invention;

[0044] Figure 3 It is a schematic diagram of an M-element uniform linear array array of a directional pattern synthesis method of a multi-mode orbital angular momentum array antenna described in an embodiment of the present invention;

[0045] Figure 4 It is a schematic diagram of array feed weights obtained from a simulation example of a method for synthesizing a pattern of a multi-mode orbital angular momentum array antenna described in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0047] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0048] This embodiment provides a method for synthesizing the directional patterns of a multi-mode orbital angular momentum array antenna.

[0049] See also Figure 1 , the figure shows that the method includes step S100, step S200, step S300, step S400 and step S500.

[0050] S100, constructing a concentric ring array, ignoring the mutual coupling effect between the units, and determining the first array factor of the concentric ring array based on the radiation pattern function of the multi-layer nested concentric rings.

[0051] It can be understood that step S100 includes steps S101 and S102, wherein:

[0052] S101. The calculation formula of the radiation pattern function of multi-layer nested concentric rings is as follows:

[0053]

[0054] In the formula, is the directional pattern function, M is the number of circular sub-arrays, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, a mn It represents the excitation phase of the nth array element in the mth layer of the ring, where n is the number of array elements, m is the number of layers on the ring, and a m is the radius of the mth ring, the pitch angle θ∈[0,π / 2], the azimuth angle Wave number k = 2π / λ, λ is the wavelength, φ mn =2π(n-1) / N m is the azimuth angle of the nth array element in the mth ring layer, j is an imaginary unit, and exp(*) is an exponential function.

[0055] It can be understood that in this step, it is necessary to consider building an M-layer concentric ring array with a radius of a. m (m=1,2,3L), the radius increases successively with the same increase, that is, the equal ring spacing distribution (the radius of the innermost ring is 0.25 times the wavelength, and the radius of the following rings increases by 0.5 times the wavelength successively), such as Figure 2 As shown, there are N m The isotropic array elements are placed at equal intervals. Assuming that the array element currents on each ring array are uniform and equal, the total current of the mth layer can be expressed as N m I m , where N m is the total number of array elements in the mth layer, I m is the current amplitude of any array element on the mth layer, and the mutual coupling between unit antennas needs to be ignored, then the radiation field pattern function of the multi-layer nested concentric circular ring array is obtained.

[0056] S102, determining the first array factor of the concentric ring array based on the radiation pattern function of the multi-layer nested concentric rings, wherein the calculation process of the first array factor is as follows:

[0057] The phase difference is introduced by the excitation of each array element, and each ring is fed with equal amplitude to ensure that the orbital angular momentum beam or array factor maintains azimuth symmetry, thereby generating an orbital angular momentum beam with an l-order mode. The calculation formula of the first array factor of the l-order mode is as follows:

[0058]

[0059] In the formula, is the first array factor, M is the number of circular sub-arrays, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, lφ mnThe excitation phase introduced to generate the l-mode OAM beam, n is the number of array elements, m is the number of layers on the ring, a m is the radius of the mth ring, the pitch angle θ∈[0,π / 2], the azimuth angle Wave number k = 2π / λ, λ is the wavelength, φ mn =2π(n-1) / N m is the azimuth angle of the nth array element in the mth ring layer, j is an imaginary unit, and exp(*) is an exponential function.

[0060] S200, according to the first array factor, converting the array factor when the number of array elements in the circular array reaches a certain threshold into an integral form, and applying Bessel function theory to derive a second array factor in its integral form.

[0061] It can be understood that the step S200 includes:

[0062] When the number of array elements on the ring reaches a certain threshold, that is, the array element spacing is less than or equal to half a wavelength, the azimuth angle of the nth array element in the mth layer is regarded as a continuous variable, and then the calculation formula of the first array factor of the l-order mode is converted into an integral form, and the second array factor approximated by the Bessel function is derived. The calculation formula is as follows:

[0063]

[0064] In the formula, is the second array factor, M is the number of circular sub-arrays, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, a m is the radius of the mth ring, the pitch angle θ∈[0,π / 2], the wave number k=2π / λ, λ is the wavelength, j is the imaginary unit, l is the mode number, J l (*) is the l-th order Bessel function.

[0065] It should be noted that when the number of array elements on the ring is large enough (based on the circumference of the ring, generally when the array element spacing on the ring is less than or equal to half the wavelength, it can be considered that the array elements are sufficient), the azimuth angle φ of the nth array element on the mth layer is mn It can be regarded as a continuously changing angle φ′, and the formula in step S100 is changed into an integral form to obtain the second array factor.

[0066] S300, utilizing the rotational symmetry of the central axis of the concentric circular ring array and the angular symmetry of the array factor, selecting an observation plane with an azimuth angle of 0 as the first condition, and inputting the first condition into the second array factor to obtain a simplified third array factor.

[0067] It can be understood that in step S300, the calculation formula of the third array factor is as follows:

[0068]

[0069] In the formula, F l (θ,0) is the third matrix factor, M is the number of circular sub-matrices, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, a m is the radius of the mth ring, the pitch angle θ∈[0,π / 2], the wave number k=2π / λ, λ is the wavelength, j is the imaginary unit, l is the mode number, J l (*) is the l-th order Bessel function.

[0070] Specifically, since the array structure and array factor of the concentric ring array have angular symmetry characteristics, we can take On this observation plane, the third matrix factor is obtained according to the formula in step S200.

[0071] S400, by comparing and analyzing the similarity between the third array factor and the preset linear array factor, the third array factor is equivalently converted into a linear array model with Bessel function factors, and the corresponding equivalent linear array factor expression is derived.

[0072] It can be understood that the calculation process of the equivalent linear array factor expression in step S400 includes:

[0073] The third array factor of the concentric ring array is based on its equidistant array element arrangement, which is equivalent to a linear array model of M Bessel function factor array elements, and the circumference of the maximum radius ring is used as the normalization basis. The calculation formula of the equivalent linear array factor expression is as follows:

[0074]

[0075] In the formula, F l (θ) is the equivalent linear array factor of the l-order mode, M is the number of circular subarrays, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, a m is the radius of the mth ring, a M is the radius of the outermost ring, the pitch angle θ∈[0,π / 2], the wave number k=2π / λ, λ is the wavelength, J l (*) is the l-th order Bessel function.

[0076] It should be noted that this step is because the distance between two adjacent array elements in each circle of the concentric ring array is equidistant. Therefore, it can be seen from the formula in step S300 that the third array factor of the multi-layer nested concentric ring array has a similar form to the array factor of the linear array, that is, it can be equivalently regarded as a linear array composed of M array elements with Bessel function directivity factors, the array elements are placed at equal intervals, and their positions are a. m (m=1,2,……M), such as Figure 3 As shown, the imaginary part symbol j l It has no effect on the power pattern of the antenna array and can be ignored. Considering that the number of antennas that can be placed in a single circular array is limited in practical applications, the circumference of the maximum radius circular array is used as a reference for normalization to obtain the equivalent linear array factor expression.

[0077] Moreover, since the interval between two adjacent antenna units is the same, the circumference of the mth layer of the ring is N m times the antenna unit spacing, assuming the unit spacing is d, then N m d is the perimeter of the mth layer, so the normalization is expressed as follows based on the perimeter of the maximum radius ring array:

[0078]

[0079] Right now

[0080]

[0081] Where N m ,N M represents the number of antenna units corresponding to the mth, Mth layer of the ring, m = 1, 2, ..., M, M is the number of rings, a m ,a M is the radius of the ring corresponding to the number of layers, and d is the antenna unit spacing.

[0082] Therefore, for the third array factor, the perimeter (because d is fixed, it can be N m Represents the perimeter) and normalizes it to get the equivalent linear array factor expression. This can reduce the two-dimensional plane array problem to one-dimensional linear array analysis, greatly reducing the complexity of array synthesis.

[0083] S500, construct a convex optimization problem based on Bessel function, apply equivalent linear array factor expression and excitation weights to form a power pattern, determine the optimized excitation weights by setting constraints and using Matlab and convex optimization solver cvx to solve, and apply the optimized excitation weights to the first array factor to obtain the final required power pattern.

[0084] It should be noted that since a universal uniform array is used, the array structure is fixed and the parameter a related to the array element position ism and φ mn Therefore, the optimization design variable of the array pattern is only the feeding amplitude parameter I of each ring antenna unit. m .

[0085] It can be understood that step S500 includes S501, S502 and S503, wherein:

[0086] S501, constructing a convex optimization problem based on Bessel function, wherein the mathematical expression of the convex optimization problem is:

[0087] min w -ε

[0088] st|wf l (θ) T |≥ε,θ∈Θ ML

[0089] |wf l (θ) T |≤ρε,θ∈Θ SL

[0090] |wf l (θ) T |==0,θ∈Θ NULL

[0091] |w|≤1.

[0092] Where min is the mathematical symbol for the minimum value, ε is the radiation intensity in the direction corresponding to the OAM divergence angle, and Θ is ML is the main beam pointing angle (also the divergence angle of the OAM beam), Θ SL is the sidelobe beam pointing angle, Θ NULL is the first zero point angle, ρ is the desired sidelobe level, w is the excitation weight and also the variable of the optimization problem, st is the English abbreviation of the constraint condition, and f l (θ) is the array factor matrix of the beam pointing in the direction of θ, and T is the matrix transpose symbol.

[0093] It can be understood that, since the integer-order Bessel function is convex, the array synthesis problem of the concentric circular ring array equivalent to the linear array can be transformed into a convex optimization problem. The present invention applies the convex optimization algorithm to the lobe width control and sidelobe suppression problems of the concentric circular ring array array factor to improve the OAM array radiation performance.

[0094] S502, setting constraints and solving using Matlab and convex optimization solver cvx, wherein setting constraints includes:

[0095] The power pattern is obtained by taking the vector product of the excitation weight and the array factor of the beam pointing direction:

[0096] P l (θ)=wf l (θ) T

[0097]

[0098] Where P l (θ) is the power pattern, f l (θ) is the array factor matrix of the beam pointing in the direction of θ, J l (*) is the l-th order Bessel function, a1, a2, ..., a M is the radius of the ring, w is the weight of the array excitation, f l (θ) is the array factor of the beam pointing in the θ direction, k is the wave number, T is the transposition symbol, indicating the matrix transposition, and the power direction diagram is used to establish the power constraint of the convex optimization problem in the above step S501.

[0099] The desired power constraint condition is set according to the power pattern so that the function of the power pattern is smaller or larger than the power value determined by the requirements of the direction corresponding to the OAM divergence angle and the sidelobe level.

[0100] S503, by setting constraints and using Matlab and convex optimization solver cvx (open source) to solve, and then determine the optimized incentive weights, including:

[0101] The convex optimization problem is realized and described by programming language, and solved by cvx program to obtain the optimal excitation weight w. Substituting it into the first array factor, the directional diagram of the corresponding mode after optimization can be obtained. It is worth noting that there are cases where the sidelobe level or zero point position does not match the actual application, but it can still provide effective optimization results for beamwidth control and sidelobe suppression of two-dimensional arrays, especially large-scale OAM-UCCA.

[0102] In this step, specifically, the optimization problem can be easily solved using the convex optimization solver cvx, and the established convex optimization problem can be solved by simply describing it in a programming language. It should be noted that since the optimized directional pattern uses an approximate solution under the condition that the number of circular array elements tends to infinity, the number of zero points is small when the circular aperture is small. The above algorithm can only achieve the optimal solution under the constraints and cannot always obtain the desired sidelobe level or zero point position. In addition, the array elements are discretely distributed in space, and spatial sampling may cause new zero points to be generated, affecting the directional pattern characteristics. Despite the above problems, this method can still provide effective optimization results for beamwidth control and sidelobe suppression of two-dimensional arrays, especially large-scale OAM-UCCA.

[0103] In some embodiments, a UCCA is taken as an example to verify the effectiveness and superiority of this beam width control and sidelobe suppression method; the antenna unit operating frequency is 10GHz, and it is arranged in a 16-layer circular array with equal spacing. Among them, the minimum radius of the circular array is 1 / 4 wavelength, and the radius of other UCAs increases by half wavelength. The spacing between UCA array elements is also about half wavelength. Correspondingly, the number of ring array elements N m They are 3, 9, 16, 22, 28, 35, 41, 47, 53, 60, 66, 72, 79, 85, 91, 97. The array is used to generate OAM beams of l=1, 2, 3 modes, where the requirement for the pattern is that the sidelobe level is the lowest under the condition that the main lobe zero power beam width is 15°.

[0104] Then the 16-layer UCA array is equivalent to a 16-element uniform linear array, the preset expectation is 15°, the SLL takes the larger value of -90dB to obtain the lowest possible sidelobe, and the calculation formula of the convex optimization problem is used to optimize the normalized current excitation weights of each layer of UCA corresponding to the l=1, 2, 3 mode OAM beams, as shown in Figure 4 shown.

[0105] Then, the weighted feeding amplitude is substituted into the first array factor to obtain the corresponding mode on the observation plane. The normalized directional pattern of the directional pattern is shown in the results. The results show that the maximum sidelobe levels of the OAM beams of l=1, 2, and 3 modes after optimization are -31dB, -32dB, and -35dB, respectively, and a good sidelobe suppression effect is obtained. The zero points corresponding to the main beam are ±15°, ±15°, and ±16°, respectively, and the zero points corresponding to the main beam are basically consistent with the expected zero point positions. It is worth noting that if the OAM mode is further increased, the array scale should also be expanded accordingly to ensure a main beam width of 15°. For high modes such as mode numbers l=5, 6, and 10, when the number of array rings is 32, the OAM beam SLLs corresponding to the modes of the optimized directional pattern are -38dB, -34dB, and -42dB, respectively, and the first zero points are all ±15°. The simulation results show that the method of the present invention has good adaptability to large-scale array synthesis.

[0106] Therefore, in order to further verify the correctness of the method of the present invention, the full-wave simulation algorithm based on the moment method is used to calculate the far-field and near-field distribution characteristics of the dipole UCCA under the same feeding setting. Compared with the comprehensive result of the full-wave simulation radiation pattern (SLL≈-30dB), the sidelobe level is slightly higher; the first zero point is ±18°, which is 3° offset from the expected zero point. Therefore, it can be concluded that this is caused by the mutual coupling between the array elements, but compared with the sidelobe level of -13dB and the first zero point of ±11° under uniform feeding, the performance is still greatly improved and can be accepted in engineering applications.

[0107] In summary, the present invention proposes a low sidelobe OAM-UCCA pattern synthesis method under the constraint of OAM beamwidth. Specifically, according to the azimuth symmetry characteristics of the OAM beam array, the UCCA arranged with equal spacing is simplified into a one-dimensional uniform linear array. In this process, a single UCA subarray is approximately equivalent to a ULA array element with a Bessel directivity function, and is modeled as a convex optimization problem of ULA synthesis. The OAM beamwidth and the sidelobe level are optimized at the same time. The method has good adaptability to large-scale arrays, simplifies the synthesis of two-dimensional arrays into a one-dimensional problem, and has the advantages of low computational complexity and high speed.

[0108] It should be noted that, regarding the system in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0109] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0110] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for synthesizing a directional pattern of a multi-mode orbital angular momentum array antenna, characterized in that: include: Construct a concentric ring array, ignore the mutual coupling effect between units, and determine the first array factor of the concentric ring array based on the radiation pattern function of multi-layer nested concentric rings; According to the first array factor, the array factor when the number of array elements in the circular array reaches a certain threshold is converted into an integral form, and the second array factor of its integral form is derived by applying the Bessel function theory; By using the rotational symmetry of the central axis of the concentric ring array and the angular symmetry of the array factor, an observation plane with an azimuth angle of 0 is selected as the first condition, and the first condition is input into the second array factor to obtain a simplified third array factor; By comparing and analyzing the similarity between the third array factor and the preset linear array factor, the third array factor is equivalently converted into a linear array model with Bessel function factors, and the corresponding equivalent linear array factor expression is derived; A convex optimization problem based on Bessel function is constructed, and the equivalent linear array factor expression and excitation weights are applied to form the power pattern. The optimized excitation weights are determined by setting constraints and using Matlab and the convex optimization solver cvx. The optimized excitation weights are applied to the first array factor to obtain the final required power pattern.

2. The method for synthesizing the directional pattern of a multi-mode orbital angular momentum array antenna according to claim 1, characterized in that: The calculation formula for determining the radiation pattern function of the multi-layer nested concentric rings in the first array factor of the concentric ring array based on the radiation pattern function of the multi-layer nested concentric rings is as follows: In the formula, is the directional pattern function, M is the number of circular sub-arrays, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, a mn It represents the excitation phase of the nth array element in the mth layer of the ring, where n is the number of array elements, m is the number of layers on the ring, and a m is the radius of the mth ring, the pitch angle θ∈[0,π / 2], the azimuth angle Wave number k = 2π / λ, λ is the wavelength, φ mn =2π(n-1) / N m is the azimuth of the nth array element in the mth ring layer, j is an imaginary unit, and exp(*) represents exponential operation.

3. The method for synthesizing the directional pattern of a multi-mode orbital angular momentum array antenna according to claim 1, characterized in that: The radiation pattern function based on the multi-layer nested concentric rings determines the first array factor of the concentric ring array, wherein the calculation process of the first array factor is as follows: The phase difference is introduced by the excitation of each array element, and each ring is fed with equal amplitude to ensure that the orbital angular momentum beam or array factor maintains azimuth symmetry, thereby generating an orbital angular momentum beam with an l-order mode. The calculation formula of the first array factor of the l-order mode is as follows: In the formula, is the first array factor of the l-order mode, M is the number of circular subarrays, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, lφ mn The excitation phase introduced to generate the l-mode OAM beam, n is the number of array elements, m is the number of layers on the ring, a m is the radius of the mth ring, the pitch angle θ∈[0,π / 2], the azimuth angle Wave number k = 2π / λ, λ is the wavelength, φ mn =2π(n-1) / N m is the azimuth of the nth array element in the mth ring layer, j is an imaginary unit, and exp(*) represents exponential operation.

4. The method for synthesizing the directional pattern of a multi-mode orbital angular momentum array antenna according to claim 3, characterized in that: The array factor when the number of array elements in the circular array reaches a certain threshold is converted into an integral form, and the Bessel function theory is applied to derive the second array factor of the integral form, which includes: When the number of array elements on the ring reaches a certain threshold, that is, the array element spacing is less than or equal to half a wavelength, the azimuth angle of the nth array element in the mth layer is regarded as a continuous variable, and then the calculation formula of the first array factor of the l-order mode is converted into an integral form, and the second array factor approximated by the Bessel function is derived. The calculation formula is as follows: In the formula, is the second array factor, M is the number of circular sub-arrays, n is the number of array elements, m is the number of layers on the ring, and N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, a m is the radius of the mth ring, the pitch angle θ∈[0,π / 2], the wave number k=2π / λ, λ is the wavelength, j is the imaginary unit, l is the mode number, J l (*) is the l-th order Bessel function.

5. The method for synthesizing the directional pattern of a multi-mode orbital angular momentum array antenna according to claim 1, characterized in that: The calculation formula for obtaining the simplified third array factor is as follows: In the formula, F l (θ,0) is the third array factor, M is the number of circular sub-arrays, n is the number of array elements, m is the number of layers on the ring, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, a m is the radius of the mth ring, the pitch angle θ∈[0,π / 2], the wave number k=2π / λ, λ is the wavelength, j is the imaginary unit, l is the mode number, J l (*) is the l-th order Bessel function.

6. The method for synthesizing the directional pattern of a multi-mode orbital angular momentum array antenna according to claim 1, characterized in that: The corresponding equivalent linear array factor expression is derived, wherein the calculation process of the equivalent linear array factor expression includes: The third array factor of the concentric ring array is based on its equidistant array element arrangement, which is equivalent to a linear array model of M Bessel function factor array elements, and the circumference of the maximum radius ring is used as the normalization basis. The calculation formula of the equivalent linear array factor expression is as follows: In the formula, F l (θ) is the equivalent linear array factor of the l-order mode, M is the number of circular subarrays, N m is the number of isotropic antenna units in the mth circular subarray, I m is the current amplitude of any array element on the mth layer of the ring, a m is the radius of the mth ring, a M is the radius of the outermost ring, the pitch angle θ∈[0,π / 2], the wave number k=2π / λ, λ is the wavelength, J l (*) is the l-th order Bessel function.

7. The method for synthesizing the directional pattern of a multi-mode orbital angular momentum array antenna according to claim 1, characterized in that: The construction is based on a convex optimization problem of Bessel function, where the calculation formula of the convex optimization problem is: Where min is the mathematical symbol for the minimum value, ε is the radiation intensity in the direction corresponding to the OAM divergence angle, and Θ is ML is the main beam pointing angle (also the divergence angle of the OAM beam), Θ SL is the sidelobe beam pointing angle, Θ NULL is the first zero point angle, ρ is the desired sidelobe level, w is the excitation weight and also the variable of the optimization problem, st is the English abbreviation of the constraint condition, and f l (θ) is the array factor matrix of the beam pointing in the direction of θ, and T is the matrix transpose symbol.

8. The method for synthesizing the directional pattern of a multi-mode orbital angular momentum array antenna according to claim 1, characterized in that: The method is solved by setting constraints and using Matlab and convex optimization solver cvx, wherein setting constraints includes: The power pattern is obtained by taking the vector product of the excitation weight and the array factor of the beam pointing direction: P(θ)=wf,(0)' Where P l (θ) is the power pattern, f l (θ) is the array factor matrix of the beam pointing in the direction of θ, J l (*) is the l-th order Bessel function, a1, a2, ..., a M is the radius of the ring, w is the weight of the array excitation, f l (θ) is the array factor of the beam pointing in the direction of θ, k is the wave number, T is the transpose symbol, indicating the matrix transpose, where the power pattern is used to establish the power constraint of the convex optimization problem; The desired power constraint condition is set according to the power pattern so that the function of the power pattern is smaller or larger than the power value determined by the requirements of the direction corresponding to the OAM divergence angle and the sidelobe level.

9. The method for synthesizing the directional pattern of a multi-mode orbital angular momentum array antenna according to claim 1, characterized in that: The optimized incentive weights are determined by setting constraints and using Matlab and the convex optimization solver cvx to solve the problem, including: The convex optimization problem is realized and described by programming language, and the solution program cvx is used to solve it, and then the optimal solution is obtained. Among them, the optimal solution is inconsistent with the sidelobe level or zero point position in actual application under the approximate condition that the number of circular array elements tends to infinity.

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