A knowledge- and data-driven array antenna design method

Abstract

The present invention discloses a method for designing an array antenna driven by a hybrid of knowledge and data. This method successfully realizes the modeling of the active pattern of antenna elements in a fast two-dimensional array environment by introducing prior electromagnetic knowledge such as planar coupling region segmentation and two-dimensional virtual array fitting technology, combined with data-driven methods such as machine learning. Compared with the traditional machine learning-assisted modeling method, the prediction accuracy of the model is improved while reducing the computational complexity. On this basis, any traditional array antenna design method can be combined to realize fast and accurate array antenna design that takes into account mutual coupling between array elements and platform effects. This method can be used for modeling and beamforming design, low sidelobe design, and multi-beam design of different types of antennas and antenna arrays.

Description

Technical Field

[0001] The present invention belongs to the technical field of antenna design, and in particular relates to an array antenna design method driven by a mixture of knowledge and data. Background Art

[0002] As a research issue that is focused on by the electromagnetic field and microwave technology, signal processing and other majors, the rapid optimization and design of antenna arrays has always been a hot topic and difficulty that the academic community has tried to solve. Traditional signal processing methods target ideal antenna units and develop different mathematical methods to perform array synthesis. Although they can achieve good results in a relatively short period of time, they often fail to take into account the mutual coupling between antenna units and the electromagnetic influence of the device platform on which the antenna is located in actual applications. In full-wave simulation and actual use, the designed performance is usually not achieved. In recent years, some algorithms that consider mutual coupling and platform electromagnetic influence have emerged, but they are usually only applicable to the optimization of antenna unit amplitude, phase or rotation angle when the antenna unit position is fixed. The antenna unit position is rarely considered as an optimization parameter, which greatly limits the optimization performance. The reason is that if the antenna unit position is used as an optimization parameter, the active radiation pattern of the array element will change with the influence of mutual coupling and platform effect brought by its position in the platform and the position of the surrounding array elements. Therefore, it is necessary to re-perform full-wave simulation every time the array position arrangement is changed to obtain the active radiation pattern of each array element, which will greatly increase the computational complexity of the optimization problem.

[0003] In the past decade, machine learning methods have been widely introduced into the design of electronic devices such as antennas, passive devices and circuit design, and have achieved good results. At present, most machine learning-assisted antenna designs only consider the design of antenna units, but cannot solve the more complex antenna array design problem. In recent years, some literatures have proposed machine learning-assisted antenna array optimization and design methods. The most advanced one is the Active Base Element Modeling (ABEM), the core idea of ​​which is to treat all the elements in the array as active elements for unified modeling. The input of the model is the absolute position information of the active element array element under consideration and the relative position information with its surrounding adjacent elements, as well as the dimensions of interest such as frequency and angle. The output is the active pattern information of the element at the corresponding frequency and angle (which can be represented by electric field or power, etc.). The ABEM method greatly improves the efficiency of obtaining the active pattern of the element in the array antenna design. Compared with the traditional modeling method based on the overall position arrangement of the array, it has better performance, including higher design freedom and higher prediction accuracy, but it still has certain defects. First, the modeling method of ABEM is based on the learning of the radiation characteristics of each radiation angle that needs to be paid attention to. As the amount of data increases during the optimization process, the modeling and prediction speed of ABEM will increase rapidly accordingly, which will seriously affect the performance of the algorithm. More importantly, the direct application of ABEM in the design and optimization of two-dimensional arrays will be limited in two aspects: 1. Compared with linear arrays, the definition of the input parameters of the active base element (ABE) in two-dimensional arrays will be more complicated, and the relative position of other antenna units that affect ABE and ABE is difficult to quantify with a small number of parameters; 2. Compared with linear arrays, the active element pattern (AEP) in two-dimensional arrays involves more angles. The array synthesis of linear arrays usually only focuses on the radiation characteristics at different elevation angles on one plane, while the array needs to focus on the radiation characteristics at different elevation angles and azimuth angles. For commonly used machine learning methods such as Gaussian Process Regression (GPR), the computational complexity is where n d Represents the dimension of the training set. A larger training set for a planar array than a linear array will seriously restrict the efficiency of the algorithm.

[0004] Therefore, how to use machine learning to obtain a more accurate array while consuming appropriate computing resources, especially the performance modeling of antenna units at different positions in a two-dimensional array, so as to achieve prediction of the model in the optimization design, is the key to solving the actual antenna array design. Summary of the invention

[0005] The purpose of the present invention is to provide an array antenna design method driven by a mixture of knowledge and data, so as to solve the technical problem of how to use machine learning to obtain a more accurate array as much as possible under the consumption of appropriate computing resources, especially the modeling of the performance of antenna units at different positions in a two-dimensional array, so as to realize the prediction of the model in the optimization design.

[0006] In order to solve the above technical problems, the specific technical solutions of the present invention are as follows:

[0007] A knowledge- and data-driven array antenna design method that introduces planar coupling region segmentation technology and planar virtual subarray fitting technology, combined with a machine learning data-driven method, realizes the modeling of active radiation patterns of active element array elements in a fast two-dimensional array environment.

[0008] Furthermore, the planar coupling region segmentation technology regards the array element under consideration as an active element, that is, the position characteristics of each element rather than the overall arrangement of the array is used as the input of the element model for learning, and then a series of regions are divided around it to define the influence of the mutual coupling of the surrounding elements on the active radiation pattern of the active element under consideration, and the inverse of the distance between the surrounding elements and the active element under consideration is used as one of its characteristics, namely the relative position feature, and for the area where the number of adjacent units in the planar coupling area is less than the number of adjacent units that need to be considered in a coupling area, the area is completed with virtual adjacent units with infinite relative distance, thereby ensuring the continuity of the relative position feature.

[0009] Furthermore, the planar virtual subarray fitting technology regards the active radiation pattern of the active element as the array radiation pattern synthesized by an equally spaced planar virtual subarray under proper excitation, thereby converting the representation of the active radiation pattern of the active element from angle-by-angle radiation information to the excitation information of the planar virtual subarray, thereby reducing the computational complexity required for learning and predicting the active element.

[0010] Furthermore, the plane coupling region segmentation technology specifically includes the following steps: c The area is defined as the mutual coupling area that will affect the active unit pattern of the active element array, and then this area is divided into M areas according to the azimuth angle φ; for each area, the adjacent units that meet the following conditions are included in the scope to be considered:

[0011]

[0012] where i m represents the serial number of the divided coupling area, and [r m,k ,φ m,k] defines the relative position of the corresponding neighboring unit to the active element in polar coordinates, where k represents the kth closest Euclidean distance between the neighboring unit and the active element in region m, and K represents the number of neighboring units to be considered in a coupling region; in the case where the number of neighboring units in the coupling region is less than K, virtual neighboring units with infinite relative distance are used to complete the region; the input parameters of the active element defined in this way are:

[0013] l n =[x n ,1 / r n ] tr (1.2)

[0014] Among them, x n represents the absolute position of the nth active element, and r n represents the relative position between multiple array elements adjacent to the active array element under consideration and the active array element, expressed as:

[0015] r n =[r 1,1,n ,...,r 1,k,n ,...,r 1,K,n ,...,r m,k,n ,...,r M,K,n ] tr (1.3)

[0016] where r m,k,n The first subscript m represents the number of the area under consideration, the second subscript k represents the number of the adjacent unit in the area, and the third subscript n represents the number of the active element under consideration; n The reciprocal treatment of ensures the continuity of the relative position parameters, that is, the relative position parameters of adjacent units at infinity are regarded as 1 / r n =0.

[0017] Furthermore, the plane virtual subarray fitting technology specifically includes the following steps:

[0018] The characterization of the radiation information of the active element array is converted from the angle-by-angle radiation characteristics to the excitation information of an equally spaced planar virtual sub-array. The fitting process is shown in the following formula:

[0019]

[0020] where g n (u,v) represents the complex value of the active unit pattern of the active element array element to be fitted in the uv coordinate system, g ave(u,v) represents the average value of the active unit directional pattern of all array elements in the array, P represents the total number of the fitted planar virtual sub-arrays in the row direction, Q represents the total number of the fitted planar virtual sub-arrays in the column direction, and c n,p,q represents the excitation of the virtual array element n at the pth row and qth column of the planar virtual subarray, d represents the array element spacing of the planar virtual subarray, u and v represent the angle point under consideration in the uv coordinate system, and the excitation c of the planar virtual subarray is calculated by the following formula: n,p,q :

[0021]

[0022] in

[0023]

[0024] g n =[g n (u 1 ,v 1 ),...,g n (u k ,v s )] tr (1.9)

[0025] where g ave (u k ,v s ) is g ave The value of (u,v) in the corresponding uv coordinate system, the superscript "tr" represents the transpose of the matrix, and the solution of equation (1.5) is obtained by calculating the following equation:

[0026]

[0027] Where Z n =GE n .

[0028] The array antenna design method of the present invention adopting a knowledge and data hybrid drive has the following advantages:

[0029] The method provided by the present invention can take into account the change in antenna unit size, mutual coupling between units, the electromagnetic environment of the array, and the platform influence for modeling, and can be used for rapid optimization design of the directional pattern of the antenna array in the actual electromagnetic environment. In the case of the same data set, compared with the traditional machine learning-assisted method, the method provided by the present invention limits the data-driven modeling process to the input features of the ABE and the excitation information of the planar virtual subarray by introducing the planar coupling region segmentation and planar virtual subarray fitting technology, thereby making the most of the existing electromagnetic knowledge and assumptions, thereby bringing about a very effective reduction in computational complexity. Therefore, the method provided by the present invention can more accurately model the performance of antenna units in an array environment. This method can be used in the fields of beamforming design, low sidelobe design, and multi-beam design for different types of antennas and antenna arrays. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flowchart of the knowledge and data hybrid driven modeling method of the present invention.

[0031] Figure 2 (a) is a diagram showing an example of a linear array design of a microstrip antenna array of the present invention;

[0032] Figure 2 (b) is a diagram showing an example of a planar array design of a microstrip antenna array according to the present invention;

[0033] Figure 3 (a) is a typical comparison diagram of the amplitude values ​​of the AEP of the array elements modeled and predicted by the HKDT and ABEM algorithms of the present invention;

[0034] Figure 3 (b) is a typical comparison diagram of the phase values ​​of the AEP of the array element modeled and predicted by the HKDT and ABEM algorithms in the present invention;

[0035] Figure 4 It is the amplitude and phase excitation data of the sub-array obtained after the ABE generated by 100 random samplings of the present invention is fitted by the plane virtual sub-array;

[0036] Figure 5 The present invention follows P=Q=P 0 Changes in the prediction performance and computation time of the HKDT algorithm when changes;

[0037] Figure 6 It is the difference between the actual AEP of the present invention and the PEP corresponding thereto;

[0038] Figure 7 This invention is t =10 when the AEP predicted by the algorithm and the difference between it and the actual AEP;

[0039] Figure 8 This invention is t =500 when the AEP predicted by the algorithm and its difference from the actual AEP;

[0040] Fig. 9 It is the normalized predicted value of the multi-beam pattern given by HKDT at the final iteration in the planar array design example of the present invention and the actual value obtained by full-wave simulation. DETAILED DESCRIPTION

[0041] In order to better understand the purpose, structure and function of the present invention, the following further describes in detail the array antenna design method using knowledge and data hybrid drive of the present invention in conjunction with the accompanying drawings.

[0042] The present invention discloses an array antenna design method using knowledge and data hybrid drive (HKDT). This method successfully realizes the modeling of active radiation patterns of antenna elements in a fast two-dimensional array environment by introducing prior electromagnetic knowledge such as planar coupling region segmentation and two-dimensional virtual array fitting technology, combined with data-driven methods such as machine learning. Compared with the traditional machine learning-assisted modeling method, the prediction accuracy of the model is improved while the computational complexity is reduced. On this basis, any traditional array antenna design method can be combined to realize fast and accurate array antenna design that takes into account mutual coupling between array elements and platform effects.

[0043] like Figure 1 As shown in the figure, for a given antenna array, the active element array (ABE) in the two-dimensional array is defined by introducing a planar coupling region segmentation method; then, through a planar virtual subarray fitting method, the representation of the radiation information of the ABE is converted from the angle-by-angle radiation characteristics to the excitation information of the planar virtual subarray, thereby greatly reducing the computational complexity required for learning and predicting the ABE. HKDT limits the data-driven modeling process to the input features of the ABE and the excitation information of the planar virtual subarray, thereby making the most of the existing electromagnetic knowledge and assumptions, which leads to a very effective reduction in computational complexity. The following are the specific steps of a knowledge- and data-driven array antenna design method:

[0044] The first step is to treat the considered element as an ABE and then divide a series of regions around it to define the effect of the mutual coupling of the surrounding elements on its AEP. Figure 2 As shown in the figure, for the ABE under consideration, the radius around it is R c The area is defined as the mutual coupling area that will affect the AEP of ABE, and then this area is divided into M areas according to the azimuth angle φ. For each area, the adjacent units that meet the following conditions are included in the scope of consideration:

[0045]

[0046] where i m represents the serial number of the divided coupling area, and [r m,k ,φ m,k ] defines the relative position of the corresponding neighboring unit to ABE in polar coordinates, where k represents the kth closest Euclidean distance between the neighboring unit and ABE in region m, and K represents the number of neighboring units to be considered in a coupling region. For those coupling regions where the number of neighboring units is less than K (for example, ABE is located at the edge of the array, and the number of neighboring units in the coupling region facing the outside of the array is less than K), virtual neighboring units with infinite relative distance are used to complete the region. The input parameters of ABE defined in this way are:

[0047] l n =[x n ,1 / r n ] tr (1.2)

[0048] Among them, x n represents the absolute position of the nth ABE, and r n represents the relative positions between multiple array elements adjacent to the ABE under consideration and the ABE, which can be expressed as:

[0049] r n =[r 1,1,n ,...,r 1,k,n ,...,r 1,K,n ,...,r m,k,n ,...,r M,K,n ] tr (1.3)

[0050] where r m,k,n The first subscript m represents the number of the region under consideration, the second subscript k represents the number of the adjacent unit in the region, and the third subscript n represents the number of the ABE under consideration. n The reciprocal treatment of ensures the continuity of the relative position parameters, that is, the relative position parameters of adjacent units at infinity are regarded as 1 / r n = 0. By properly setting the K, M and R c The planar coupling region partitioning method fixes the number of input parameters of ABE including the design parameters.

[0051] The traditional ABEM method uses angle information as input features for training and prediction, which is a direct way to model AEP. traThe training data set of units can be expressed as:

[0052] D tra ={(u w ),y tra,w )|w=1,...,W tra} (1.4)

[0053] Where w is the serial number of the data in the training set, and the input data u w The dimension is W tra ×X tra , which can be expressed as:

[0054] u w =[l w f obj,w u obj,w v obj,w ] tr (1.5)

[0055] The number of columns of training data is X tra , l w is the input of the wth ABE, and the output data is y tra,w =[Mag{g AEP} w Pha{g AEP} w ], where Mag{g AEP} w and Pha{g AEP} w Respectively represent the amplitude and phase value of the AEP corresponding to the wth ABE, f obj,w represents the frequency value of interest, u obj,w and v obj,w They represent the values ​​of the angle points of interest in the uv coordinate system. The number of columns of training data is X tra =KM+5, and the number of rows is W tra =W ABE W f W u W v , where W ABE represents the number of ABEs in the training set, W f represents the number of frequency points in the training set, W u and W v Respectively represent the number of angle points in the training set in the uv coordinate system. As mentioned before, when W ABE As the design process grows, W traMore importantly, when dealing with the design problem of a two-dimensional array, the number of angle points that need to be processed will increase dramatically. Consider a typical two-dimensional array design problem. Assume that the algorithm requires 5 iterations to achieve the design goal. Each iteration needs to process the full-wave simulation data of 20 array elements. Considering 1 design frequency point and the angle points with an interval of 1° in the upper hemisphere, the training set will eventually grow to W. tra = 3,240,000 dimensions, making it difficult to learn and predict in engineering problems that require rapid iteration.

[0056] Therefore, the second step of HKDT is the planar virtual subarray fitting method, which converts the representation of ABE radiation information from the angle-by-angle radiation characteristics to the excitation information of an equally spaced planar virtual subarray, thereby greatly reducing the computational complexity required for learning and predicting ABE. The fitting process is shown in the following formula:

[0057]

[0058] where g n (u,v) represents the complex value of the AEP of the ABE to be fitted in the uv coordinate system, g ave (u,v) represents the average value of the AEP of all elements in the array, P and Q represent the total number of the fitted planar virtual sub-arrays in the row and column directions, respectively, and c n,p,q represents the excitation of virtual array element n at the pth row and qth column of the planar virtual subarray, d represents the array element spacing of the planar virtual subarray, and u and v represent the angle point under consideration in the uv coordinate system. The excitation c of the planar virtual subarray can be calculated by the following formula: n,p,q :

[0059]

[0060] in

[0061]

[0062] g n =[g n (u 1 ,v 1 ),...,g n (u k ,v s )] tr . (1.11)

[0063] where g ave (u k ,v s ) is g aveThe value of (u,v) in the corresponding uv coordinate system, the superscript "tr" represents the transpose of the matrix. The solution of equation (1.7) can be obtained by calculating the following equation:

[0064]

[0065] Where Z n =GE n .

[0066] Using the above-mentioned planar virtual subarray fitting method, the radiation characteristics of a given ABE can be obtained by c n This formula (1.4) can be converted into a set of T sub-training sets:

[0067] D app,t = {l t ,y app,t )|t=1,...,T} (1.13)

[0068] Where T = 2PQW f represents the number of sub-training sets, that is, a sub-training set is created for the amplitude and phase excitation of each element in the planar virtual sub-array at each frequency point;

[0069] y app,t =[c 1,t ,...,c n,t ] tr (1.14)

[0070] Each sub-training set contains X app =KM+5 columns and W app =W ABE For the above-mentioned example of actual two-dimensional array synthesis, if P=Q=5 is selected, HKDT will generate 50 sub-training sets with W rows. app =100, compared to the number of data rows W of the ABEM method tra =3240000, achieving a significant reduction in computational complexity.

[0071] The commonly used GPR machine learning method is used to discuss the difference in computational complexity between ABEM and HKDT. In the process of GPR training the hyperparameter θ, a common method is to minimize the negative log likelihood function (NLML) h NLML The computational complexity of solving the hyperparameter training mainly comes from the matrix inversion operation, and its computational complexity is where n d is the dimension of the matrix; in the process of GPR predicting the design point, its computational complexity is In general, the dimension n of the training set in data-driven methods is d It will directly determine the computational complexity of the algorithm, including the training and prediction process. By adopting the HKDT method, the computational complexity of the original ABEM training can be reduced from Reduce to The computational complexity of ABEM prediction is reduced from Reduce to The following studies the efficiency and capability of HKDT modeling from the perspectives of linear array and area array applications.

[0072] Consider Figure 2 The figure shows a design example of a 16-element microstrip antenna array. The antenna array operates at 10 GHz, and the arrangement of the elements is randomly sampled to form a training set and a validation set. In the published literature, researchers have verified that when the array element position is fixed, the AEP of each actual array element can be well fitted by a virtual linear array. Here, it will be verified that the excitation of the fitted linear array through the HKDT method can well characterize the radiation characteristics of the ABE under variable input, and can achieve better performance than ABEM.

[0073] In the published literature, a dilution factor r for the training set can be introduced in ABEM s The computational complexity is reduced at the expense of the model's predictive power. Table 1 shows the results of microstrip antenna array design at different N t and r s The performance comparison between ABEM and HKDT methods under the following parameters. The other algorithm parameters of HKDT are P=1, Q=11, K=1 and M=2. Figure 3 A typical set of HKDT and ABEM (N t =16, r s =50) algorithm modeling and predicted AEP of array elements 1-3, 7-8 and 15-16. As shown in Table 1, in N t = 16, only a set of randomly generated full-wave simulation data of microstrip antenna arrays is used to establish the training data set; while in N t =160, 10 sets of microstrip antenna arrays were generated by random algorithm and full-wave simulation was performed to establish a training data set. In addition, 10 sets of microstrip antenna arrays were generated by random algorithm and full-wave simulation was performed to establish a validation data set. RMSE was used to evaluate the prediction performance of the machine learning models constructed by ABEM and HKDT algorithms.

[0074] It can be clearly seen that compared with the ABEM method, HKDT has obvious advantages in prediction accuracy and algorithm efficiency: compared with the ABEM method without data dilution, HKDT can bring a 100-1000 times training and prediction speed advantage; in this example, ABEM needs to dilute the data 50 times to achieve similar computational efficiency as HKDT, but this will lead to a significant deterioration in prediction accuracy. More importantly, even compared with the ABEM algorithm without data dilution (that is, the performance limit of the ABEM algorithm), HKDT can still achieve better prediction accuracy performance. This means that the HKDT method can better learn the radiation characteristics of the AEP corresponding to different ABEs.

[0075] Table 1 shows the design of microstrip antenna array at different N t and r s The performance comparison between ABEM and HKDT under the parameters. Compared with the one-dimensional linear array design problem, the two-dimensional area array design is more difficult to solve directly using traditional ABEM. Consider a Figure 2 The 10-element planar microstrip antenna array shown in the figure first generates 100 groups of microstrip antenna arrays through a random algorithm, and then uses full-wave simulation to establish a data set. Figure 4 The amplitude and phase excitation data of the subarray obtained after 100 randomly sampled ABEs were fitted with a planar virtual subarray (P=Q=5) are given. It can be seen that the excitation amplitude of the array element located at the center of the virtual subarray (i.e., the array element at the same position as the ABE of interest) after fitting is near 1, while the excitation amplitudes of other array elements are near 0 and different; and the excitation phase of the array element located at the center of the virtual subarray after fitting is close to 0, while the excitation phases of other array elements are evenly distributed within a variable range. For other combinations of P and Q, the amplitude and phase excitation data of the subarray after the planar virtual subarray fitting also present a similar distribution. It can be seen that the central array element of the planar virtual subarray has the greatest influence on the AEP of the actual ABE, while other virtual array elements will also affect the AEP, thereby jointly constructing the AEP of different ABEs. The selection of parameters P and Q will have an important impact on the fitting accuracy, modeling accuracy and computational complexity of the HKDT algorithm, including fitting, training and prediction. Figure 5 The results of HKDT algorithm under different P=Q=P are given in 0 The training set is selected from 50 microstrip antenna arrays generated by the random algorithm, and the remaining 50 arrays are selected as the validation set to verify the model generated by the HKDT algorithm. It can be seen that as P 0 As the value of P increases, the calculation time of the algorithm increases rapidly, while the fitting effect of the plane virtual subarray gradually increases. 0= 3, a good fit is achieved. On the other hand, the predictive ability of the proxy model constructed by the algorithm is 0 =3 and P 0 =5, and as $P_0$ increases further, the prediction ability shows a trend of deterioration. This phenomenon indicates that for P 0 The selection should tend to be moderate, such as P 0 =3 and P 0 =5, while the larger planar virtual sub-array fitting will restrict the acquisition of the radiation characteristics of AEP by machine learning methods.

[0076] Under the influence of mutual coupling effect and platform effect between array elements, each array element has different AEP, which is obviously different from the passive element pattern (PEP). Figure 6 The actual AEP obtained by full-wave simulation of each unit in a typical 10-element 2D planar array and its difference from PEP are given. HKDT can predict the actual AEP, such as Figure 7 and Figure 8 As shown, HKDT gives the training set size of N t =10 and N t =500, that is, the prediction of the proxy model generated by the algorithm for the new array and its deviation from the actual AEP under the training set consisting of 1 and 50 randomly generated 10-element 2D microstrip antenna arrays respectively. It can be seen that in both cases, the algorithm can achieve a good prediction of the actual AEP, that is, its predicted AEP is consistent with Figure 6 As the size of the training set increases, the algorithm can achieve better predictions for new arrays, and the worst case deviation between the predicted AEP and the actual value will decrease from -11.23dB to -17.48dB.

[0077] The proposed HKDT modeling method can be used to guide the design of linear and planar array antennas considering mutual coupling and platform effects: the algorithm follows the classic MLAO architecture and implements its core modeling steps through HKDT. The specific steps are as follows:

[0078] Step 1, initialization: This step includes the preparation of parameters and data. Under given design constraints and optimization goals, the algorithm establishes the initial training set D of AEP and S parameters through full-wave simulation method. i =(u i ,y iThe initial training set can be obtained by random sampling or by optimizing the array arrangement using the ideal unit radiation pattern, followed by full-wave simulation. The ideal unit radiation pattern can be specified as an omnidirectional pattern, PEP, or the average of the AEP obtained in the previous design.

[0079] Step 2: Modeling: Using the initial training set obtained in step 1, the radiation and reflection characteristics including AEP and S parameters are modeled by the HKDT method to obtain the proxy model R s,i (u). Considering the smaller training set used by HKDT, GPR can be used to train the initial training set.

[0080] Step 3, optimization: Use the proxy model R obtained in step 3 s,i (u), under given constraints, optimize for given design goals to obtain the optimized array distribution and excitation u opt,i , and the predicted value y of AEP given by the surrogate model opt,pre,i The optimization method here can adopt classic evolutionary algorithms or convex optimization methods.

[0081] Step 4: Verify: Optimize the array distribution and excitation results u opt,i The full-wave simulation method is used for verification, and the verified result y opt,val,i , and add it to the training set to obtain the updated training set D i ′=(u i ′,y i ′). The optimal result in the training set is checked to see if it meets the algorithm termination condition. If not, it returns to step 2 and re-uses HKDT to update the proxy model online, and i=i+1. If the termination condition is met, the result is output.

[0082] The following will demonstrate the application of HKDT in array synthesis through a planar antenna array design example. In recent years, with the rapid development of 5G and B5G applications, the beam scanning capability of the array has become one of the most important design indicators in the design of modern mobile communication arrays. Consider a 40-element microstrip antenna array design. In the initialization step, the array element pattern is used. Perform initial optimization on the array arrangement. Multi-beam includes normal beam (u s1 =v s1 = 0) and the beam deviating from the normal direction (u s2 =v s2 =-sin(π / 9),u s3 =-sin(π / 9),v s3 =0,u s4 =0,v s4=-sin(π / 9),u s5 =sin(π / 9),v s5 =0,u s6 =0 and v s6 =sin(π / 9)). The minimum spacing between array elements is set to d min =0.5λ, the main lobe radius of the beam is set to r b =0.23. The position area of ​​the array element is limited to L max =5λ, and a series of metal blocks are placed at random positions to simulate the more complex electromagnetic environment in actual applications. The optimization goal is to achieve the lowest multi-beam SLL under the same array position arrangement.

[0083] The array was optimized using the HKDT method and GA with algorithm parameters of P=5, Q=5, K=4 and M=8. In the initialization step, the array position was optimized using the ideal unit pattern and verified using full-wave simulation. The optimization result was that the worst SLL index of the multi-beam was -12.95dB. After full-wave simulation verification, the index deteriorated to -11.14dB, where the SLL indicators of the six beams were -13.05dB, -12.33dB, -12.39dB, -11.14dB, -11.67dB and -11.82dB respectively. The radiation performance of the array after algorithm optimization is as follows Fig. 9 As shown in the figure, its SLL index is improved to -13.04dB, and the SLL indexes of the six beams are -14.36dB, -13.25dB, -13.22dB, -13.10dB, -13.11dB and -13.04dB respectively. During the iteration process, the RMSE between the HKDT prediction value and the verification value is reduced from 0.8319 to 0.3199.

[0084] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A knowledge and data driven array antenna design method, characterized in that: The introduction of planar coupling region segmentation technology and planar virtual sub-array fitting technology, combined with machine learning data-driven methods, realizes the modeling of active directional patterns of active element array elements in a fast two-dimensional array environment; The plane coupling region segmentation technology regards the considered array element as an active element, that is, the position feature of each array element rather than the arrangement of the entire array is used as the input of the array element model for learning, and then a series of regions are divided around it to define the influence of the mutual coupling of the surrounding array elements on the active radiation pattern of the considered active element array element, and the reciprocal of the distance between the surrounding array elements and the considered active element array element is used as one of its features, namely, the relative position feature, and for the area where the number of adjacent units in the plane coupling area is less than the number of adjacent units required to be considered in a coupling area, the virtual adjacent units with infinite relative distance are used to complete the area, thereby ensuring the continuity of the relative position feature; The planar virtual subarray fitting technology regards the active radiation pattern of the active element array as an array radiation pattern synthesized by an equally spaced planar virtual subarray under proper excitation, thereby converting the representation of the active radiation pattern of the active element array element from angle-by-angle radiation information to the excitation information of the planar virtual subarray, thereby reducing the computational complexity required for learning and predicting the active element array element; The planar coupling region segmentation technology specifically includes the following steps: c The area is defined as the mutual coupling area that will affect the active unit pattern of the active element array, and then this area is divided into M areas according to the azimuth angle φ; for each area, the adjacent units that meet the following conditions are included in the scope to be considered: where i m represents the serial number of the divided coupling area, and [r m,k ,φ m,k ] defines the relative position of the corresponding neighboring unit to the active element in polar coordinates, where k represents the kth closest Euclidean distance between the neighboring unit and the active element in region m, and K represents the number of neighboring units to be considered in a coupling region; in the case where the number of neighboring units in the coupling region is less than K, virtual neighboring units with infinite relative distance are used to complete the region; the input parameters of the active element defined in this way are: l n ＝[x n ,1 / r n ] tr (1.2) Among them, x n represents the absolute position of the nth active element, tr represents the transpose of the matrix, and r n represents the relative position between multiple array elements adjacent to the active array element under consideration and the active array element, expressed as: r n ＝[r 1,1,n ,...,r 1,k,n ,...,r 1,K,n ,...,r m,k,n ,...,r M,K,n ] tr (1.3) where r m,k,n The first subscript m represents the number of the area under consideration, the second subscript k represents the number of the adjacent unit in the area, and the third subscript n represents the number of the active element under consideration; n The reciprocal treatment of ensures the continuity of the relative position parameters, that is, the relative position parameters of adjacent units at infinity are regarded as 1 / r n =0; The planar virtual subarray fitting technology specifically includes the following steps: The characterization of the radiation information of the active element array is converted from the angle-by-angle radiation characteristics to the excitation information of an equally spaced planar virtual sub-array. The fitting process is shown in the following formula: where g n (u,v) represents the complex value of the active unit pattern of the active element array element to be fitted in the uv coordinate system, g ave (u,v) represents the average value of the active unit directional pattern of all array elements in the array, P represents the total number of the fitted planar virtual sub-arrays in the row direction, Q represents the total number of the fitted planar virtual sub-arrays in the column direction, and c n,p,q represents the excitation of the virtual array element n at the pth row and qth column of the planar virtual subarray, d represents the array element spacing of the planar virtual subarray, u and v represent the angle point under consideration in the uv coordinate system, and the excitation c of the planar virtual subarray is calculated by the following formula: n,p,q : in g n =[g n (u1,v1),...,g n (u k ,v s )] tr (1.9) where g ave (u k ,v s ) is g ave The value of (u,v) in the corresponding uv coordinate system is obtained by calculating the following formula to obtain the solution of equation (1.5): Where Z n =GE n .

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