Characteristic mode multi-criterion rapid tracking method based on Pearson correlation coefficient

Abstract

The invention relates to a characteristic mode multi-criterion rapid tracking method based on a Pearson correlation coefficient, which belongs to the technical field of antennas and comprises pre-processing and post-processing. According to the first filtering method of the pretreatment, a characteristic value threshold value is set for different radiation structures, the threshold value is compared with all characteristic values of the same mode so that useless modes can be eliminated in a self-adaptive mode, and the modes influencing the antenna are screened out; according to the second filtering method, the number of modes for calculating correlation coefficients is limited, and calculation time is saved; in the post-processing, correlation coefficients between two adjacent frequency points are classified according to absolute values of the correlation coefficients, the correlation coefficients are divided into a strong correlation coefficient, a weak correlation coefficient and an ircorrelation coefficient, four criteria are provided to judge mode degeneracy, and then characteristic values corresponding to the degeneracy mode are exchanged. Compared with a traditional method, the number of modes needing mode tracking is reduced through a screening mechanism in the pre-processing stage, the tracking time is saved, and the accuracy of a tracking result is guaranteed in correlation classification and multi-criterion correction in the post-processing stage.

Description

Technical Field

[0001] The invention belongs to the technical field of antennas and relates to a characteristic mode multi-criteria fast tracking method based on Pearson correlation coefficient. Background Art

[0002] The characteristic mode theory can intuitively provide the radiation and scattering characteristics of structures of arbitrary shapes, regardless of the external excitation source. Therefore, it is widely used to guide the design of antennas, such as achieving broadband or multi-band characteristics, synthesizing the required radiation pattern, reducing the coupling between MIMO antennas, etc. In general, the surface current of the antenna can be decomposed into a series of mutually orthogonal characteristic modes, which can be solved by the antenna impedance matrix [Z]. However, the mode at each discrete frequency point is disordered, so a mode tracking method is needed to correctly connect all modes at all discrete frequencies so as to obtain the correct physical characteristics of the antenna. Therefore, the accuracy of the mode analysis depends largely on the accuracy and reliability of the tracking method.

[0003] In order to solve the problems of mode crossing and mode degeneration in the process of mode tracking, scholars at home and abroad have proposed many methods. Among them, the correlation method is relatively mature, which is mainly divided into three types. The first is based on the bounded linear eigenvector correlation method, such as the literature "Capek M, Hazdra P, Hamouz P, et al. A method for tracking characteristic numbers and vectors [J]. Progress In Electromagnetics Research B, 2011, 33: 115-134." This method divides mode tracking into the association stage and the arbitration stage. In the association stage, the characteristic value is set to a threshold for filtering, and useless modes are removed. In the arbitration stage, for the case of fuzzy correlation or large correlation, an adaptive frequency interval is proposed to increase the correlation by reducing the frequency interval. Although the problem of mode exchange has been solved and most modes can be correctly tracked over the entire frequency band, the problem of mode degeneration still exists. The second method is based on the surface current correlation method, such as the literature "Safin E, Manteuffel D. Advanced eigenvalue tracking of characteristic modes [J]. IEEE Transactions on Antennas and Propagation, 2016, 64 (7): 2628-2636.", which uses the orthogonal characteristics of eigenvectors to improve accuracy. Due to the inaccurate segmentation accuracy, the modes that should be orthogonal in theory are not orthogonal. Therefore, a set of new modes that are mutually orthogonal at the next frequency point are calculated by calculating all the theoretically mutually orthogonal modes at the previous frequency point. The advantage of this algorithm is that the new modes obtained are mutually orthogonal, and the mode tracking will not have the problem of mode degeneration due to the fuzzy correlation between modes. All mode cross-degeneration problems can be correctly corrected. However, this solution is accompanied by an increase in calculation time and certain limitations on the number of modes that can be processed while reducing mode degeneration. The third method is based on the characteristic far-field correlation method. At two adjacent frequencies, when the antenna surface current changes significantly, these changes often only occur at certain segmentation grids of the antenna.When using surface current to calculate correlation, the current changes on these meshes will have a serious impact on the current correlation calculation results. The radiation far field is generated by the common radiation of currents at various locations on the entire antenna structure. Therefore, the changes in the antenna surface current have limited impact on the radiation far field. For example, the literature "Miers Z, Lau B K. Wideband characteristic mode tracking utilizing far-field patterns [J]. IEEE Antennas and Wireless Propagation Letters, 2015, 14: 1658-1661." proposed a mode tracking algorithm for tracking complex structures through radiation far fields. The main advantage of this method is that compared with the changes in mode currents, the changes in radiation far fields are relatively slow. Therefore, using radiation far fields to calculate correlation allows for a larger frequency step size. At the same time, this method can reduce the errors caused by small changes in currents and mirror currents in symmetrical structures. However, since the radiation far field that needs to be calculated is very complex and time-consuming, this method is not widely used. Summary of the invention

[0004] In view of this, the purpose of the present invention is to address the existing problems of mode crossing, mode degeneration being difficult to correct and time-consuming, and propose a method for rapid tracking of characteristic mode patterns based on the Pearson correlation coefficient based on bounded linear eigenvector correlation. The present invention is divided into two parts, pre-processing and post-processing. 1) The pre-processing part introduces two special filtering methods. The first filtering method sets an eigenvalue threshold for different radiation structures, and compares the threshold with all eigenvalues ​​of the same mode to adaptively exclude useless modes, screen out modes that have an impact on the antenna, and save subsequent mode matching time. The number of filtered modes can be adaptively changed according to the complexity of the antenna structure when the eigenvalue threshold is constant. The second filtering method is for when calculating the Pearson correlation coefficient, because the mode tracking error only occurs within the range of several modes close to the mode, so the number of modes for calculating the correlation coefficient is limited, further reducing the amount of calculation and saving mode matching time. 2) In the post-processing part, the calculated correlation coefficients between two adjacent frequency points are classified according to their absolute values ​​into three categories: strong correlation, weak correlation, and irrelevant, so as to solve the problem of mode crossing, and four criteria are proposed to judge the mode degeneration and then exchange the eigenvalues ​​corresponding to the degenerate mode. For the strongly correlated items, they are directly matched, and for the irrelevant items, the mode is deleted. For the weakly correlated items, the mode degeneration is searched and corrected according to the four proposed criteria. According to the characteristics of the mode degeneration, the mode pairs that meet the mode degeneration phenomenon are screened out by criteria 1 and 2, and then the mode degeneration is judged and corrected by criteria 3 and 4. The correlation classification and further screening and correction in the post-processing can not only ensure the correctness of mode tracking but also further reduce the amount of calculation. Compared with the traditional method, the present invention greatly reduces the number of modes that need to be tracked by the screening mechanism in the pre-processing stage, thereby saving the tracking time, and ensures the accuracy of the tracking results in the correlation classification and multi-criteria correction in the post-processing stage, and has good application value.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for fast tracking of characteristic mode patterns based on Pearson correlation coefficient and multiple criteria comprises the following steps:

[0007] Pre-processing stage:

[0008] Step 1: According to the specific structure of the antenna, the characteristic impedance, eigenvalue and eigenvector of the antenna are solved by electromagnetic simulation software and stored in frequency order;

[0009] Step 2: Filtering method 1: Adopt the adaptive filtering mode number method and set the eigenvalue threshold λ threshold, construct a counter count for counting the number of patterns that do not meet the screening conditions, set its initial value and upper limit; traverse each row of the eigenvalue matrix stored in step 1, if there is an eigenvalue less than the threshold λ threshold If the eigenvalues ​​of a row are all greater than the threshold, the counter count is incremented by 1, and the screening is stopped when the upper limit set by the counter is reached.

[0010] Step 3: Filtering method 2: According to the complexity of the antenna structure, the j modes that need to be processed are screened out, and only the Pearson correlation coefficients between the j modes near the current mode between adjacent frequency points are calculated, thereby reducing unnecessary calculations;

[0011] Step 4: According to the absolute value of the Pearson correlation coefficient, set the strong correlation critical value and the irrelevant critical value. If the absolute value of the correlation coefficient is greater than the strong correlation critical value, it is classified as strongly correlated. If the absolute value of the correlation coefficient is less than the irrelevant critical value, it is classified as irrelevant. The rest are classified as weakly correlated.

[0012] Post-processing stage:

[0013] Step 5: For the strong correlation defined in step 4, store the corresponding eigenvalues ​​in the pattern tracking table according to the strong correlation pattern. If there is no correlation, delete the pattern and do not store it. For the weak correlation pattern, proceed to step 6.

[0014] Step 6: Propose four criteria to judge and correct pattern degeneration; traverse the weakly correlated patterns, first pre-match according to the principle of eigenvalue proximity, and store the eigenvalues ​​with the smallest difference in the pattern tracking table, and then execute the criterion judgment on the weak correlation. If all the criteria are met, it is judged as pattern degeneration, and the pre-matched eigenvalues ​​in its pattern tracking table are exchanged; if one of the criteria fails, it is not judged as pattern degeneration, and the order of pre-matched eigenvalues ​​in its pattern tracking table is not exchanged.

[0015] Furthermore, in step 1, according to the generalized eigenvalue equation of the characteristic mode theory:

[0016] XJ n =λ n RJ n (1)

[0017] Where X is the imaginary part of the characteristic impedance Z, R is the real part of the characteristic impedance Z, λ n , J n are eigenvalues ​​and eigenvectors;

[0018] X and R are obtained by analyzing the antenna structure parameters using the moment method, or derived by eigenmode analysis using electromagnetic simulation software; X and R are matrices distributed according to frequency. Substituting the obtained [X] and [R] matrices at each frequency point, (1) is used to solve λ n , J n ; Then store its eigenvalues ​​and eigenvectors according to frequency distribution.

[0019] Further, step 2 specifically includes the following steps:

[0020] Step 2.1: Set the feature value threshold λ threshold ; When the eigenvalue λ of a mode at a certain frequency point in the characteristic mode analysis n When it is close to zero, that is:

[0021] λ n =0 (2)

[0022] The corresponding pattern significance MS is close to 1, that is:

[0023]

[0024] This means that the mode has a great impact on the antenna performance. Traverse each row of the eigenvalue matrix, and initially regard a row of the eigenvalue matrix as a mode. If there is a situation where the eigenvalue of a mode is less than the threshold, store the eigenvalue of the mode in the matrix table to be tracked in frequency order, and then traverse the next row; if the eigenvalues ​​of a mode are all greater than the threshold, proceed to step 2.2;

[0025] Step 2.2: Set a counter count with an initial value of 0. When the feature values ​​of a pattern are all greater than the threshold, the counter is incremented by 1. If all feature values ​​of the current pattern are greater than λ threshold , then the k patterns to be traversed subsequently are judged. If the eigenvalue of a pattern is less than the threshold, the traversal operation of step 2.1 is continued. If the eigenvalues ​​of the k patterns are all greater than the threshold, the k patterns are stored in the matrix table to be tracked, and then the current step is terminated and step 3 is executed; k is the upper limit value set by the counter. The matrix table to be tracked is in the form of an a×b matrix, a is the number of patterns to be tracked after screening, b is the number of discrete frequency points, and any row is a pattern.

[0026] Furthermore, in step 3, the Pearson correlation coefficient formula is used to calculate the correlation coefficient between adjacent frequency points, and the calculation formula is as follows:

[0027]

[0028] J m , J n is the eigenvector corresponding to mode m and mode n, and are the means of the two eigenvectors, r is the calculated correlation coefficient, and the Pearson correlation coefficient ranges from -1 to 1; when r = 1, it indicates a completely positive correlation; when r = -1, it indicates a completely negative correlation; when r = 0, it indicates no linear correlation;

[0029] If the row number of the stored matrix table to be tracked is used as the mode index, since modes with large differences in mode indices will not experience mode crossing and mode degeneration, the number of correlation coefficients calculated between modes is limited, and only the correlation coefficients of the j modes adjacent to the current mode are calculated, and the mode pairs that will not experience mode crossing and mode degeneration are removed, thereby reducing the time for calculating the correlation coefficients. j can be determined depending on the complexity of the antenna structure.

[0030] Further, step 4 specifically includes the following steps:

[0031] Step 4.1: First, divide the strongly correlated mode. The strongly correlated conditions are as follows:

[0032]

[0033] ρ k is the absolute value of the correlation coefficient between the current mode and the next frequency mode k, ρ n is the absolute value of the correlation coefficient between all modes except mode k; when there is ρ k is greater than 0.99, or there is ρ k When the other correlation coefficients are less than 0.6 under the condition that the correlation coefficients are greater than 0.95, the pattern indexes that meet the condition are stored in the strong correlation index table;

[0034] Step 4.2: Then perform irrelevant partitioning, the irrelevant conditions are as follows:

[0035] ρ k <0.3,k=1,2...n (6)

[0036] That is, the ρ calculated for all modes of the current mode at subsequent frequency points k If all of them are less than 0.3, they are considered to be weakly correlated; the pattern index that meets this condition is stored in the irrelevant index table; the pattern index is the row number of the eigenvalue corresponding to the irrelevant pattern in the pattern tracking table;

[0037] Step 4.3: The remaining patterns are weakly correlated, and the weakly correlated pattern indexes are stored in the weakly correlated index table; the pattern index is the row number of the eigenvalue corresponding to the weakly correlated pattern in the pattern tracking table.

[0038] Further, step 5 specifically includes the following steps:

[0039] Step 5.1: Process strongly correlated pattern pairs, traverse the strongly correlated index table, and store the eigenvalues ​​of each strongly correlated pattern pair into the pattern tracking table. The order of the eigenvalues ​​stored in the pattern tracking table is the tracking result;

[0040] Step 5.2: Process irrelevant pattern pairs, traverse the irrelevant index table, and do not perform matching operations on the eigenvalues ​​represented by the pattern index, that is, the eigenvalues ​​of the pattern in the pattern tracking table are no longer stored at subsequent frequency points.

[0041] Further, step 6 specifically includes the following steps:

[0042] Step 6.1: traverse the weak correlation index table and pre-match each weak correlation pattern according to the principle of eigenvalue proximity; for the weak correlation pattern, the eigenvalue closest to the weak correlation pattern among all the eigenvalues ​​of the next frequency point is stored in the corresponding pattern tracking table in advance, which is pre-matching;

[0043] Step 6.2: Combine the pre-matched pattern pairs in pairs and calculate the four criteria; assuming there are m weakly correlated patterns, combine them in pairs, and there are a total of For each pair of combinations, four criteria are calculated. The four criteria are as follows:

[0044] Criterion 1: Determine the number of weakly correlated modes at the current frequency point. If the number of modes is 1, the mode can be matched directly. If the number of modes is greater than 1, check whether the eigenvalue at the current frequency has been matched at the previous frequency point, remove the unmatched modes, and then hand over the remaining modes to Criterion 2 for further processing.

[0045] Criterion 2: Assume that the current frequency is f i , is working with f i+1 When the frequency points are matched, weak correlation occurs; if mode degeneration occurs at this frequency point, the characteristic value curves of the two modes appear to be close to each other. i At |λ m-n |Should be greater than f i+1 |λ m-n |, if this condition is not met, it is not judged as mode degeneration;

[0046] Criterion 3: For both modes, at frequency point f i ,f i+1 Calculate the modal energy If the energy curves intersect, it means that mode degeneration has occurred; then the pre-matched eigenvalues ​​of the two modes are exchanged for correction; after the modes are exchanged here, the mode pair involving the currently matched mode in the eigenvalue difference calculated in criterion 2 is deleted;

[0047] Criterion 4: For f1,f2,…,f i-2 ,fi-1 ,f i+1 The eigenvalues ​​of are used to fit the polynomial data using the least squares method. If i If the characteristic value at the frequency is within the error range of the data fitting curve, it is confirmed that the exchanged mode is correct;

[0048] If all four criteria are passed, it is considered to be a pattern degeneration, and its pre-matched eigenvalues ​​are exchanged. If one does not pass, matching is performed according to the pre-matched pattern.

[0049] Furthermore, in the criterion 3, the modal energy is calculated by the following formula:

[0050]

[0051] Among them, J i is the eigenvector corresponding to mode i at the current frequency, X e is the energy storage operator, is the electric energy stored in mode i, the electric energy storage operator X e It is obtained from the following relationship:

[0052] X m -X e =X (8)

[0053]

[0054]

[0055] Among them, X e ,X m are the electric energy and magnetic energy storage operators respectively, X is the imaginary part of the characteristic impedance, and ω is the frequency; the electric energy storage operator X is calculated using the imaginary part X of the characteristic impedance Z obtained in step 1 and the frequency set by the antenna solution e , and then use the obtained electric energy storage operator X e The modal energy is calculated by combining the eigenvector of mode i solved in step 1.

[0056] Furthermore, the least squares polynomial data fitting of the criterion 4 is as follows:

[0057]

[0058] Among them, x i1 ,x i2 …x im is the frequency, representing the independent variable, y i is the eigenvalue that changes with frequency, representing the dependent variable, b0, b1…b mis the coefficient of each independent variable that minimizes the target S; the eigenvalues ​​of the current weak correlation mode that have been tracked at the previous frequency point and the pre-matched eigenvalues ​​are substituted into the y i , the frequency corresponding to each eigenvalue is substituted into the x in the formula i1 ,x i2 …x im , so that S reaches the minimum, solve b0,b1…b m The value of is finally obtained as a polynomial function, and the trend of the eigenvalue trajectory of the mode is estimated through the polynomial function curve.

[0059] The beneficial effect of the present invention is that the present invention proposes a method for fast tracking of characteristic mode patterns based on the Pearson correlation coefficient. The core of the invention is to calculate the Pearson correlation coefficient between adjacent frequency points and then perform pattern matching. By introducing two unique filtering methods in the pre-processing part, compared with the traditional method, filtering method one can adaptively screen out the patterns that have an impact on the antenna according to the complexity of the antenna structure, and then filtering method two greatly reduces the number of pattern logarithms for calculating the Pearson correlation coefficient, thereby reducing the time used for the pattern tracking method. In the post-processing part, by distinguishing strong and weak irrelevance, the number of pattern logarithms that need to be corrected is screened again, and then the four criteria are used to judge the pattern degeneration of the screened weakly correlated patterns. On the whole, the pre-processing part of the invention reduces the computational complexity of the entire method, and the post-processing part ensures the accuracy of the pattern tracking results. Therefore, the invention can successfully correct the problems of pattern crossing and pattern degeneration while taking into account the time-consuming calculation, and has good application value.

[0060] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0062] Figure 1 The overall process of pattern tracking;

[0063] Figure 2 It is the pre-processing flow chart;

[0064] Figure 3 is the post-processing flow chart;

[0065] Figure 4This is the flow chart of the adaptive filtering mode, and the preset value of count is 0;

[0066] Figure 5 Two classic antenna structures, (a) is a rectangular patch antenna, and (b) is a fractal antenna;

[0067] Figure 6 is the characteristic angle curve obtained by using method 1 and method 2 for the rectangular patch;

[0068] Figure 7 Current distribution of mode 1 and mode 10 at 3.88 GHz, 4.04 GHz, 4.2 GHz, and 4.36 GHz;

[0069] Figure 8 is the characteristic angle curve obtained by using method 3 for the rectangular patch;

[0070] Fig. 9 The characteristic angle curve obtained by using method 1 for the fractal antenna;

[0071] Fig.10 The characteristic angle curve obtained by using method 2 for the fractal antenna;

[0072] Fig.11 The characteristic angle curve obtained by using method 3 for the fractal antenna;

[0073] Fig.12 It is the modal current around the frequency of 2.49 GHz. DETAILED DESCRIPTION

[0074] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0075] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0076] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it is obvious to those skilled in the art that the embodiments of the present invention can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present invention difficult to understand.

[0077] like Figure 1 As shown in FIG. 1 , the present invention proposes a method for fast tracking of characteristic mode patterns based on the Pearson correlation coefficient. The core of the method is to calculate the Pearson correlation coefficient of the characteristic vector corresponding to the characteristic value. The present invention is divided into six steps, as follows: Figure 2-3 As shown, steps 1-4 belong to the pre-processing stage, and steps 5-6 belong to the post-processing stage. The specific steps are as follows:

[0078] Step 1: Based on the specific structure of the specific antenna, the characteristic impedance of the antenna is solved through electromagnetic simulation software, and then the eigenvalues ​​and eigenvectors are solved and stored in frequency order. It can be preliminarily determined that its pattern has been partially tracked.

[0079] Step 2: If Figure 4 As shown, the filtering method 1 is implemented, using the adaptive filtering mode number method and setting the characteristic value threshold λ threshold , and set a counter count to count the number of patterns that do not meet the screening conditions. Its initial value is 0, and the upper limit of the counter is set. Traverse each row of the eigenvalue matrix stored in step 1. If there is an eigenvalue less than the threshold λ threshold If the eigenvalues ​​of a row are all greater than the threshold, the counter count is incremented by 1, and the screening is stopped when the upper limit set by the counter is reached. The function is to expand the range of the number of modes to be screened and increase the tracking accuracy.

[0080] Step 3: Implement filtering method 2. According to the complexity of the antenna structure, the pattern tracking error only occurs within the range of j adjacent patterns of the pattern, so only the Pearson correlation coefficient between the j patterns near the pattern between adjacent frequency points is calculated.

[0081] Step 4: According to the absolute value of the Pearson correlation coefficient, set the strong correlation critical value and the irrelevant critical value. If the absolute value of the correlation coefficient is greater than the strong correlation critical value, it is classified as strongly correlated. If the absolute value of the correlation coefficient is less than the irrelevant critical value, it is classified as irrelevant. The rest are classified as weakly correlated.

[0082] Step 5: For the strong correlation defined in step 4, store the corresponding eigenvalues ​​in the pattern tracking table according to the strong correlation pattern. If there is no correlation, delete the pattern and do not store it. For the weak correlation pattern, proceed to step 6.

[0083] Step 6: Propose four criteria to judge and correct pattern degeneration. Traverse the weakly correlated patterns, first pre-match according to the principle of eigenvalue proximity, and store the eigenvalue with the smallest difference in the pattern tracking table. Then, perform four criteria on the weak correlation. If all of them are met, it is judged as pattern degeneration, and the pre-matched eigenvalues ​​in its pattern tracking table are exchanged. If one of the criteria fails, it is not judged as pattern degeneration, and the order of the pre-matched eigenvalues ​​in its pattern tracking table is not exchanged.

[0084] The present invention proposes a method for fast tracking of characteristic mode patterns based on Pearson correlation coefficient. Step 1 is mainly to solve the eigenvalue and eigenvector. The specific contents are as follows:

[0085] Since the generalized eigenvalue equation of the characteristic mode theory is:

[0086] XJ n =λ n RJ n (12)

[0087] Where X is the imaginary part of the characteristic impedance Z, R is the real part of the characteristic impedance Z, λ n , J n are eigenvalues ​​and eigenvectors. X and R can be obtained by analyzing the antenna structure parameters using the moment method, or derived by eigenmode analysis using electromagnetic simulation software. Since the characteristic impedance is a matrix that changes with frequency, X and R are both matrices distributed according to frequency. Substituting the obtained [X] and [R] matrices at each frequency point, λ can be obtained by solving (1) n , J n . Then store its eigenvalues ​​and eigenvectors according to the frequency distribution. Taking the eigenvalue as an example, an m×n eigenvalue matrix will be formed, where m is the total number of modes existing in the antenna being solved under the current segmentation accuracy, and n is the number of discrete frequency points. There is a characteristic in the form of the stored eigenvalue matrix, that is, the absolute value of the eigenvalue in each column does not strictly decrease in order of magnitude. It can be preliminarily determined that its mode has been partially tracked and some modes have errors.

[0088] The present invention proposes a method for fast tracking of characteristic mode patterns based on Pearson correlation coefficient, wherein step 2 is mainly to adaptively filter characteristic values, and the specific contents are as follows:

[0089] Step 2.1: Set the feature value threshold λ thresholdTo filter out the modes that have little effect on the antenna performance. Since a mode has a greater impact on the antenna performance in the characteristic mode analysis, its characteristic value λ at a certain frequency point n should be close to zero, that is:

[0090] λ n =0 (13)

[0091] The corresponding pattern significance MS should be close to 1, that is:

[0092]

[0093] This means that the mode has a great influence on the antenna performance. Therefore, the threshold of the eigenvalue is set according to this characteristic, and each row of the eigenvalue matrix is ​​traversed. As described in step 1, a row of the eigenvalue matrix can be preliminarily regarded as a mode. If the eigenvalue of a mode is less than the threshold, it means that the mode has a great influence on the antenna performance. The eigenvalue of the mode is stored in the matrix table to be tracked in frequency order and then the next row is traversed. If the eigenvalues ​​of a mode are all greater than the threshold, step 2.2 is performed to filter the mode and save matching time.

[0094] Step 2.2: Add a counter count, whose initial value is 0. When the characteristic values ​​of a pattern are all greater than the threshold, the counter is incremented by 1 to expand the pattern screening range. As described in step 1, the current pattern does not perform pattern tracking, and some patterns are exchanged with other adjacent patterns. Therefore, according to the complexity of the antenna structure, a counter count is set. If all the characteristic values ​​of the current pattern are greater than λ threshold , then the k patterns to be traversed subsequently are judged. If the characteristic value of a certain pattern is less than the threshold, the traversal operation of step 2.1 is continued. If the characteristic values ​​of the k patterns are all greater than the threshold, the k patterns are stored in the matrix table to be tracked and then the current step is terminated to execute step 3. k is the maximum value set by the counter. The matrix table to be tracked is in the form of an a×b matrix, a is the number of patterns to be tracked after screening, b is the number of discrete frequency points, and any row is a pattern. This can expand the number of patterns for pattern matching. Although it will increase the calculation time to a certain extent, it greatly guarantees the accuracy of the calculation results.

[0095] The present invention proposes a method for fast tracking of characteristic mode patterns based on Pearson correlation coefficient, wherein the main content of step 3 is to calculate the correlation coefficient, and the specific content is as follows:

[0096] The present invention adopts the Pearson correlation coefficient formula to calculate the correlation coefficient between adjacent frequency points, and the calculation formula is as follows:

[0097]

[0098] J m , J n is the eigenvector corresponding to mode m and mode n, and are the means of the two eigenvectors, r is the calculated correlation coefficient, and the Pearson correlation coefficient is a statistic used to measure the degree of linear correlation between two variables. It is often used to describe the relationship between two continuous variables, and its value range is between -1 and 1. When r = 1, it indicates a complete positive correlation, that is, as one variable increases, the other variable will also increase in a certain proportion. When r = -1, it indicates a complete negative correlation, that is, as one variable increases, the other variable will decrease in a certain proportion. When r = 0, it means that there is no linear correlation, that is, there is no linear relationship between the two variables, but it does not mean that there is no other type of relationship between the two variables.

[0099] If the row number of the stored matrix table to be tracked is used as the mode index, since modes with large differences in mode indices will not experience mode crossing and mode degeneration, the number of correlation coefficients calculated between modes is limited, and only the correlation coefficients of the j modes adjacent to the current mode are calculated, and the mode pairs that will not experience mode crossing and mode degeneration are removed, thereby reducing the time for calculating the correlation coefficients. j can be determined depending on the complexity of the antenna structure.

[0100] The present invention proposes a method for fast tracking of characteristic mode patterns based on Pearson correlation coefficient. The main content of step 4 is to divide the strong and weak irrelevance of the pattern. The specific content is as follows:

[0101] Step 4.1: First, divide the strongly correlated mode. The strongly correlated conditions are as follows:

[0102]

[0103] ρ k is the correlation coefficient between the current mode and the next frequency mode k, ρ n is the correlation coefficient between all modes except mode k, where ρ k , ρ n is the absolute value of the correlation coefficient between patterns. That is, when there is ρ k is greater than 0.99, or there is ρ k When the other correlation coefficients are less than 0.6 under the condition that the correlation coefficient is greater than 0.95, the pattern index that meets the condition is stored in the strong correlation index table.

[0104] Step 4.2: Then perform irrelevant partitioning, the irrelevant conditions are as follows:

[0105] ρ k <0.3,k=1,2...n (17)

[0106] That is, the ρ calculated for all modes of the current mode at subsequent frequency points k If the values ​​are all less than 0.3, they are considered weakly correlated. Then the pattern indexes that meet this condition are stored in the irrelevant index table. The pattern index is the row number of the feature value corresponding to the irrelevant pattern in the pattern tracking table.

[0107] Step 4.3: The remaining patterns are weakly correlated, and the pattern indexes of the weakly correlated patterns are stored in the weakly correlated index table. The pattern index is the row number of the feature value corresponding to the weakly correlated pattern in the pattern tracking table.

[0108] The present invention proposes a method for fast tracking of characteristic mode patterns based on Pearson correlation coefficient, wherein step 5 is to process strongly correlated and uncorrelated mode pairs, and the specific contents are as follows:

[0109] Step 5.1: Process the strongly correlated pattern pairs, traverse the strongly correlated index table, and store the eigenvalues ​​of each strongly correlated pattern pair into the pattern tracking table. The number of rows in the pattern tracking table represents the number of patterns that have a greater impact on the antenna, and the number of columns is the total number of discrete frequency points. The order of the eigenvalues ​​stored in the pattern tracking table is the tracking result of the present invention. And through the strict division of strong correlation, the pattern crossing phenomenon can be corrected.

[0110] Step 5.2: Process irrelevant pattern pairs, traverse the irrelevant index table, and do not perform matching operations on the eigenvalues ​​represented by the pattern index, that is, the eigenvalues ​​of the pattern in the pattern tracking table are no longer stored at subsequent frequency points.

[0111] The present invention proposes a method for fast tracking of characteristic mode patterns based on Pearson correlation coefficient, in which the main content of step 6 is to process weakly correlated mode pairs. The specific content is as follows:

[0112] Step 6.1: Traverse the weak correlation index table and pre-match each weak correlation pattern according to the principle of eigenvalue proximity. Specifically, for a pattern, its eigenvalue changes slowly according to the frequency. Therefore, for a weak correlation pattern, pre-matching is to store the eigenvalue closest to the weak correlation pattern among all the eigenvalues ​​of the next frequency point in the corresponding pattern tracking table.

[0113] Step 6.2: Combine the pre-matched pattern pairs in pairs and calculate the four criteria. Assuming there are m weakly correlated patterns, combine them in pairs, and there are a total of For each pair of combinations, four criteria are calculated. The four criteria are as follows:

[0114] Criterion 1: Determine the number of weakly correlated patterns at the current frequency. If the number of patterns is 1, the pattern can be matched directly. If the number of patterns is greater than 1, check whether the eigenvalue at the current frequency has been matched at the previous frequency, remove the unmatched patterns, and then hand over the remaining patterns to Criterion 2 for further processing.

[0115] Criterion 2: Assume that the current frequency is f i , is working with f i+1 When matching the frequency points, weak correlation occurs. If mode degeneration occurs at this frequency point, the characteristic value curves of the two modes should appear close to each other. Specifically, at f i At |λ m-n |Should be greater than f i+1 |λ m-n If this condition is not met, it is not considered as mode degeneration.

[0116] Criterion 3: For both modes, at frequency point f i ,f i+1 Calculate the modal energy If the energy curves intersect, it means that mode degeneration has occurred. Then the pre-matched eigenvalues ​​of the two modes are exchanged for correction. After exchanging the modes here, the mode pair involving the currently matched mode in the eigenvalue difference calculation in criterion 2 should be deleted.

[0117] Criterion 4: For f1,f2,…,f i-2 ,f i-1 ,f i+1 The eigenvalues ​​of are used to fit the polynomial data using the least squares method. If i If the characteristic value at the frequency is within the error range of the data fitting curve, it is confirmed that the exchanged mode is correct.

[0118] If all four criteria are passed, it is considered to be a pattern degeneration, and its pre-matched eigenvalues ​​are exchanged. If one does not pass, matching is performed according to the pre-matched pattern.

[0119] The present invention proposes a method for fast tracking characteristic mode patterns based on Pearson correlation coefficient, wherein the formula for calculating the modal energy of criterion 3 in step 6 is:

[0120]

[0121] Among them, J i is the eigenvector corresponding to mode i at the current frequency, X e is the energy storage operator, is the electric energy stored in mode i. e It can be obtained from the following relationship:

[0122] Xm -X e =X (19)

[0123]

[0124]

[0125] Among them, X e ,X m are the electric energy and magnetic energy storage operators respectively, X is the imaginary part of the characteristic impedance, and ω is the frequency. Substituting the imaginary part X of the characteristic impedance Z obtained in step 1 and the frequency set by the antenna solution into (10), the electric energy storage operator X can be obtained: e , and then the obtained electric energy storage operator X e The modal energy can be obtained by substituting the eigenvector of mode i obtained in step 1 into (7).

[0126] The least squares polynomial data fitting of criterion 4 in step 6. Its formula is

[0127]

[0128] Among them, x i1 ,x i2 …x im is the frequency, representing the independent variable. i is the eigenvalue that changes with frequency, representing the dependent variable, b0, b1…b m is the coefficient of each independent variable that minimizes the target S. Substitute the eigenvalues ​​of the current weak correlation mode that have been tracked at the previous frequency point and the pre-matched eigenvalues ​​into y in formula (11): i , the frequency corresponding to each eigenvalue is substituted into x in formula (11) i1 ,x i2 …x im , so that S is minimized, then b0, b1…b can be solved m The value of , finally a polynomial function can be obtained, and the function curve can estimate the trend of the characteristic value trajectory of the mode.

[0129] Example 1

[0130] Embodiment 1 is a rectangular patch antenna, and its structure is as follows Figure 5 As shown in (a), the size is 120mm×60mm, combined with Figure 1 The model was built using FEKO commercial software and then the solution was set to characteristic mode analysis. The operating frequency range of FEKO software was set to 1GHz to 5GHz, the number of simulation frequency points was 26, the frequency interval was 160MHz, and the number of triangles was 286. Figure 2 , Figure 3The pre-processing and post-processing flow chart is shown in Figure 1. After solving the characteristic mode using FEKO commercial software, the impedance matrix is ​​exported to MATLAB. Then, the built-in function eig of MATLAB is called to solve the characteristic impedance for its eigenvalue and eigenvector, and store them in frequency order. For Example 1, the eigenvalue matrix dimension is 405×26, where 405 represents the total number of modes of the rectangular patch antenna at the current segmentation accuracy, and 26 is the number of discrete frequency points.

[0131] Set the threshold to 1 and the maximum value of the counter count to 5, which means to traverse the rows of the eigenvalue matrix. If a row has an eigenvalue less than 1, store the row in the matrix table to be tracked and continue to traverse the next row. If the eigenvalues ​​of a row are all greater than 1, continue to determine whether the 5 subsequent rows have eigenvalues ​​less than 1. If so, continue the previous traversal judgment operation. If not, store these 5 rows in the matrix table to be tracked. The adaptive filtering flow chart is as follows Figure 4 After the adaptive filtering mode number operation, the dimension of the final tracking matrix is ​​20×26, which means that after the adaptive filtering operation, only 20 modes pass the screening, and the remaining modes have little effect on the antenna and are filtered out, which greatly reduces the workload of subsequent calculation of correlation coefficients.

[0132] Then, when calculating the correlation coefficient between modes, compared with the traditional method of calculating the correlation coefficients between all modes between adjacent frequency points, the present invention only calculates the correlation coefficients of the 11 modes adjacent to the current mode according to the complexity of the antenna structure, which saves calculation time again. In addition, modes with very different mode indices will not have mode crossing and mode degeneracy, so this will not cause mode tracking errors.

[0133] The absolute value of the correlation coefficient is divided into strong correlation, weak correlation and no correlation according to three classification standards. For this rectangular patch antenna, due to its simple structure, the linear correlation of the eigenvectors corresponding to the eigenvalues ​​of each mode is very obvious, indicating that the currents of each mode change slowly with frequency and are independent of each other, resulting in strong correlation between the 20 modes at most frequency points. Taking the tracking frequency band 4.2-4.36GHz as an example, weak correlation terms appear at this adjacent frequency, and the weakly correlated mode indexes are 1 and 10. This indicates that mode 1 and mode 10 may have mode degeneration errors. The occurrence of mode degeneration is confirmed by pre-matching and calculation of four criteria, and then the eigenvalues ​​are exchanged to correct the mode degeneration.

[0134] To illustrate the performance and time advantages of this method, it is compared with two other pattern tracking methods. Method 1: Sort the eigenvalues, take the first 40 eigenvalues ​​to calculate the Pearson correlation coefficient between all patterns of adjacent frequency points, and then track the pattern according to the eigenvalue corresponding to the maximum correlation coefficient. Method 2: Remove the post-processing multi-criteria correction pattern degeneration process in the method proposed in this paper.

[0135] Under the same conditions, the pattern matching results of Algorithm 1 and Algorithm 2 are as follows: Figure 6 As shown in the figure, due to the relatively simple antenna structure, the linear correlation of the eigenvectors corresponding to the eigenvalues ​​of each mode is very obvious, so the mode tracking results of the two algorithms are mostly correct, but when tracking the frequency band 4.2-4.36GHz, there are still errors in mode 1 and mode 10. To further illustrate the tracking problem, the eigenvectors of mode 1 and mode 10 at four adjacent frequencies near 4.2GHz are as follows Figure 7 As shown in the figure, the results show that the mode can be correctly tracked between the two frequencies before 4.2GHz, but due to the mode degeneration between 4.2-4.36GHz, the eigenvalues ​​are close, the eigenvectors of the two modes are confused, and the eigenvectors at 4.36GHz are similar, so correlation cannot be used for correct tracking. Then the multi-criteria tracking method proposed in this invention is applied to the entire frequency band, and a new tracking result is obtained as shown in Figure 8 As shown in Figure 1, at 4.2 GHz, Mode 1 and Mode 10 successfully correct the traditional mode tracking error problem based only on the Pearson correlation coefficient, and the time comparison of the three methods is shown in Table 1:

[0136] Table 1

[0137]

[0138] From Table 1, we can see that the proposed method is superior to the tracking method based on Pearson correlation coefficient in terms of accuracy and efficiency. And the method 2 without post-processing only takes 0.22 seconds less time than the method 3 (this method), which is very valuable for improving the accuracy of the tracking results.

[0139] Example 2

[0140] Embodiment 2 is a fractal antenna, and its structure is as follows Figure 5As shown in (b), the FEKO software is set to be placed 10mm away from the infinite ground plane, with a size of 100mm×64mm. The model is modeled by the FEKO commercial software and then the solution is set to characteristic mode analysis. The operating frequency set by the FEKO software is 2.1GHz-2.8GHz, the number of simulation frequency points is 71, the frequency interval is 10MHz, and the number of triangles subdivided is 650. After using the FEKO commercial software to solve the characteristic mode, its impedance matrix is ​​exported to matlab, and then the built-in function eig of matlab is called to solve the characteristic impedance for its eigenvalue and eigenvector, and store them in frequency order. For Example 2, the dimension of its eigenvalue matrix is ​​843×71, 843 represents the total number of modes of the fractal antenna at the current subdivision accuracy, and 71 is the number of discrete frequency points.

[0141] Set the threshold to 1 and the counter count to 5, perform the adaptive filtering eigenvalue operation, and then store the filtered eigenvalues ​​in the matrix table to be tracked. After the adaptive filtering eigenvalue operation, the dimension of the matrix to be tracked is 12×71, which means that after the adaptive filtering operation, only 12 modes pass the screening, and most of the other modes have little effect on the antenna and are filtered out, which greatly reduces the workload of subsequent calculation of correlation coefficients. Then, only the correlation coefficients of the 11 modes adjacent to the current mode are calculated, which saves calculation time again.

[0142] Similarly, under the same conditions, three methods are used to track the pattern of the fractal antenna. Fig. 9 The pattern tracking results of method 1 are very poor due to the complex structure. Pattern tracking errors occurred at 2.34GHz, 2.49GHz, 2.61GHz, 2.65GHz, 2.73Ghz, and 2.74GHz. Method 2 is used to track and analyze the structure. The results are as follows: Fig.10 As shown in the figure, it can be seen that the mode tracking errors at 1, 4, and 5 can be successfully corrected, but mode degeneration occurs at 2, 3, and 6. Fig.10 The illustration of the model can more clearly see the phenomenon of mode degeneration. Because the eigenvalues ​​are very close, the eigenvectors of the two modes near this point are chaotic, resulting in the fact that the correlation-based algorithm is no longer applicable. Therefore, the multi-criteria fast tracking method proposed in this paper is used to correct the above-mentioned mode tracking errors. The tracking results are shown in Fig.11 As shown in the figure, the results show that the mode crossing and mode degeneracy problems occurring at all frequency points have been correctly corrected. Taking the modal current near the frequency of 2.49GHz as an example, Fig.12 As shown in Figure 2, the continuity of the modal current shows that the mode degeneration has been successfully corrected. The time efficiency comparison results of the three methods are shown in Table 2:

[0143] Table 2

[0144]

[0145] It can be seen from Table 2 that the proposed method of fast tracking of characteristic mode patterns based on the Pearson correlation coefficient is significantly better than the traditional algorithm in terms of performance. Compared with the algorithm 2 without post-processing, the proposed method only adds a small amount of time cost, but can greatly correct the problems of mode crossing and mode degeneration. This not only improves the accuracy of pattern tracking, but also has obvious advantages in overall efficiency, and is suitable for scenarios that require efficient and accurate pattern tracking.

[0146] In the above embodiments, the description's reference to "this embodiment" indicates that a particular feature, structure, or characteristic described in conjunction with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple occurrences of "this embodiment" do not necessarily all refer to the same embodiment.

[0147] In the above-described embodiments, although the invention has been described in conjunction with specific embodiments of the invention, many substitutions, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art based on the foregoing description. For example, other storage structures (e.g., dynamic RAM (DRAM)) may use the embodiments discussed. Embodiments of the invention are intended to encompass all such substitutions, modifications, and variations that fall within the broad scope of the appended claims.

[0148] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A multi-criteria fast tracking method for characteristic mode patterns based on Pearson correlation coefficient, characterized in that: The following steps are involved: Pre-processing stage: Step 1: According to the specific structure of the antenna, the characteristic impedance, eigenvalue and eigenvector of the antenna are solved by electromagnetic simulation software and stored in frequency order; Step 2: Filtering method 1: Adopt the adaptive filtering mode number method and set the eigenvalue threshold λ threshold , construct a counter count for counting the number of patterns that do not meet the screening conditions, set its initial value and upper limit; traverse each row of the eigenvalue matrix stored in step 1, if there is an eigenvalue less than the threshold λ threshold If the eigenvalues ​​of a row are all greater than the threshold, the counter count is incremented by 1, and the screening is stopped when the upper limit set by the counter is reached. Step 3: Filtering method 2: According to the complexity of the antenna structure, the j modes that need to be processed are screened out, and only the Pearson correlation coefficients between the j modes near the current mode between adjacent frequency points are calculated; Step 4: According to the absolute value of the Pearson correlation coefficient, set the strong correlation critical value and the irrelevant critical value. If the absolute value of the correlation coefficient is greater than the strong correlation critical value, it is classified as strongly correlated. If the absolute value of the correlation coefficient is less than the irrelevant critical value, it is classified as irrelevant. The rest are classified as weakly correlated. Post-processing stage: Step 5: For the strong correlation defined in step 4, store the corresponding eigenvalues ​​in the pattern tracking table according to the strong correlation pattern. If there is no correlation, delete the pattern and do not store it. For the weak correlation pattern, proceed to step 6. Step 6: Propose four criteria to judge and correct pattern degeneration; traverse the weakly correlated patterns, first pre-match according to the principle of eigenvalue proximity, store the eigenvalue with the smallest difference in the pattern tracking table, and then perform the criterion judgment on the weak correlation. If all the criteria are met, it is judged as pattern degeneration, and the pre-matched eigenvalues ​​in the pattern tracking table are exchanged; If one of the criteria fails, the pattern is not judged as degenerate, and the order of pre-matched eigenvalues ​​in the pattern tracking table is not exchanged.

2. The characteristic mode multi-criteria rapid tracking method based on Pearson correlation coefficient according to claim 1 is characterized in that: In step 1, according to the generalized eigenvalue equation of characteristic mode theory: XJ n =λ n RJ n (1) Where X is the imaginary part of the characteristic impedance Z, R is the real part of the characteristic impedance Z, λ n , J n are eigenvalues ​​and eigenvectors; X and R are obtained by analyzing antenna structural parameters using the moment method, or derived from eigenmode analysis using electromagnetic simulation software; X and R are matrices distributed according to frequency. Substituting the obtained [X] and [R] matrices at each frequency point, (1) is used to solve λ n , J n ; Then store its eigenvalues ​​and eigenvectors according to frequency distribution.

3. The characteristic mode multi-criteria rapid tracking method based on Pearson correlation coefficient according to claim 1 is characterized in that: Step 2 specifically includes the following steps: Step 2.1: Set the feature value threshold λ threshold ; When the eigenvalue λ of a mode at a certain frequency point in the characteristic mode analysis n When it is close to zero, that is: l n =0(2) The corresponding pattern significance MS is close to 1, that is: This indicates that the mode has a significant impact on the antenna performance; traverse each row of the eigenvalue matrix, and a row of the eigenvalue matrix is ​​initially regarded as a mode. If there is a situation where the eigenvalue of a mode is less than the threshold, the eigenvalue of the mode is stored in the matrix table to be tracked in frequency order, and then traverse the next row; if the eigenvalues ​​of a mode are all greater than the threshold, proceed to step 2.2; Step 2.2: Set a counter count with an initial value of 0. When the feature values ​​of a pattern are all greater than the threshold, the counter is incremented by 1. If all feature values ​​of the current pattern are greater than λ threshold , then the k patterns to be traversed subsequently are judged. If the eigenvalue of a pattern is less than the threshold, the traversal operation of step 2.1 is continued. If the eigenvalues ​​of the k patterns are all greater than the threshold, the k patterns are stored in the matrix table to be tracked, and then the current step is terminated and step 3 is executed; k is the upper limit value set by the counter. The matrix table to be tracked is in the form of an a×b matrix, a is the number of patterns to be tracked after screening, b is the number of discrete frequency points, and any row is a pattern.

4. The method for rapid tracking of characteristic mode patterns based on Pearson correlation coefficient according to claim 1, characterized in that: In step 3, the Pearson correlation coefficient formula is used to calculate the correlation coefficient between adjacent frequency points. The calculation formula is as follows: J m , J n is the eigenvector corresponding to mode m and mode n, and are the means of the two eigenvectors, r is the calculated correlation coefficient, and the Pearson correlation coefficient ranges from -1 to 1; when r = 1, it indicates a completely positive correlation; when r = -1, it indicates a completely negative correlation; when r = 0, it indicates no linear correlation; If the row number of the stored matrix table to be tracked is used as the mode index, only the correlation coefficients of the j modes adjacent to the current mode are calculated, and the mode pairs that will not cause mode crossing and mode degeneration are removed. j depends on the complexity of the antenna structure.

5. The characteristic mode multi-criteria fast tracking method based on Pearson correlation coefficient according to claim 1 is characterized in that: Step 4 specifically includes the following steps: Step 4.1: First, divide the strongly correlated mode. The strongly correlated conditions are as follows: ρ k is the absolute value of the correlation coefficient between the current mode and the next frequency mode k, ρ n is the absolute value of the correlation coefficient between all modes except mode k; when there is ρ k is greater than 0.99, or there is ρ k When the other correlation coefficients are less than 0.6 under the condition that the correlation coefficients are greater than 0.95, the pattern indexes that meet the condition are stored in the strong correlation index table; Step 4.2: Then perform irrelevant partitioning, the irrelevant conditions are as follows: r k <0.3,k=1,2...n(6) That is, the ρ calculated for all modes of the current mode at subsequent frequency points k If all of them are less than 0.3, they are considered to be weakly correlated; the pattern index that meets this condition is stored in the irrelevant index table; the pattern index is the row number of the eigenvalue corresponding to the irrelevant pattern in the pattern tracking table; Step 4.3: The remaining patterns are weakly correlated, and the weakly correlated pattern indexes are stored in the weakly correlated index table; the pattern index is the row number of the eigenvalue corresponding to the weakly correlated pattern in the pattern tracking table.

6. The characteristic mode multi-criteria fast tracking method based on Pearson correlation coefficient according to claim 1 is characterized in that: Step 5 specifically includes the following steps: Step 5.1: Process strongly correlated pattern pairs, traverse the strongly correlated index table, and store the eigenvalues ​​of each strongly correlated pattern pair into the pattern tracking table. The order of the eigenvalues ​​stored in the pattern tracking table is the tracking result; Step 5.2: Process irrelevant pattern pairs, traverse the irrelevant index table, and do not perform matching operations on the eigenvalues ​​represented by the pattern index, that is, the eigenvalues ​​of the pattern in the pattern tracking table are no longer stored at subsequent frequency points.

7. The method for rapid tracking of characteristic mode patterns based on Pearson correlation coefficient according to claim 1, characterized in that: Step 6 specifically includes the following steps: Step 6.1: traverse the weak correlation index table and pre-match each weak correlation pattern according to the principle of eigenvalue proximity; for the weak correlation pattern, the eigenvalue closest to the weak correlation pattern among all the eigenvalues ​​of the next frequency point is stored in the corresponding pattern tracking table in advance, which is pre-matching; Step 6.2: Combine the pre-matched pattern pairs in pairs and calculate the four criteria; assuming there are m weakly correlated patterns, combine them in pairs, and there are a total of For each pair of combinations, four criteria are calculated. The four criteria are as follows: Criterion 1: Determine the number of weakly correlated modes at the current frequency point. If the number of modes is 1, the mode can be matched directly. If the number of modes is greater than 1, check whether the eigenvalue at the current frequency has been matched at the previous frequency point, remove the unmatched modes, and then hand over the remaining modes to Criterion 2 for further processing. Criterion 2: Assume that the current frequency is f i , is working with f i+1 When the frequency points are matched, weak correlation occurs; if mode degeneration occurs at this frequency point, the characteristic value curves of the two modes appear to be close to each other. i At |λ m-n |Should be greater than f i+1 |λ m-n |, if this condition is not met, it is not judged as mode degeneration; Criterion 3: For both modes, at frequency point f i ,f i+1 Calculate the modal energy If the energy curves intersect, it means that mode degeneration has occurred; then the pre-matched eigenvalues ​​of the two modes are exchanged for correction; after the modes are exchanged here, the mode pair involving the currently matched mode in the eigenvalue difference calculated in criterion 2 is deleted; Criterion 4: For f1,f2,…,f i-2 ,f i-1 ,f i+1 The eigenvalues ​​of are used to fit the polynomial data using the least squares method. If i If the characteristic value at the frequency is within the error range of the data fitting curve, it is confirmed that the exchanged mode is correct; If all four criteria are passed, it is considered to be a pattern degeneration, and its pre-matched eigenvalues ​​are exchanged. If one does not pass, matching is performed according to the pre-matched pattern.

8. The characteristic mode multi-criteria rapid tracking method based on Pearson correlation coefficient according to claim 7 is characterized in that: In the criterion 3, the modal energy is calculated by the following formula: Among them, J i is the eigenvector corresponding to mode i at the current frequency, X e is the energy storage operator, is the electric energy stored in mode i, the electric energy storage operator X e It is obtained from the following relationship: X m -X e =X(8) Among them, X e ,X m are the electric energy and magnetic energy storage operators respectively, X is the imaginary part of the characteristic impedance, and ω is the frequency; the electric energy storage operator X is calculated using the imaginary part X of the characteristic impedance Z obtained in step 1 and the frequency set by the antenna solution e , and then use the obtained electric energy storage operator X e The modal energy is calculated by combining the eigenvector of mode i solved in step 1.

9. The method for rapid tracking of characteristic mode patterns based on Pearson correlation coefficient according to claim 7, characterized in that: The least squares polynomial data fitting of the criterion 4 is as follows: Among them, x i1 ,x i2 …x im is the frequency, representing the independent variable, y i is the eigenvalue that changes with frequency, representing the dependent variable, b0, b1…b m is the coefficient of each independent variable that minimizes the target S; the eigenvalues ​​of the current weak correlation mode that have been tracked at the previous frequency point and the pre-matched eigenvalues ​​are substituted into the y i , the frequency corresponding to each eigenvalue is substituted into the x in the formula i1 ,x i2 …x im , so that S reaches the minimum, solve b0,b1…b m The value of , finally a polynomial function is obtained, and the trend of the characteristic value trajectory of the mode can be estimated through the polynomial function curve.

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