An Adaptive Unweighted Optimization Method for a Dual-Frequency Orbital Angular Momentum Antenna Array

Abstract

This invention discloses an adaptive unweighted optimization method for dual-frequency orbital angular momentum antenna arrays. The method first iterates through the geometric layout parameters of the dual-ring array under equal amplitude and phase feeding conditions, determining the optimal layout based on maximizing the electric field strength. Then, under the optimal layout, it iterates through the excitation parameters for a single frequency point, constructing a Pareto front for amplitude and purity, and adaptively determining the inflection point based on the range ratio, automatically balancing radiation amplitude and modal purity. Finally, for the two operating frequencies, it extracts a common excitation parameter set and performs Pareto front adaptive inflection point detection again on the dual-frequency quality plane, automatically obtaining the optimal excitation parameters that simultaneously consider dual-frequency performance. This invention requires no manual weight setting, achieving objective and automatic optimization entirely based on the data's own distribution characteristics. It is suitable for the rapid design of multi-frequency, multi-mode OAM arrays, significantly improving design efficiency and versatility.

Description

Technical Field

[0001] This invention belongs to the field of antenna design and electromagnetic field optimization technology, specifically relating to an adaptive unweighted optimization method for a dual-frequency orbital angular momentum antenna array. Background Technology

[0002] Orbital angular momentum (OAM), as an independent dimension of electromagnetic waves besides amplitude, phase, and polarization, offers new degrees of freedom for improving communication capacity and imaging resolution due to the orthogonality between its different modes. Generating vortex electromagnetic waves carrying specific OAM modes using uniform concentric ring arrays has become a research hotspot.

[0003] However, existing OAM array designs still face several challenges. On one hand, there is an inherent contradiction between the array's radiation amplitude and modal purity: radiation amplitude determines the detection range and signal-to-noise ratio, while modal purity directly affects the accuracy of pattern recognition; the two often have an inverse relationship. Traditional design methods often use weighted summation to construct a single objective function, where the weighting coefficients need to be repeatedly adjusted by the designer based on experience. This is not only highly subjective but also difficult to generalize to different application scenarios. On the other hand, the antenna's excitation parameters are highly sensitive to the operating frequency; parameters optimized for one frequency often show a sharp decline in performance at another. Existing research mostly focuses on optimization at a single frequency. For dual-frequency or multi-frequency applications, manual setting of weights between frequency bands is usually required to make trade-offs, lacking a systematic automatic balancing mechanism. Furthermore, the array's geometric parameters—such as ring radius and element spacing—have a fundamental impact on the energy distribution of the vortex field, but most optimization work only focuses on adjusting the excitation parameters, neglecting the optimization potential of the geometric layout.

[0004] Therefore, there is an urgent need for a systematic, unweighted optimization method that can automatically handle multi-objective trade-offs of amplitude and purity, automatically balance dual-frequency performance, and be extended to geometric layout optimization. Summary of the Invention

[0005] The purpose of this invention is to provide an adaptive unweighted optimization method for dual-frequency orbital angular momentum antenna arrays to solve the problems mentioned in the background art. This method is applicable to vortex wave generation and control in near-field dielectric damage detection, microwave imaging, and wireless communication systems.

[0006] The technical solution to achieve the purpose of this invention is: an adaptive unweighted optimization method for a dual-frequency orbital angular momentum antenna array, comprising the following steps:

[0007] S1. Under the condition of equal amplitude and equal phase feeding, the geometric layout parameters of the double ring array are traversed, and the optimal layout is determined based on the maximum electric field strength.

[0008] S2, under the optimal layout, for each preset OAM mode and single operating frequency point, traverse the combination of excitation parameters, and automatically determine the optimal excitation parameters based on the adaptive inflection point detection of the Pareto front and the range ratio of amplitude to purity.

[0009] S3 extracts a common excitation parameter set for each preset OAM mode and two operating frequency points, and automatically determines the optimal excitation parameters for the dual frequencies based on adaptive inflection point detection of the dual-frequency Pareto front.

[0010] Compared with existing technologies, this invention has the following advantages: It eliminates the need for designers to preset any amplitude-purity weights or dual-frequency weights, automatically determining the compromise point based entirely on the data's own distribution characteristics, thus avoiding subjectivity and trial-and-error costs. The segmentation rules dynamically adjust the target based on the actual range ratio, providing a reasonable engineering compromise regardless of whether amplitude or purity changes are dominant. Through a common parameter set and the Pareto front on the dual-frequency quality plane, it automatically finds excitation parameters that simultaneously consider the performance of both frequency bands, preventing the optimal single-frequency parameter from failing in another frequency band. Furthermore, this method is independent of specific antenna structures and can be extended to array optimization problems with any number of frequencies and modes, achieving fully automated design across the entire link. Attached Figure Description

[0011] Figure 1 This is an overall flowchart of the method of the present invention.

[0012] Figure 2 The diagram shows the structure of a concentric circular array antenna with 4 inner ring elements and 6 outer ring elements. (a) Top view and (b) Side view.

[0013] Figure 3 Scatter plots of candidate points, Pareto front and adaptive inflection point for each mode under 10.0 GHz left-hand circular polarization: (a) l=-2, (b) l=-1, (c) l=0, (d) l=+1, (e) l=+2.

[0014] Figure 4 Scatter plots of candidate points, Pareto front and adaptive inflection point for each mode under 10.0 GHz right-hand circular polarization: (a) l=-2, (b) l=-1, (c) l=0, (d) l=+1.

[0015] Figure 5 Scatter plots of candidate points, Pareto front and adaptive inflection point for each mode under left-handed circular polarization at 14.0 GHz: (a) l=-1, (b) l=0, (c) l=+1, (d) l=+2.

[0016] Figure 6Scatter plots of candidate points, Pareto front and adaptive inflection point for each mode under right-hand circular polarization at 14.0 GHz, (a) l=-2, (b) l=-1, (c) l=0, (d) l=+1.

[0017] Figure 7 Left-handed circular polarization at 10 GHz Comparison of the adaptive inflection point and the maximum purity point of the mode. The top row (ac) shows the adaptive inflection point; the bottom row (df) shows the maximum purity point. The meanings of each column are: (a, d) Modal purity distribution, (b, e) Near-field amplitude distribution, and (c, f) Near-field phase distribution.

[0018] Figure 8 Left-handed circular polarization at 14 GHz Comparison of the adaptive inflection point and the maximum purity point of the mode. The top row (ac) shows the adaptive inflection point; the bottom row (df) shows the maximum purity point. The meanings of each column are: (a, d) Modal purity distribution, (b, e) Near-field amplitude distribution, and (c, f) Near-field phase distribution.

[0019] Figure 9 Scatter plots of candidate points, Pareto front and adaptive inflection point for each mode under dual-frequency integrated optimization of left-hand circular polarization, (a) l=-1, (b) l=0, (c) l=+1, (d) l=+2.

[0020] Figure 10 Scatter plots of candidate points, Pareto front and adaptive inflection point for each mode under dual-frequency integrated optimization of right-hand circular polarization: (a) l=-2, (b) l=-1, (c) l=0, (d) l=+1.

[0021] Figure 11 Right-handed circular polarization The results of the dual-frequency adaptive inflection point of the modes are as follows: left group (ac): 10 GHz; right group (df): 14 GHz; meaning of each sub-plot: (a, d) modal purity distribution plot, (b, e) near-field amplitude distribution plot, (c, f) near-field phase distribution plot.

[0022] Figure 12 Right-handed circular polarization The results of the dual-frequency adaptive inflection point of the modes are as follows: left group (ac): 10 GHz; right group (df): 14 GHz; meaning of each sub-plot: (a, d) modal purity distribution plot, (b, e) near-field amplitude distribution plot, (c, f) near-field phase distribution plot. Detailed Implementation

[0023] like Figure 1As shown, this invention proposes an adaptive unweighted optimization method for a dual-frequency orbital angular momentum antenna array, comprising the following steps:

[0024] S1, Geometric Layout Optimization:

[0025] Under constant amplitude and phase feeding conditions, the geometric layout parameters of the double-ring array are traversed, including the inner ring radius, outer ring radius, and ring spacing. Electromagnetic simulation is used to obtain the near-field electric field distribution for each layout, and the optimal geometric layout is determined based on maximizing the electric field intensity on the observation plane.

[0026] The design of this step is based on the fact that electric field strength is a direct measure of the energy of vortex electromagnetic waves, determining the transmission distance and noise immunity of the system. Under the same excitation conditions, the difference in electric field strength is entirely determined by the array geometry. Therefore, using the maximum electric field strength as the criterion for geometric layout optimization ensures that subsequent excitation optimization is based on a structure with optimal energy distribution.

[0027] S2, Excitation parameter optimization steps:

[0028] For a dual-ring array with a given geometric layout (or the optimal layout determined by S1), at a single operating frequency Next, perform the following sub-steps:

[0029] S2.1: Traverse all feasible combinations of excitation parameters, including the excitation amplitude of each unit in the inner circle. Inner ring excitation phase Excitation amplitude of each unit in the outer ring Outer ring excitation phase .

[0030] S2.2: Perform electromagnetic simulation for each set of excitation parameters to obtain the near-field electric field distribution. Calculate the complex amplitude of each OAM mode through circular polarization conversion, circular sampling, and Fourier decomposition. and purity .

[0031] S2.3: The selected dominant mode equals the target mode All parameter combinations, with normalized amplitude x-axis represents purity Using the ordinate as the vertical axis, construct the Pareto front (set of non-dominated points), purity It is the ratio of the power of the dominant mode to the total power.

[0032] S2.4: Calculation of amplitude range and extremely poor purity , defined range .

[0033] S2.5: If The target normalization magnitude is determined according to the following piecewise linear rule. :

[0034] when At that time, the normalized amplitude value of the standard inflection point (the point on the Pareto front with the largest perpendicular distance from the line connecting the two endpoints) is taken. ;

[0035] when hour, ;

[0036] when hour, ;

[0037] when hour, .

[0038] like Then, applying the same rules to the purity axis yields the target purity. .

[0039] S2.6: Select the point on the Pareto front whose coordinates are closest to the target value as the adaptive inflection point. The excitation parameters corresponding to this point are the optimal excitation parameters for this frequency and mode.

[0040] S3, Dual-Frequency Optimization Steps:

[0041] For two operating frequencies and Execute S1 to obtain the amplitude and purity data of all excitation parameter combinations at each frequency point. Then execute:

[0042] S3.1: Filter the common parameter set where the excitation parameters are exactly the same at two frequency points and the main modes are both the target modes.

[0043] S3.2: Define the single-frequency integrated quality for each common parameter. ,in This is the normalized amplitude of the mode at that frequency (equal to the amplitude of the mode at that frequency divided by the maximum amplitude of all candidate points of the mode). To correspond to purity, the point set is obtained. .

[0044] S3.3: Construct the dual-frequency Pareto front and calculate... and The range and range ratio are used to determine the target value (horizontal or vertical axis) according to the same segmentation rules as S2.5, and the normalized amplitude or purity is replaced with... The value is taken as the point closest to the front edge as the dual-frequency adaptive inflection point, and the corresponding excitation parameter is the dual-frequency optimal excitation parameter.

[0045] As a preferred embodiment, the dual-ring array consists of an inner ring... Units, outer ring The system comprises several units, and the geometric layout parameters include the inner circle radius, outer circle radius, and ring spacing. In a preferred embodiment, the number of inner circle units... Number of outer ring units .

[0046] As a preferred embodiment, the excitation parameters include the excitation amplitude of the inner circle unit. Inner ring element excitation phase , outer ring unit excitation amplitude and outer ring unit excitation phase In a preferred embodiment, the inner ring excitation amplitude The range of values ​​is Step size 0.1; inner circle excitation phase Values ; Incentive range of the outer circle The range of values ​​is Step size 0.1; outer ring excitation phase Values .

[0047] As a preferred embodiment, the preset OAM mode includes At least one mode in.

[0048] As a preferred embodiment, the traversal range of the dual-ring geometric layout in S1 is preset according to the size of the dielectric substrate, and the step size is set according to the accuracy requirements.

[0049] As a preferred option, the standard inflection point described in S2 is the point on the Pareto front that has the largest vertical distance from the line connecting the two endpoints.

[0050] As a preferred option, the single-frequency integrated quality described in S3 In the calculation, the normalized amplitude It is the amplitude of the mode at that frequency point divided by the maximum amplitude of all candidate points of the mode.

[0051] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings.

[0052] Example

[0053] This embodiment uses a concentric dual-ring microstrip antenna array operating at 10GHz and 14GHz, with 4 inner ring elements and 6 outer ring elements, as the optimization object to specifically verify the method of the present invention.

[0054] I. Geometric Layout Optimization

[0055] Establish a parameterized model of the concentric double-ring antenna in HFSS and set the inner ring radius. Spacing between outer and inner rings The parameters are variable, with a traversal range of: inner circle radius 8–12 mm, outer circle to inner circle spacing 10–15 mm, and step size 0.5 mm. All array elements are set to constant amplitude (1W) and constant phase (0°) feeding to eliminate excitation interference. An automated script is used to traverse all combinations and extract the observation plane (…). The maximum near-field electric field amplitude is measured at a radius of mm. Simulation results show that when the inner radius is... mm, distance between outer and inner rings The electric field strength reaches its maximum at a radius of 23.2 mm. Therefore, this geometric layout (outer radius 23.2 mm) is determined to be the optimal layout. Subsequent optimization of excitation parameters is based on this layout.

[0056] II. Optimization of Single-Frequency Excitation Parameters

[0057] Under optimal layout, for a single operating frequency (e.g., 10GHz), the range and step size of the inner and outer loop excitation parameters are set, generating a list of all possible excitation parameter combinations. Inner loop amplitude. Value range: 0.1 to 1.0 (step size: 0.1), outer circle amplitude Value range: 0.1 to 1.0 (step size: 0.1), inner circle phase The values ​​are 0°, 90°, 180°, and 270°, representing the outer phase. The parameters are set to 0°, 60°, 120°, 180°, 240°, and 300°, totaling 2400 sets. An automated script is used to perform electromagnetic simulations on all parameter combinations to obtain near-field electric field distribution data for each parameter set.

[0058] For each set of data, circular polarization conversion, circular sampling, and Fourier decomposition are performed to obtain the complex amplitude and purity of each OAM mode, and the dominant mode is determined. For a preset target mode set (such as...), ... The candidate set is formed by selecting parameter combinations where the dominant mode equals the target mode. The amplitude values ​​in the candidate set are normalized (divided by the maximum amplitude under that mode), and a Pareto front is constructed with the normalized amplitude as the x-axis and purity as the y-axis.

[0059] Calculate the amplitude range in the candidate set and extremely poor purity The range is obtained With 10 GHz left-hand circularly polarized (LHCP) For example, , , The amplitude change is much greater than the purity change. Therefore, according to the adaptive rule, the target normalized amplitude is set to 1.0 (i.e., the point of maximum amplitude), and the corresponding parameter is... The point on the Pareto front that is closest to the target value is taken as the adaptive inflection point, and the corresponding excitation parameters are the optimal parameters at that frequency. The above process is repeated for other modes to obtain the adaptive inflection point parameters for each mode at 10 GHz and 14 GHz.

[0060] III. Dual-frequency point optimization (dual-frequency adaptive inflection point method)

[0061] For the two operating frequencies (10GHz and 14GHz), the above steps are performed separately to obtain the amplitude and purity data for all parameter combinations at each frequency. A common parameter set is then selected where the excitation parameters are identical across both frequencies and the dominant mode is the target mode. For each common parameter, a single-frequency synthesized quality is defined. (The product of normalized amplitude and purity) yields the point set. Construct a two-frequency Pareto front and calculate... and The range and range ratio are used to determine the target value according to the same segmentation rule. The point closest to the front edge is taken as the dual-frequency adaptive inflection point, and the corresponding excitation parameter is the dual-frequency optimal excitation parameter.

[0062] This embodiment uses a concentric dual-ring microstrip antenna array operating at 10GHz and 14GHz, with 4 inner ring elements and 6 outer ring elements, as the optimization object to specifically verify the method of the present invention.

[0063] (1) Results of geometric layout optimization

[0064] Use a script to automatically traverse all ( ) combination, extract the observation plane ( The maximum amplitude of the near-field electric field on the [data point]. The results are shown in the table below (selecting some representative data):

[0065] Table 1. Results of electric field intensity variation with location during double-ring position optimization (partial data)

[0066]

[0067] The data in the table shows that when the double-ring position parameters are... mm, When mm, the electric field intensity on the observation plane reaches its maximum value. Therefore, this location is determined to be the optimal layout for a double ring system. For example... Figure 2 The diagram shows a concentric double-ring array antenna with an inner ring of 4 elements and an outer ring of 6 elements. (a) is a top view, and (b) is a side view. The following key dimensions are marked in the diagram:

[0068] The radius of the circle containing the inner ring unit, corresponding to the optimized value. ;

[0069] The radius of the circle containing the outer ring unit, corresponding to the optimized value. ;

[0070] The distance between the inner and outer rings, i.e. (corresponding spacing) ).

[0071] This figure visually illustrates the dual-ring array geometry used in this invention, providing a model basis for subsequent traversal of geometric layout parameters.

[0072] (2) Analysis of the results of excitation parameter optimization

[0073] In the best layout mm, Based on mm, the adaptive inflection point method was used to optimize the excitation parameters at the two frequency points of 10GHz and 14GHz respectively, and the adaptive inflection point parameters of each mode were obtained, as shown in Table 2 (10GHz) and Table 3 (14GHz).

[0074] Table 2 Adaptive inflection point parameters for each spin direction and target mode at 10GHz

[0075]

[0076] Table 3 Adaptive inflection point parameters for each spin direction and target mode at 14GHz

[0077]

[0078] To illustrate the effectiveness of adaptive inflection points, two specific single-frequency point comparison cases are given below.

[0079] Left-hand circular polarization at 10 GHz Mode: In this mode, the amplitude range Extremely poor purity , range The amplitude change is much greater than the purity change. The adaptive rule selects the point of maximum amplitude as the inflection point, i.e. At this point, the near-field peak value is 2426.31 V / m, and the purity is 0.9999. For comparison, the point of maximum purity (…) The purity given is 1.0000, but the near-field peak is only 1404.43 V / m. The purity gain is extremely small (0.0001), while the amplitude loss is as high as about 42%. Therefore, choosing the point with the maximum amplitude as the adaptive inflection point is reasonable.

[0080] 14GHz Left-hand circular polarization Mode: The point of maximum amplitude in this mode ( The near-field peak value is given as 1081.15 V / m, and the purity is 0.9900; the maximum purity point is ( The purity is given as 0.9913, but the near-field peak is only 872.99 V / m. The purity gain is only 0.13%, while the amplitude loss exceeds 19%. The adaptive inflection point is also selected at the maximum amplitude point because the small increase in purity is not worth sacrificing a large amount of radiated power.

[0081] Figure 3 — Figure 6 The distribution of candidate points (gray scatter dots), Pareto front points (red circles), and adaptive inflection points (blue stars) for each rotation direction and mode at two frequency points are presented. Figure 3 (10GHz left-handed) Figure 4 (10GHz right-handed) Figure 5 (14GHz left-handed) Figure 6 (14GHz right-hand rotation). Observation shows that:

[0082] The Pareto front shapes differ significantly across modes. For modes where purity changes are much smaller than amplitude changes (e.g., 10 GHz LHCP), the differences are more pronounced. The leading edge is almost vertical, and the adaptive inflection point falls at the maximum amplitude end; for modes where the amplitude and purity change equally, the leading edge has obvious curvature, and the inflection point is located at the maximum curvature (near the standard inflection point).

[0083] The distribution range of candidate points for the same mode differs at different frequencies, indicating that the excitation parameters are sensitive to frequency.

[0084] The adaptive rule can stably output inflection points at all frequencies and modes without the need for manual weight setting.

[0085] Figure 7 and Figure 8 The actual field distributions at the adaptive inflection point and the maximum purity point were further compared. Figure 7 10GHz left-handed circular polarization For the modal, the upward (ac) mode is the adaptive inflection point, and the downward (df) mode is the maximum purity point. It can be seen that the near-field amplitude (b) at the adaptive inflection point is much higher than that at the maximum purity point (e), while the modal purity distribution (a, d) and phase distribution (c, f) are almost indistinguishable, which confirms the rationality of amplitude priority. Figure 8 14GHz left-handed circular polarization The modal analysis also shows that the adaptive inflection point (upward) is significantly better than the maximum purity point (downward) in terms of radiation amplitude, while the purity loss is negligible.

[0086] (3) Analysis of dual-frequency point optimization results

[0087] Following the dual-frequency optimization steps, a common parameter set is extracted for frequencies where the excitation parameters are identical at 10 GHz and 14 GHz, and the dominant modes are both the target modes. The single-frequency integrated quality is then calculated for each common parameter. (Normalized amplitude × purity) yields the point set. Construct a two-frequency Pareto front and calculate... and The range and range ratio were used to determine the dual-frequency adaptive inflection point according to the same segmentation rules. The results are shown in Table 4.

[0088] Table 4 Dual-frequency integrated adaptive inflection point parameters

[0089]

[0090] To verify the effectiveness of the dual-frequency adaptive inflection point, two comparative cases are given below.

[0091] Right-hand circular polarization Modality: The common parameters selected for the dual-frequency adaptive inflection point are as follows At 10GHz 14GHz If the optimal parameters for a single 14GHz frequency are used ( The quality of 14GHz will be slightly improved. However, performance at 10GHz will drop sharply. Adaptive trade-offs avoid the failure of single-frequency optimality in another frequency band, ensuring availability in both bands.

[0092] Right-hand circular polarization Modality: The common parameters selected for the dual-frequency adaptive inflection point are as follows ,get , If using the 14GHz maximum amplitude point ( The amplitude increases at 14GHz, but the purity drops to 0.5196, and the performance at 10GHz is also very poor; if the maximum purity point of 14GHz is used ( The purity at 14GHz can reach 0.9917, but the amplitude is very low (only 951.23V / m), and the performance at 10GHz is also poor. The adaptive inflection point automatically selects a compromise solution that is acceptable for both frequency bands.

[0093] Figure 9 and Figure 10 Demonstrates dual-frequency quality plane The candidate point set (gray scattered points), the two-frequency Pareto front (red circle), and the adaptive inflection point (blue star) are shown on the graph. Figure 9 It is left-handed circularly polarized. Figure 10It is right-handed circular polarization. As can be seen from the figure: the performance of the two frequency points mutually restricts each other, forming a clear Pareto boundary; the adaptive inflection point is located at a reasonable position on the leading edge determined by the range ratio, neither biased towards one frequency point nor causing the other frequency point to fail; for different modes, the degree of bending of the leading edge is different, but the adaptive rule can automatically give a compromise solution.

[0094] Figure 11 and Figure 12 Right-hand circular polarization is given respectively and Detailed field distribution of the mode at the dual-frequency adaptive inflection point. Figure 11 In the diagram, the left group (ac) is at 10 GHz, and the right group (df) is at 14 GHz. It can be seen that both frequency points maintain clear vortex phases and considerable amplitudes, with purities of 0.9387 and 0.9455, respectively. Figure 12 In the data, the phase distributions at 10GHz and 14GHz also exhibit a complete spiral structure, with overall qualities of 0.6857 and 0.8153, respectively. This indicates that the dual-frequency adaptive inflection point can automatically select compromise parameters that balance performance at both frequency points from the common parameter set, avoiding the problem of performance degradation of the optimal single-frequency parameter in another frequency band.

[0095] The results above show that the adaptive inflection point method can automatically determine the optimal excitation parameters for each mode based on the distribution characteristics of the data itself, achieving a reasonable performance balance in both frequency bands without the need for manual weighting.

[0096] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An adaptive unweighted optimization method for a dual-frequency orbital angular momentum antenna array, characterized in that, Includes the following steps: S1. Under the condition of equal amplitude and equal phase feeding, the geometric layout parameters of the double ring array are traversed, and the optimal layout is determined based on the maximum electric field strength. S2, under the optimal layout, for each preset OAM mode and single operating frequency point, traverse the combination of excitation parameters, and automatically determine the optimal excitation parameters based on the adaptive inflection point detection of the Pareto front and the range ratio of amplitude to purity. S3 extracts a common excitation parameter set for each preset OAM mode and two operating frequency points, and automatically determines the optimal excitation parameters for the dual frequencies based on adaptive inflection point detection of the dual-frequency Pareto front.

2. The method according to claim 1, characterized in that, The geometric layout parameters include the inner circle radius, the outer circle radius, and the ring spacing.

3. The method according to claim 1, characterized in that, In S2, the specific method for Pareto front adaptive inflection point detection is as follows: all parameter combinations in which the principal mode equals the target mode are selected, and the amplitude is normalized. and purity Construct the Pareto front for the coordinate system; calculate the amplitude range. and extremely poor purity , defined range ; like The target normalization magnitude is determined according to the following segmentation rules. : when At that time, the normalized amplitude value of the standard inflection point is taken. ; when hour, ; when hour, ; when hour, ; like The same rules apply to the purity axis; the point on the Pareto front that is closest to the target value is taken as the adaptive inflection point.

4. The method according to claim 3, characterized in that, The standard inflection point is the point on the Pareto front that has the largest vertical distance from the line connecting the two endpoints.

5. The method according to claim 3, characterized in that, In S3, the specific method for dual-frequency adaptive inflection point detection is as follows: Let the two operating frequencies be... and ; Select a common parameter set where the excitation parameters are exactly the same at two frequency points and the principal modes are both the target modes; For each set of parameters in the common parameter set, define it at the frequency point Single-frequency overall quality ,in This represents the normalized amplitude of the mode at that frequency. To determine the corresponding purity, the point set is obtained. ; Construct a two-frequency Pareto front and calculate and The range and range ratio are used to determine the target value according to the segmentation rule of Pareto front adaptive inflection point detection, and the point on the Pareto front that is closest to the target value is taken as the dual-frequency adaptive inflection point.

6. The method according to claim 1, characterized in that, The dual-ring array consists of an inner ring Units, outer ring The inner ring consists of several units, with the number of units... Number of outer ring units .

7. The method according to claim 1, characterized in that, The excitation parameters include the excitation amplitude of the inner ring unit. Inner ring element excitation phase , outer ring unit excitation amplitude and outer ring unit excitation phase .

8. The method according to claim 7, characterized in that, The inner circle excitation amplitude The range of values ​​is Step size 0.1; inner circle excitation phase Values ; Incentive range of the outer circle The range of values ​​is Step size 0.1; outer ring excitation phase Values .

9. The method according to claim 1, characterized in that, The preset OAM mode includes At least one mode in.

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