A method for synthesizing the directional pattern of a multi-mode orbital angular momentum array antenna

Abstract

The application provides a directional diagram synthesis method of a multi-mode orbital angular momentum array antenna, relates to the technical field of multi-mode orbital angular momentum array antennas, and comprises the following steps: constructing a concentric circular ring array, determining a first array factor of the concentric circular ring array based on a radiation directional diagram function of a multi-layer nested concentric circular ring; applying a Bessel function theory to derive a second array factor in an integral form; obtaining a third array factor by utilizing the central axis rotational symmetry of the concentric circular ring array and the angular symmetry of the array factor; equivalently converting the third array factor into a straight line array model with a Bessel function factor, and deriving a corresponding equivalent straight line array factor expression; and applying the optimized excitation weight to the first array factor to obtain a final required power directional diagram by setting a constraint condition, using Matlab, and solving by using a convex optimization solving program cvx. The application has good adaptability to large-scale arrays, simplifies two-dimensional array synthesis into a one-dimensional problem, and has the advantages of low calculation complexity and high speed.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-mode orbital angular momentum array antenna, in particular to a pattern synthesis method of multi-mode orbital angular momentum array antenna. BACKGROUND

[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, so it has become a research hotspot in the field of radar detection and communication. Uniform circular array (UCA) is a common scheme for generating OAM beams in radio frequency. By adding a corresponding phase shift to each antenna element, different modes of OAM beams can be realized. However, the OAM beams generated by UCA generally have high sidelobe levels and divergent angles that expand with the increase of OAM mode number, which greatly limits its practical application.

[0003] In recent years, scholars at home and abroad have made a lot of research on array synthesis of generating OAM beams. Some scholars use the weighting effect of multi-layer ring array to adjust different modes of OAM beams to the same divergent angle, and accordingly propose a vortex electromagnetic wave two-dimensional imaging method based on uniform concentric circular array (UCCA) antenna, which effectively improves the imaging effect. Scholars such as Kou Na propose an improved Bayliss synthesis method, which extends the difference beam synthesis of linear array to UCCA. However, with the increase of OAM mode number, the beam divergence angle and beam width gradually increase. To solve this problem, some scholars use Fourier-Bessel expansion function to realize OAM beam synthesis, which can suppress sidelobe level and control main beam divergence angle. 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 firefly optimization algorithm and genetic algorithm 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 multipole moment expansion method can improve the optimization speed and realize multi-mode OAM beam multiplexing, but the sidelobe suppression effect is limited. SUMMARY

[0004] The present application relates to the technical field of multi-mode orbital angular momentum array antenna, in particular to a pattern synthesis method of multi-mode orbital angular momentum array antenna.

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

[0006] Concentric ring arrays are constructed, ignoring the mutual coupling effect between elements, and the first array factor of the concentric ring array is determined based on the radiation pattern function of multi-layer nested concentric rings.

[0007] Based on 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 Bessel function theory is applied to derive the second array factor in its integral form.

[0008] By utilizing the rotational symmetry of the central axis of the concentric ring array and the angular symmetry of the array factors, the 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 the simplified third array factor.

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

[0010] A convex optimization problem based on Bessel functions is constructed. An equivalent linear matrix factor expression and excitation weights are applied to form a power pattern. Constraints are set, and Matlab and the convex optimization solution program cv are used. x Solve the equation to determine the optimized excitation weights, and then apply the optimized excitation weights to the first matrix factor to obtain the final required power pattern.

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

[0012]

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

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

[0015] Each array element excitation introduces a phase difference, and equal amplitude feeding is adopted for each circular ring to ensure that the orbital angular momentum beam or array factor remains azimuthally symmetric, thereby generating an orbital angular momentum beam with l order mode.

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

[0017] When the number of array elements on the circular 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 mth layer nth array element is regarded as a continuous variable, and then the first array factor calculation formula 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 of the simplified third array factor is as follows:

[0019]

[0020] In the formula, F l (θ,0) is the third array factor, M is the number of circular ring subarrays, N m is the number of isotropic antenna elements of the mth circular ring subarray, I m is the current amplitude of any array element on the mth circular ring, a m is the radius of the mth circular ring, the elevation 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, and J l (*) is the l 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 includes:

[0022] The third array factor of the concentric circular ring array is based on the equidistant array element arrangement, which is equivalent to the linear array model of M Bessel function factor array elements, and the circumference of the maximum radius circular ring is taken as the normalization reference.

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

[0024] min w -ε

[0025] s.t.|w f​l (θ) T |≥ε, θ∈Θ ML

[0026] |w f l (θ) T |≤ρε, θ∈Θ SL

[0027] |w f l (θ) T |==0, θ∈Θ NULL

[0028] |w|≤1.

[0029] In the formula, min is the mathematical symbol of taking the minimum value, ε is the radiation intensity of the direction corresponding to the OAM divergence angle, Θ ML is the main beam pointing angle (also the divergence angle of the OAM beam), Θ SL is the side lobe beam pointing angle, Θ NULL is the first zero angle, ρ is the expected side lobe level, w is the excitation weight and also the variable of the optimization problem, s.t. is the English abbreviation of the constraint condition, f l (θ) is the array factor matrix of the beam pointing θ direction, and T is the matrix transpose symbol.

[0030] Preferably, the constraint condition is set and solved by using Matlab and the convex optimization solving program cvX, wherein setting the constraint condition comprises:

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

[0032] P l (θ)=w f l (θ) T

[0033]

[0034] In the formula, P l (θ) is the power pattern, f l (θ) is the array factor matrix of the beam pointing θ direction, J l (*) is the l-order Bessel function, a1, a2,..., a M is the circular ring radius, w is the weight of array excitation, f l (θ) is the array factor of the beam pointing θ direction, k is the wave number, and T is the transpose symbol, indicating matrix transposition. The power pattern is used to establish the power constraint of the convex optimization problem.

[0035] According to the power pattern setting, the expected power constraint condition is set, so that the function of the power pattern is less than or greater than the power value determined by the requirement of the OAM divergence angle corresponding direction and the sidelobe level.

[0036] Preferably, the excitation weight value after optimization is determined by setting the constraint condition and using Matlab and a convex optimization solver cvx.

[0037] The convex optimization problem is realized and described by a programming language, and the optimal solution is obtained by calling the program cvx, wherein the optimal solution exists under the approximate condition that the number of annular array elements tends to infinity, and the sidelobe level or zero position in the actual application does not match.

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

[0039] The present application provides a pattern synthesis method of a multi-mode orbital angular momentum array antenna, which is characterized in that a two-dimensional OAM array with angular symmetry characteristics is equivalent to a one-dimensional uniform linear array, the equivalent array pattern is in the form of a Bessel function with convexity, a convex optimization algorithm is used to obtain the global optimal solution of the array feed weight under the constraint condition, the multi-mode beam zero control and sidelobe level suppression are realized, the theoretical analysis and simulation experiment prove the effectiveness of the method, the present application has good adaptability to large-scale arrays, simplifies the two-dimensional array synthesis into a one-dimensional problem, and has the advantages of low calculation complexity and high speed.

[0040] Other features and advantages of the present application will be described in the following description, and some will become apparent from the description, or will be understood from the practice of the present application. The purpose and other advantages of the present application can be achieved and obtained by the structure specifically pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as limiting the scope. For those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0042] Figure 1 The flow chart of the pattern synthesis method of the multi-mode orbital angular momentum array antenna described in the embodiments of the present application is shown in the figure.

[0043] Figure 2 The M-layer concentric ring array of the pattern synthesis method of the multi-mode orbital angular momentum array antenna described in the embodiments of the present application is shown in the figure.

[0044] Figure 3 A schematic diagram of an M-element uniform linear array for the pattern synthesis method of the multi-mode orbital angular momentum array antenna described in the embodiments of the present application;

[0045] Figure 4 A schematic diagram of array feeding weight values obtained from a simulation example of the pattern synthesis method of the multi-mode orbital angular momentum array antenna described in the embodiments of the present application. DETAILED DESCRIPTION

[0046] In order to make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

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

[0048] The embodiments provide a pattern synthesis method of a multi-mode orbital angular momentum array antenna.

[0049] Referring to Figure 1 , the method includes steps S100, S200, S300, S400 and S500.

[0050] S100, a concentric circular array is constructed, the mutual coupling effect between units is ignored, and a first array factor of the concentric circular array is determined based on a radiation pattern function of the multi-layer nested concentric circular array.

[0051] It can be understood that the step S100 includes S101 and S102.

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

[0053]

[0054] wherein, is the radiation pattern function, M is the number of circular ring subarrays, N m is the number of isotropic antenna elements of the mth circular ring subarray, I m is the current amplitude of any element on the mth circular ring, a mn represents the excitation phase of the nth element on the mth circular ring, n is the number of elements, m is the number of layers on the circular ring, a m is the radius of the mth circular ring, the pitch angle θ ∈ [0, π / 2], the azimuth angle is the wave number k = 2π / λ, λ is the wavelength, φ mn = 2π(n-1) / N m is the azimuth angle of the nth element in the mth circular ring, j is the imaginary unit, and exp(*) is the exponential function.

[0055] It can be understood that in this step, an M-layer concentric circular array is needed to be considered, the radius of which is a m (m = 1, 2, 3L), the radius increases in turn, the increase amplitude is the same, that is, the equal ring spacing distribution (the innermost ring radius is 0.25 times the wavelength, and the following increases by 0.5 times the wavelength), as shown in FIG. 1, there are N Figure 2 isotropic elements on the ring. m It is assumed that the element current on each ring array is uniform and equal, the total current of the mth layer can be represented as N m I m , wherein N m is the total number of elements in the mth layer, I m is the current amplitude of any element on the mth layer, and the mutual coupling between the element antennas is ignored, and the radiation field pattern function of the multi-layer nested concentric circular array is obtained.

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

[0057] The excitation of each element introduces a phase difference, and equal amplitude feeding is adopted on each circular ring to ensure that the orbital angular momentum beam or the array factor is azimuthally symmetric, thereby generating an orbital angular momentum beam with l-order mode, wherein the first array factor calculation formula of the l-order mode is as follows:

[0058]

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

[0060] S200, 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 is derived by applying the Bessel function theory.

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

[0062] When the number of array elements on the circular 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 element in the mth layer is regarded as a continuous variable, and then the first array factor calculation formula of the l-order mode is converted into an integral form, and the second array factor approximated by the Bessel function is derived, and the calculation formula is as follows:

[0063]

[0064] In the formula, is the second array factor, M is the number of circular ring subarrays, N m is the number of isotropic antenna elements of the mth circular ring subarray, I m is the current amplitude of any array element on the mth layer of the circular ring, a m is the radius of the mth layer of the circular 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-order Bessel function.

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

[0066] S300, using the central axis rotational symmetry 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 the calculation formula of the third array factor in the present step S300 is as follows:

[0068]

[0069] In the formula, F l (θ,0) is the third array factor, M is the number of circular ring subarrays, N m is the number of isotropic antenna elements of the mth circular ring subarray, I m is the current amplitude of any element on the mth circular ring, a m is the radius of the mth circular ring, the pitch angle θ∈[0,π / 2], the wave number k=2π / λ, λ is the wavelength, and j is the imaginary unit. l (*) is the lth Bessel function.

[0070] Specifically, since the array structure of the concentric circular ring array and the array factor both have angular symmetry characteristics, without loss of generality, the observation plane is taken as the xoy plane. On the observation plane, the third array factor is obtained according to the formula in step S200.

[0071] S400, by comparing and analyzing the similarity of the third array factor and the preset linear array factor, the third array factor is equivalent to a linear array model with a Bessel function factor, and a 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 the present step S400 includes:

[0073] The third array factor of the concentric circular ring array is equivalent to a linear array model of M Bessel function factor elements based on the equidistant arrangement of the elements, and the circumference of the circular ring with the maximum radius is taken as the normalization reference, wherein the calculation formula of the equivalent linear array factor expression is as follows:

[0074]

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

[0076] It should be noted that this step is necessary because the distance between two adjacent elements in each ring of the concentric ring array is equal. Therefore, as can be seen from the formula in step S300, the third array factor of the multi-layer nested concentric ring array has a similar form to the array factor of a linear array. It can be equivalently regarded as a linear array composed of M elements with Bessel function directional factors, with the elements placed at equal intervals at position a. m (m = 1, 2, ..., M), such as Figure 3 As shown, the imaginary part symbol j l The effect on the power pattern of the antenna array is negligible. Considering that the number of antennas that can be placed in a single circular array is limited in practical applications, normalization is performed with the circumference of the largest radius circular array as a reference to obtain the equivalent linear array factor expression.

[0077] Furthermore, since the spacing between two adjacent antenna elements is the same, the circumference of the m-th ring is N. m If the antenna element spacing is d, then N m d is the perimeter of the m-th layer. Therefore, normalization using the perimeter of the largest radius annular array as a reference results in:

[0078]

[0079] Right now

[0080]

[0081] In the formula, N m N M This represents the number of antenna elements corresponding to the m-th and M-th rings, where m = 1, 2, ..., M, and M is the number of rings. m ,a M d is the radius of the annulus corresponding to the layer number, and d is the antenna element spacing.

[0082] Therefore, the factor of the third matrix is ​​determined by the perimeter (since d is fixed, N can be used). m Normalizing the perimeter (representing the linear matrix) yields the equivalent linear matrix factor expression. This reduces the two-dimensional planar matrix problem to a one-dimensional linear matrix analysis, significantly decreasing the complexity of array synthesis.

[0083] S500. Construct a convex optimization problem based on Bessel functions, apply the equivalent linear matrix factor expression and excitation weights to form a power pattern, set constraints and use Matlab and the convex optimization solver cvx to solve the problem, thereby determining the optimized excitation weights, and applying the optimized excitation weights to the first matrix factor to obtain the final required power pattern.

[0084] It should be noted that, because a general uniform array is used and the array structure is fixed, the parameter 'a' related to the position of the array elements is...m and φ mn is a limited value. Therefore, the array pattern optimization design variable is only the feed amplitude parameter I m .

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

[0086] S501, the convex optimization problem based on the Bessel function is constructed, and the mathematical expression of the convex optimization problem is:

[0087] min w -ε

[0088] s.t. |w f l (θ) T |≥ε, θ∈Θ ML

[0089] |w f l (θ) T |≤ρε, θ∈Θ SL

[0090] |w f l (θ) T |==0, θ∈Θ NULL

[0091] |w|≤1.

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

[0093] It can be understood that, since the integer order Bessel function has convexity, the array synthesis problem of the concentric circular ring array equivalent linear array can be converted into a convex optimization problem, and the convex optimization algorithm is applied to the problem of the side lobe suppression and the beam width control of the concentric circular ring array array factor, so as to improve the OAM array radiation performance.

[0094] S502, the constraint condition is set and solved by using Matlab and a convex optimization solving program cvx, and the constraint condition setting includes:

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

[0096] P l (θ)=w f 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 θ direction, J l (*) is the l-th order Bessel function, a1, a2,..., a M is the radius of the circular ring, w is the weight of the array excitation, f l (θ) is the array factor of the beam pointing θ direction, k is the wave number, T is the transpose symbol, indicating matrix transposition, and the power pattern 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 less than or greater than the power value determined by the requirement of the OAM divergence angle corresponding direction and the sidelobe level.

[0100] S503, the constraint condition is set and solved by using Matlab and the convex optimization solving program cvx (open source), and then the optimized excitation weight is determined, which includes:

[0101] The convex optimization problem is realized and described by a programming language, and is solved by the cvx program, so as to obtain the optimal excitation weight w, which is substituted into the first array factor to obtain the optimized direction pattern of the corresponding mode. It should be noted that there are cases where the sidelobe level or zero position does not match the actual application, but the method can still provide effective optimization results for the beam width control and sidelobe suppression of the large-scale OAM-UCCA of the two-dimensional array.

[0102] In this step, the optimization problem can be easily solved by using the convex optimization solving program cvx, as long as the established convex optimization problem is described by a programming language. It should be noted that since the optimized direction pattern adopts the approximate solution under the condition that the number of circular ring elements tends to infinity, the number of zeros is small when the circular ring aperture is small, and the above algorithm can only achieve the optimal solution under the constraint condition, and cannot always obtain the desired sidelobe level or zero position. In addition, the array elements are discretely distributed in space, and spatial sampling may cause new zeros to be generated, affecting the characteristics of the direction pattern. Despite the above problems, the method can still provide effective optimization results for the beam width control and sidelobe suppression of the large-scale OAM-UCCA of the two-dimensional array.

[0103] In some embodiments, the effectiveness and superiority of the beam width control and sidelobe suppression method are verified by taking one UCCA as an example; the working frequency of the antenna unit is 10 GHz, and the antenna units are arranged in an equidistant manner to form a 16-layer circular array. Among them, the minimum radius of the circular array is 1 / 4 wavelength, and the other UCA radii increase by half wavelength with equal amplitude. The spacing between the UCA elements is also about half a wavelength. Correspondingly, the number of elements N of each ring array is 3, 9, 16, 22, 28, 35, 41, 47, 53, 60, 66, 72, 79, 85, 91, and 97. The array is used to generate OAM beams of l=1, 2, 3 modes, and 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°. m

[0104] Then the 16-layer UCA array is equivalent to a 16-element uniform linear array, and the expected value is 15°. The SLL is taken as a larger value of -90 dB to obtain the lowest sidelobe as possible, and the normalized current excitation weight of each layer UCA corresponding to the l=1, 2, 3 mode OAM beam is obtained by using the calculation formula of the convex optimization problem, as shown in the following formula. Figure 4

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

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

[0107] In summary, the application proposes a low-sidelobe OAM-UCCA pattern synthesis method under OAM beam width constraint, which is specifically to simplify the equidistantly arranged UCCA into a one-dimensional uniform linear array according to the azimuthal symmetry characteristics of the OAM beam array, in the process, the single UCA subarray is approximately equivalent to a ULA element with Bessel directivity function, and is modeled as a convex optimization problem of ULA synthesis, while optimizing the OAM beam width and the sidelobe level, which has good adaptability to large-scale arrays, and simplifies the two-dimensional array synthesis into a one-dimensional problem, which has the advantages of low computational complexity and fast speed.

[0108] It should be noted that, as for the system in the above-mentioned embodiments, the specific manner in which each module performs operations has been described in detail in the embodiments related to the method, and will not be described in detail here.

[0109] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Those skilled in the art can make various modifications and changes to the present application. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.

[0110] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which shall be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims

1. A method of pattern synthesis for a multi-mode orbital angular momentum array antenna, characterized in that, The application relates to a method for constructing a power pattern of a concentric circular array. A concentric circular array is constructed, mutual coupling effects between elements are ignored, and a first array factor of the concentric circular array is determined based on a radiation pattern function of a multilayer nested concentric circular array; When the number of elements in the circular array reaches a certain threshold, the array factor is converted into an integral form, and a second array factor in integral form is derived by applying a Bessel function theory based on the first array factor; A third array factor is obtained by selecting an observation plane with an azimuth angle of 0 as a first condition based on the rotational symmetry of the central axis of the concentric circular array and the angular symmetry of the array factor, and inputting the first condition into the second array factor; The third array factor is equivalent to a linear array model with a Bessel function factor by comparing and analyzing the similarity between the third array factor and a preset linear array factor, and an equivalent linear array factor expression is derived; A convex optimization problem based on the Bessel function is constructed, the equivalent linear array factor expression and excitation weights are applied to form a power pattern, and the excitation weights are determined by setting a constraint condition and using Matlab and a convex optimization solving program cvx to solve, and the optimized excitation weights are applied to the first array factor to obtain a final required power pattern.

2. The method of pattern synthesis of a multi-mode orbital angular momentum array antenna according to claim 1, wherein, The calculation formula of the radiation pattern function of the multilayer nested concentric circular array in the first array factor of the concentric circular array determined based on the multilayer nested concentric circular array is as follows: wherein, is the pattern function, M is the number of circular sub-arrays, N m is the number of isotropic antenna elements in the mth circular sub-array, I m is the current amplitude of any element on the mth circular sub-array, a mn represents the excitation phase of the nth element on the mth circular sub-array, n is the number of elements, m is the number of layers on the circular sub-array, a m is the radius of the mth circular sub-array, the pitch angle θ ∈ [0, π / 2], the azimuth angle is the wave number k = 2π / λ, λ is the wavelength, φ mn = 2π(n-1) / N m is the azimuth angle of the nth element in the mth circular sub-array, j is the imaginary unit, exp(*) represents the exponential operation.

3. The method of pattern synthesis of a multi-mode orbital angular momentum array antenna according to claim 1, wherein, The first array factor is determined based on the multilayer nested concentric circular array, and the calculation process of the first array factor is as follows: Each element excitation introduces a phase difference, and equal-amplitude feeding is adopted for each circular ring to ensure that the orbital angular momentum beam or the array factor is azimuthally symmetric, thereby generating an orbital angular momentum beam with an l-order mode, and the calculation formula of the first array factor of the l-order mode is as follows: wherein is the first array factor of the lth mode, M is the number of circular sub-arrays, N m is the number of isotropic antenna elements in the mth circular sub-array, I m is the current amplitude of any element on the mth layer of the circular ring, lφ mn is the excitation phase introduced to generate the lth mode OAM beam, n is the number of elements, m is the number of layers on the circular ring, a m is the radius of the mth layer of the circular ring, the pitch angle θ ∈ [0, π / 2], the azimuth angle is the wave number k = 2π / λ, λ is the wavelength, φ mn = 2π(n - 1) / N m is the azimuth angle of the nth element in the mth layer of the circular ring, j is the imaginary unit, exp(*) represents the exponential operation.

4. The method of pattern synthesis of a multi-mode orbital angular momentum array antenna according to claim 3, wherein, When the number of elements in the circular array reaches a certain threshold, the array factor is converted into an integral form, and a second array factor in integral form is derived by applying a Bessel function theory based on the first array factor, and the second array factor includes: When the number of elements on the circular ring reaches a certain threshold, i.e. the element spacing is less than or equal to half a wavelength, the azimuth angle of the mth layer and the nth element is regarded as a continuous variable, the calculation formula of the first array factor of the l-order mode is converted into an integral form, and a second array factor approximated by a Bessel function is derived, and the calculation formula is as follows: wherein, 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 circular ring, N m is the number of isotropic antenna elements of the mth circular sub-array, I m is the current amplitude of any array element on the mth layer of the circular ring, a m is the radius of the mth layer of the circular 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 lth order Bessel function.

5. The method of pattern synthesis of a multi-mode orbital angular momentum array antenna according to claim 1, wherein, The calculation formula of the third array factor after simplification is as follows: where 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 circular ring, N m is the number of isotropic antenna elements of the mth circular sub-array, I m is the current amplitude of any element on the mth layer of the circular ring, a m is the radius of the mth layer of the circular 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 lth order Bessel function.

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

7. The method of pattern synthesis of a multi-mode orbital angular momentum array antenna according to claim 1, wherein, The convex optimization problem based on the Bessel function is constructed, and the calculation formula of the convex optimization problem is as follows: where min is the mathematical symbol for taking the minimum value, ε is the radiation intensity in the direction corresponding to the OAM divergence angle, Θ ML is the main lobe pointing angle (also the divergence angle of the OAM beam), Θ SL is the side lobe pointing angle, Θ NULL is the first null angle, p is the desired side lobe level, w is the excitation weight and is also the variable of the optimization problem, s.t. is the English abbreviation for the constraint condition, f l (θ) is the array factor matrix for the beam pointing in the direction θ, T is the matrix transpose symbol.

8. The method of pattern synthesis of a multi-mode orbital angular momentum array antenna according to claim 1, wherein, The constraint condition is set, and Matlab and a convex optimization solving program cvx are used to solve, and the constraint condition includes: The power pattern is obtained by performing a vector multiplication on the excitation weights and the array factor of the beam pointing direction: P(0) = wf(0) where P l (θ) is the power pattern, f l (θ) is the array factor matrix for beam pointing in the direction θ, J l (*) is the l-th order Bessel function, a1, a2,..., a M is the circular ring radius, w is the weight of array excitation, f l (θ) is the array factor for beam pointing in the direction θ, k is the wave number, T is the transpose symbol, and the matrix transposition is indicated, wherein the power pattern is used for establishing 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 less than or greater than the power value determined by the requirement of the OAM divergence angle corresponding direction and the side lobe level.

9. The method of pattern synthesis of a multi-mode orbital angular momentum array antenna according to claim 1, wherein, The optimized excitation weight is determined by setting the constraint condition, using Matlab and the convex optimization solver cvx, and further including: The convex optimization problem is realized and described by a programming language, and the optimal solution is obtained by using the solver cvx, and under the condition that the number of annular array elements tends to be infinite, the optimal solution does not match the side lobe level or the zero position in actual application.

Images