Sparse array beam synthesis method based on equivalent subarray strategy

Abstract

The invention discloses a sparse array beam synthesis method based on an equivalent subarray strategy, and relates to the technical field of array antenna beam synthesis. The method comprises the following steps: firstly, equivalently deriving a large-scale sparse array scattering field by using a small-scale sparse sub-array scattering field according to an equivalent sub-array strategy; the relation between a sparse array scattering matrix and a radiation field is obtained through theoretical derivation, and calculation of a large-scale sparse array radiation field is achieved; and finally, comprehensively optimizing a sparse array directional diagram by using a HyGADE algorithm, and introducing a large-scale sparse array radiation field into a fitness function of the algorithm to realize sparse array beam synthesis based on an equivalent subarray strategy. According to the method, the mutual coupling effect between the antenna units is considered, and accurate design of the sparse array is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of array antenna beam synthesis, and in particular to a sparse array beam synthesis method based on an equivalent subarray strategy. Background Art

[0002] Sparse array antennas are antenna elements that are sparsely arranged over a certain aperture. Compared to uniform arrays, sparse arrays can achieve antenna radiation characteristics with fewer array elements, which can simplify the antenna feed structure, reduce the weight of the antenna system, and reduce the cost of the antenna. Sparse arrays have been widely used in wireless communications, radar, navigation and other fields.

[0003] Sparse array beam synthesis technology is the core and difficult problem in the study of sparse array antennas. The traditional sparse array synthesis method usually adopts the pattern product theorem and combines it with the intelligent optimization algorithm for optimization calculation. This method regards all antenna units as independent units that are completely identical and do not affect each other, ignoring the mutual coupling effect between antenna units, resulting in a certain difference between the design results and the actual results. In addition, the performance of traditional intelligent optimization algorithms has its own characteristics. Therefore, it is particularly important to find an accurate and efficient sparse array beam synthesis method that takes into account the mutual coupling effect. Summary of the invention

[0004] In view of this, the present invention proposes a sparse array beam synthesis method based on an equivalent subarray strategy. The method realizes the equivalent derivation of a large-scale sparse array scattering field using a small-scale sparse subarray scattering field, thereby realizing sparse array beam synthesis under mutual coupling conditions.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A sparse array beam synthesis method based on an equivalent subarray strategy comprises the following steps:

[0007] Step 1: According to the index requirements of the sparse array radiation pattern, determine the parameters of the sparse array antenna: specifically including antenna unit design, subarray scale and antenna unit spacing; wherein the subarray scale includes the upper limit M of the number of antenna unit rows, the upper limit N of the number of antenna unit columns and the total number T of antenna units in the sparse array antenna, T∈[1,MN-1]; the direction of the antenna unit row is recorded as the x-axis direction, the direction of the antenna unit column is recorded as the y-axis direction, and the direction perpendicular to the xy plane of the sparse array antenna and facing outward is recorded as the z-axis direction; the distance between the center points of the antenna units in two adjacent rows is recorded as , the distance between the center points of two adjacent columns of antenna units is recorded as ;

[0008] Step 2, construct multiple small-scale sparse subarray models, and calculate the scattering field of each small-scale sparse subarray model according to the antenna unit design;

[0009] Step 3, create a sparse array initial population, each individual in the population represents a sparse array beam synthesis scheme; set the maximum number of iterations and the fitness value threshold;

[0010] Step 4: Based on the current population, a new population of the same size is generated using the differential evolution method, and the new population is mixed with the current population;

[0011] Step 5, according to the scattering fields corresponding to various small-scale sparse subarray models, combined with the equivalent subarray strategy, calculate the radiation field of the sparse array antenna corresponding to each individual in the mixed population;

[0012] Step 6, based on the radiation field of the sparse array antenna corresponding to each individual in the mixed population, calculate the fitness value corresponding to each individual, sort the individuals in order from small to large fitness values, and retain half of the individuals with small fitness values;

[0013] Step 7: For the retained individuals, perform the selection, crossover, and mutation operations of the genetic algorithm to generate a new generation of population;

[0014] Step 8, calculate the fitness value of each individual in the new generation population, and record the individual corresponding to the minimum fitness value as the optimal individual. If the fitness value of the optimal individual in the current iteration process is less than the fitness value threshold, or the maximum number of iterations has been reached, the sparse array beam synthesis scheme corresponding to the optimal individual in the current iteration process is used as the sparse array beam synthesis scheme outputted finally. Otherwise, execute step 4 based on the new generation population to proceed to the next round of iteration.

[0015] Furthermore, the specific method of step 2 is:

[0016] Construct multiple 3*3 sparse subarray models: Specifically, the spacing between two adjacent rows of antenna units in each 3*3 sparse subarray model is The spacing between two adjacent columns of antenna units is ; An antenna unit is set at the center position of each 3*3 sparse subarray model. According to whether there are antenna units at the four positions of the first row and second column, the second row and first column, the second row and third column, and the third row and second column of the 3*3 sparse subarray model, 16 3*3 sparse subarray models are constructed, and their corresponding scattering fields are calculated according to the antenna unit design.

[0017] Furthermore, the specific method of creating the sparse array initial population in step 3 is:

[0018] Step 301, setting the population size P;

[0019] Step 302, randomly sorting T 1s and MN-T 0s, so as to construct a sparse array matrix with M rows and N columns; wherein 1 indicates that an antenna unit is provided at the corresponding position of the sparse array antenna, and 0 indicates that there is no antenna unit at the corresponding position of the sparse array antenna;

[0020] Step 303, repeating step 302 until P different M-row and N-column sparse array matrices are generated;

[0021] Step 304 , for each sparse array matrix with M rows and N columns, extract each row of data in turn, and splice them in order to obtain a binary chromosome with a length of MN, which is recorded as an individual in the sparse array initial population.

[0022] Furthermore, the specific method of step 4 is:

[0023] Step 401, randomly select three individuals in the current population, then randomly select two individuals from the selected three individuals, calculate the vector difference between the two individuals and sum the vector difference with the third individual, thereby generating a new individual;

[0024] Among them, in the process of calculating the vector difference of two individuals and the sum of the vector difference and the third individual, the corresponding bit data are calculated separately. For the summed individuals, if a bit data is 2, it is updated to 1, and if a bit data is -1, it is updated to 0;

[0025] Step 402, judging the newly generated individual: if the number of 1s in its binary chromosome is greater than T, randomly select some 1s in the binary chromosome and change them to 0s, so that the number of 1s in the binary chromosome remains at T;

[0026] If the number of 1s in the binary chromosome is less than T, some 0s in the binary chromosome are randomly selected and changed to 1s so that the number of 1s in the binary chromosome remains T;

[0027] If the number of 1s contained in its binary chromosome is exactly T, no change is made;

[0028] Step 403, repeating steps 401 and 402 until a new population of size P is generated, and the new population is mixed with the current population.

[0029] Furthermore, the specific method of step 5 is:

[0030] Step 501, for each individual in the mixed population, obtain its corresponding sparse array matrix. If the value at the position of the mth row and the nth column in the sparse array matrix is ​​1, then according to the values ​​of the four adjacent upper, lower, left and right positions, m=1,2,3,...,M, n=1,2,3,...,N, a certain 3*3 sparse subarray model is matched, and the scattering field of the matched 3*3 sparse subarray model is recorded as the scattering field corresponding to the current position. ; If the value at the position of the mth row and nth column in the sparse array matrix is ​​0, then the scattering field corresponding to the current position is recorded =0;

[0031] Among them, for the values ​​of the first row, Mth row, first column, and Nth column in the sparse array matrix, if they do not have values ​​in any of the four adjacent upper, lower, left, and right positions, the values ​​of the corresponding missing adjacent upper, lower, left, and right positions are recorded as 0, and the 3*3 sparse subarray model is matched accordingly;

[0032] Step 502, based on the scattering field corresponding to each position in the sparse array matrix, calculate the radiation field E of the corresponding sparse array antenna:

[0033] ;

[0034] in, is the radiation field of the antenna unit when excited by a unit voltage source, is the wave number, ; is the wavelength; is the incident voltage of the antenna unit at the position of the mth row and the nth column in the sparse array antenna. If there is no antenna unit at the position of the mth row and the nth column in the sparse array antenna, then ; j represents the imaginary unit, is the angle between the beam direction and the z-axis direction of the sparse array, It is the angle between the projection of the beam direction on the xoy plane and the x-axis.

[0035] Furthermore, the specific method of calculating the fitness value corresponding to each individual in step 6 is:

[0036] Step 601, for the radiation field E of the current individual, calculate its corresponding directivity pattern, and further calculate the maximum sidelobe level of the sparse array antenna corresponding to the current individual And gain ;

[0037] Step 602: Calculate the fitness value corresponding to the current individual :

[0038] ;

[0039] in, is a coefficient, the value range is 0~1, and it satisfies ; is the target sidelobe level in the specification requirements of the sparse array pattern, is the target gain in the specification requirement for the sparse array pattern.

[0040] Furthermore, the specific method of step 7 is:

[0041] Step 701, sort all the retained individuals in order of fitness value from small to large, and select Q individuals with small fitness values, 1<Q<P-1;

[0042] Step 702, randomly select q individuals from the selected Q individuals, and record the individual with the smallest fitness value among the q individuals as a parent individual, 1<q<Q-1;

[0043] Step 703, repeating step 702 until 2P parent individuals are obtained, grouping the 2P parent individuals into groups of two, performing a crossover operation on each group of parent individuals, and obtaining P offspring individuals;

[0044] Step 704, performing a mutation operation on the P offspring individuals after the crossover to obtain P mutated offspring individuals;

[0045] Step 705, for each mutated offspring individual, a judgment is made: if the number of 1s in its binary chromosome is greater than T, some 1s in the binary chromosome are randomly selected and changed to 0s, so that the number of 1s in the binary chromosome remains at T;

[0046] If the number of 1s in the binary chromosome is less than T, some 0s in the binary chromosome are randomly selected and changed to 1s so that the number of 1s in the binary chromosome remains T;

[0047] If the number of 1s contained in its binary chromosome is exactly T, no change will be made; thus a new generation of population is generated.

[0048] Due to the adoption of the above technical solution, the beneficial effects of the present invention compared with the prior art are:

[0049] 1. The present invention derives the relationship between the scattering matrix and the radiation field of a sparse array. On this basis, combined with the equivalent subarray strategy, the calculation of the radiation field of a large-scale sparse array under the condition of mutual coupling of antenna units is realized. The sparse array radiation field calculated by this method is very close to the simulation result. This method realizes the rapid calculation of the radiation field of a large-scale sparse array, laying the foundation for realizing sparse array beam synthesis considering mutual coupling.

[0050] 2. The present invention improves the intelligent optimization algorithm used in beam synthesis, which combines the genetic algorithm with the differential evolution algorithm and improves the algorithm's operator, effectively improving the performance of the optimization algorithm. This method can perform sparse array beam synthesis under the condition of mutual coupling, realizes the precise design of sparse array antennas, and has certain engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of a 3*3 sparse subarray model corresponding to a unit adjacent to a central unit of a sparse array beam synthesis method based on an equivalent subarray strategy in an embodiment of the present invention.

[0052] Figure 2 Schematic diagram of a 3*3 sparse subarray model corresponding to two adjacent units of a central unit in an embodiment of the present invention.

[0053] Figure 3 Schematic diagram of a 3*3 sparse subarray model corresponding to three adjacent units of a central unit in an embodiment of the present invention.

[0054] Figure 4 Schematic diagram of a 3*3 sparse subarray model corresponding to four adjacent units of a central unit in an embodiment of the present invention.

[0055] Figure 5 Schematic diagram of a 3*3 sparse subarray model corresponding to 0 adjacent units of a central unit in an embodiment of the present invention.

[0056] Figure 6 Schematic diagram of equivalent sub-array strategy in an embodiment of the present invention.

[0057] Figure 7 Schematic diagram of an N-element uniform linear array in an embodiment of the present invention.

[0058] Figure 8 Schematic diagram of a Ka-band antenna unit in an embodiment of the present invention.

[0059] Fig. 9 It is a schematic diagram of the arrangement of sparse array units in an embodiment of the present invention.

[0060] Fig.10 Schematic diagram of the convergence performance curve in an embodiment of the present invention.

[0061] Fig.11 1 is the E-plane normalized radiation pattern of the sparse array and the uniform array at the frequency of 19.5 GHz in the embodiment of the present invention.

[0062] Fig.12 1 is the H-plane normalized radiation pattern of the sparse array and the uniform array at the frequency of 19.5 GHz in the embodiment of the present invention.

[0063] Fig.13 It is the E-plane sparse array directional pattern obtained by using simulation software, classical directional pattern superposition method and the method of the present invention in the embodiment of the present invention.

[0064] Fig.14 It is the H-plane sparse array directional pattern obtained by using simulation software, classical directional pattern superposition method and the method of the present invention in the embodiment of the present invention. DETAILED DESCRIPTION

[0065] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0066] A sparse array beam synthesis method based on an equivalent subarray strategy comprises the following steps:

[0067] Step 1: According to the index requirements of the sparse array radiation pattern, determine the parameters of the sparse array antenna: specifically including antenna unit design, subarray scale and antenna unit spacing; wherein the subarray scale includes the upper limit M of the number of antenna unit rows, the upper limit N of the number of antenna unit columns and the total number T of antenna units in the sparse array antenna, T∈[1,MN-1]; the direction of the antenna unit row is recorded as the x-axis direction, the direction of the antenna unit column is recorded as the y-axis direction, and the direction perpendicular to the xy plane of the sparse array antenna and facing outward is recorded as the z-axis direction; the distance between the center points of the antenna units in two adjacent rows is recorded as , the distance between the center points of two adjacent columns of antenna units is recorded as ; and are larger than the unit size of the antenna unit;

[0068] Step 2, construct multiple small-scale sparse subarray models, and calculate the scattering field of each small-scale sparse subarray model according to the antenna unit design;

[0069] Step 3, create a sparse array initial population, each individual in the population represents a sparse array beam synthesis scheme; set the maximum number of iterations and the fitness value threshold;

[0070] Step 4: Based on the current population, a new population of the same size is generated using the differential evolution method, and the new population is mixed with the current population;

[0071] Step 5, according to the scattering fields corresponding to various small-scale sparse subarray models, combined with the equivalent subarray strategy, calculate the radiation field of the sparse array antenna corresponding to each individual in the mixed population;

[0072] Step 6, based on the radiation field of the sparse array antenna corresponding to each individual in the mixed population, calculate the fitness value corresponding to each individual, sort the individuals in order from small to large fitness values, and retain half of the individuals with small fitness values;

[0073] Step 7: For the retained individuals, perform the selection, crossover, and mutation operations of the genetic algorithm to generate a new generation of population;

[0074] Step 8, calculate the fitness value of each individual in the new generation population, and record the individual corresponding to the minimum fitness value as the optimal individual. If the fitness value of the optimal individual in the current iteration process is less than the fitness value threshold, or the maximum number of iterations has been reached, the sparse array beam synthesis scheme corresponding to the optimal individual in the current iteration process is used as the sparse array beam synthesis scheme outputted finally. Otherwise, execute step 4 based on the new generation population to proceed to the next round of iteration.

[0075] Furthermore, the specific method of step 2 is:

[0076] Construct multiple 3*3 sparse subarray models: Specifically, the spacing between two adjacent rows of antenna units in each 3*3 sparse subarray model is The spacing between two adjacent columns of antenna units is ; An antenna unit is set at the center position of each 3*3 sparse subarray model. According to whether there are antenna units at the four positions of the first row and second column, the second row and first column, the second row and third column, and the third row and second column of the 3*3 sparse subarray model, 16 3*3 sparse subarray models are constructed, and their corresponding scattering fields are calculated according to the antenna unit design.

[0077] Furthermore, the specific method of creating the sparse array initial population in step 3 is:

[0078] Step 301, setting the population size P;

[0079] Step 302, randomly sorting T 1s and MN-T 0s, so as to construct a sparse array matrix with M rows and N columns; wherein 1 indicates that an antenna unit is provided at the corresponding position of the sparse array antenna, and 0 indicates that there is no antenna unit at the corresponding position of the sparse array antenna;

[0080] Step 303, repeating step 302 until P different M-row and N-column sparse array matrices are generated;

[0081] Step 304 , for each sparse array matrix with M rows and N columns, extract each row of data in turn, and splice them in order to obtain a binary chromosome with a length of MN, which is recorded as an individual in the sparse array initial population.

[0082] Furthermore, the specific method of step 4 is:

[0083] Step 401, randomly select three individuals in the current population, then randomly select two individuals from the selected three individuals, calculate the vector difference between the two individuals and sum the vector difference with the third individual, thereby generating a new individual;

[0084] Among them, in the process of calculating the vector difference of two individuals and the sum of the vector difference and the third individual, the corresponding bit data are calculated separately. For the summed individuals, if a bit data is 2, it is updated to 1, and if a bit data is -1, it is updated to 0;

[0085] Specifically, the vector difference between two individuals is the difference in the corresponding gene code, and the sum of the vector difference and the third individual is the sum of the corresponding gene code, 0-0=0, 0-1=-1, 1-0=1, 1-1=0, 0+0=0, 0+1=1, 1+1=2, -1+0=-1, -1+1=0, 1+1=2;

[0086] Step 402, judging the newly generated individual: if the number of 1s in its binary chromosome is greater than T, randomly select some 1s in the binary chromosome and change them to 0s, so that the number of 1s in the binary chromosome remains at T;

[0087] If the number of 1s in the binary chromosome is less than T, some 0s in the binary chromosome are randomly selected and changed to 1s so that the number of 1s in the binary chromosome remains T;

[0088] If the number of 1s contained in its binary chromosome is exactly T, no change is made;

[0089] Step 403, repeating steps 401 and 402 until a new population of size P is generated, and the new population is mixed with the current population.

[0090] Furthermore, the specific method of step 5 is:

[0091] Step 501, for each individual in the mixed population, obtain its corresponding sparse array matrix. If the value at the position of the mth row and the nth column in the sparse array matrix is ​​1, then according to the values ​​of the four adjacent upper, lower, left and right positions, m=1,2,3,...,M, n=1,2,3,...,N, a certain 3*3 sparse subarray model is matched, and the scattering field of the matched 3*3 sparse subarray model is recorded as the scattering field corresponding to the current position. ; If the value at the position of the mth row and nth column in the sparse array matrix is ​​0, then the scattering field corresponding to the current position is recorded =0;

[0092] Among them, for the values ​​of the first row, Mth row, first column, and Nth column in the sparse array matrix, if they do not have values ​​in any of the four adjacent upper, lower, left, and right positions, the values ​​of the corresponding missing adjacent upper, lower, left, and right positions are recorded as 0, and the 3*3 sparse subarray model is matched accordingly;

[0093] Step 502, based on the scattering field corresponding to each position in the sparse array matrix, calculate the radiation field E of the corresponding sparse array antenna:

[0094] ;

[0095] in, is the radiation field of the antenna unit when excited by a unit voltage source, is the wave number, ; is the wavelength; is the incident voltage of the antenna unit at the position of the mth row and the nth column in the sparse array antenna. If there is no antenna unit at the position of the mth row and the nth column in the sparse array antenna, then ; j represents the imaginary unit, is the angle between the beam direction and the z-axis direction of the sparse array, It is the angle between the projection of the beam direction on the xoy plane and the x-axis.

[0096] Furthermore, the specific method of calculating the fitness value corresponding to each individual in step 6 is:

[0097] Step 601, for the radiation field E of the current individual, calculate its corresponding directivity pattern, and further calculate the maximum sidelobe level of the sparse array antenna corresponding to the current individual And gain ;

[0098] Step 602: Calculate the fitness value corresponding to the current individual :

[0099] ;

[0100] in, is a coefficient, the value range is 0~1, and it satisfies ; is the target sidelobe level in the specification requirements of the sparse array pattern, is the target gain in the specification requirement for the sparse array pattern.

[0101] Furthermore, the specific method of step 7 is:

[0102] Step 701, sort all the retained individuals in order of fitness value from small to large, and select Q individuals with small fitness values, 1<Q<P-1;

[0103] Step 702, randomly select q individuals from the selected Q individuals, and record the individual with the smallest fitness value among the q individuals as a parent individual, 1<q<Q-1;

[0104] Step 703, repeating step 702 until 2P parent individuals are obtained, grouping the 2P parent individuals into groups of two, performing a crossover operation on each group of parent individuals, and obtaining P offspring individuals;

[0105] Step 704, performing a mutation operation on the P offspring individuals after the crossover to obtain P mutated offspring individuals;

[0106] Step 705, for each mutated offspring individual, a judgment is made: if the number of 1s in its binary chromosome is greater than T, some 1s in the binary chromosome are randomly selected and changed to 0s, so that the number of 1s in the binary chromosome remains at T;

[0107] If the number of 1s in the binary chromosome is less than T, some 0s in the binary chromosome are randomly selected and changed to 1s so that the number of 1s in the binary chromosome remains T;

[0108] If the number of 1s contained in its binary chromosome is exactly T, no change will be made; thus a new generation of population is generated.

[0109] Specifically, in a sparse array, since the arrangement of antenna units is random, it is impossible to generalize the scattering field of a sparse array using a single sparse subarray. Therefore, it is necessary to analyze the scattering field of sparse subarrays with different arrangements. In the mutual coupling analysis of sparse arrays, in order to simplify the calculation, only the influence of the four antenna units closest to a specific antenna unit in the array can be considered. Figure 1 to Figure 5 As shown in the figure, there are 3*3 sparse sub-arrays with different arrangements, where red represents the central unit of the sub-array and yellow represents the edge unit of the sub-array. Including 1 unit around, 2 units around, 3 units around, 4 units around and no units around. The scattering matrix of the sparse sub-array can be obtained by simulation software. Figure 6 As shown in the figure, it is a schematic diagram of the equivalent subarray strategy for using 3*3 sparse subarrays to derive the scattering field of a 5*5 sparse array. In the target sparse array to be solved, according to Figure 1 to Figure 5 By determining the sparse subarray arrangement corresponding to each unit in turn and performing equivalent substitution, the scattering field of a large-scale sparse array can be equivalently deduced using the scattering field of a small-scale sparse subarray, and finally the scattering matrix of the large-scale sparse array can be obtained.

[0110] Among them, Figure 6 For the antenna unit in the second row and the first column, the antenna unit on its left is recorded as None. For the antenna unit in the first row and the fifth column, the antenna units on the upper, left, and right sides are recorded as None. For the antenna unit in the fifth row and the fifth column, the antenna units on the left, right, and bottom sides are recorded as None. Figure 1 to Figure 5 An equivalent replacement for the 3*3 sparse submatrix in .

[0111] The derivation of the relationship between the sparse array scattering matrix and the radiation field is given below.

[0112] We generally believe that the total radiation field of an array is equal to the superposition of the radiation fields of all units in the array. The definition of unit radiation field is: in the array environment, only this unit is excited by a unit source, and all other units are connected to the array radiation field under matching loads. This radiation field is called the active unit radiation pattern. Sparse arrays can be regarded as those obtained by removing some units from a uniform array, so sparse arrays can be studied from the perspective of uniform arrays. Figure 7 As shown in Figure 1, for a uniform linear array of N units, it can be regarded as an N-port network. Assuming that all units are excited by voltage sources, the incident voltage waves of each antenna unit in the array are , , ..., , the reflected voltage waves are , , ..., , then the relationship between the incident wave and the reflected wave can be expressed as:

[0113] (1)

[0114] Its matrix form can be expressed as:

[0115] [ V 1 − V 2 − ⋮ V N − ] = [ S 11 S 12 ⋯ S 1 N S 21 S 21 ⋯ S 2 N ⋮ ⋮ ⋮ ⋮ S N 1 S N 2 ⋯ S NN ] [ V 1 + V 2 + ⋮ V N + ] (2)

[0116] in, is the scattering matrix.

[0117] In the array, the total port voltage of the nth unit is:

[0118] (3)

[0119] Therefore, the far-field radiation field of a uniform linear array composed of N identical antenna elements can be expressed as:

[0120] (4)

[0121] in, is the radiation field of the unit when excited by a unit voltage source, is the wave number, ; is the wavelength; is the unit spacing; is the angle between the beam direction and the z-axis direction of the sparse array, It is the angle between the projection of the beam direction on the xoy plane and the x-axis.

[0122] Substituting formula (3) into formula (4), we can get:

[0123] (5)

[0124] If each unit is excited by a unit voltage source, that is, , then formula (5) can be expressed as:

[0125] (6)

[0126] The above calculation method of array antenna radiation pattern is also applicable to uniform planar array antenna, except that the calculation formula of linear array antenna array factor needs to be replaced by the calculation formula of planar array array factor. Assume that the uniform planar array is located in the xoy plane, the number of units in the x-axis direction is M, and the unit spacing is , the number of units in the y-axis direction is N, and the unit spacing is , the total port voltage of the (m, n)th unit of the planar array is:

[0127] (7)

[0128] Therefore, the radiation field of the planar array can be written as follows:

[0129] (8)

[0130] Since a sparse array is considered to be a uniform array with some units removed, the above conclusions about uniform planar arrays are extended to planar sparse arrays. If the units of the sparse array are all excited by a unit voltage source, then the retained units , the discarded unit , this method can be used to obtain the relationship between the sparse array scattering matrix and the radiation field.

[0131] The specific steps of the HyGADE algorithm are given below.

[0132] Step 1: Set optimization parameters and create an initial population.

[0133] Step 2: Generate a new population using the differential evolution algorithm and mix it with the current population. The steps of the differential evolution algorithm to generate a new population are: first randomly select three individuals from the original population, then select any two individuals from them, calculate the vector difference between the two individuals and sum it with the third individual, and then generate new individuals. Repeat this process many times to generate a new population of the same size as the original population.

[0134] Step 3: Sort the individuals in the population according to their fitness and retain the first half of the better individuals.

[0135] Step 4: Execute the genetic algorithm operators (selection, crossover, mutation) to generate the next generation population. The selection operator is an improvement on the traditional random competition strategy. The steps are: first, select Q individuals with better fitness in the population, then randomly select q individuals from them, and finally select the best individual from these q individuals as the parent generation for the next crossover operation.

[0136] Step 5: Determine whether the optimal individual meets the termination condition. If so, output the optimization result. Otherwise, return to step 2.

[0137] The radiation field of the sparse array is introduced into the fitness function of the HyGADE algorithm, and its fitness function is:

[0138] (9)

[0139] in, is a coefficient, ranging from 0 to 1, and satisfies ; is the target sidelobe level; is the actual maximum sidelobe level; For target gain; is the actual gain.

[0140] Under the guidance of the above theory, sparse array beam synthesis based on equivalent subarray strategy can be realized by following the following design steps.

[0141] Step 1: According to the index requirements of the desired sparse array pattern, determine the parameters of the sparse sub-array (unit design, sub-array size, unit spacing, etc.);

[0142] Step 2: Simulate the sparse subarray to obtain the scattering field of the sparse subarray;

[0143] Step 3: Using the equivalent subarray strategy, the scattering field of a large-scale sparse array is equivalently derived based on the scattering field of the sparse subarray;

[0144] Step 4: Derive the relationship between the scattering matrix and the radiation field of the sparse array, and calculate the radiation field of the large-scale sparse array;

[0145] Step 5: Use the HyGADE algorithm to perform large-scale sparse array beam synthesis and introduce the radiation field of the sparse array into the fitness function of the algorithm;

[0146] Step 6: After completing the large-scale sparse array beam synthesis, use simulation software to verify the results.

[0147] The following is a specific example of sparse array beam synthesis:

[0148] The HyHGADE algorithm is used for sparse array beam synthesis, and a high-gain, low-sidelobe sparse array is designed considering mutual coupling. The array size of the sparse array is 8*8, and the central operating frequency is 19.5GHz. In order to achieve better optimization results, no requirements are made on the sparse array's sparse rate, and the sparse array's sparse rate is limited by the gain index during optimization. The design goals of the sparse array are as follows: sidelobe level ≤-20dB, gain ≥19dB.

[0149] First, set the parameters of the optimization algorithm. The population size is 50, the maximum number of iterations is 500, and the unit spacing is The binary coding method is used, 0 indicates that there is no antenna unit here, and 1 indicates that there is an antenna unit here. The fitness function is shown in formula (9).

[0150] (9)

[0151] like Figure 8 The figure shows the designed Ka-band antenna unit. The antenna unit uses a multi-layer microstrip antenna and a multi-layer dual-feed circular polarization patch as the basic model. In terms of bandwidth design, a double-layer patch is used to expand the antenna bandwidth. At the same time, the coupling slot is used as the feeding structure to further expand the antenna bandwidth. The lower patch of the antenna is a dual-feed circular polarization patch, and the upper patch is a parasitic patch. Through optimization design, the two patches resonate at different frequencies to widen the antenna bandwidth. In terms of polarization design and implementation, dual feed points are used to achieve broadband circular polarization. Different excitation phases can be used at the dual feed points to achieve left-handed or right-handed circular polarization, respectively, and can meet the compact design requirements in terms of physical size. The antenna structure has a total of 5 layers of printed circuit boards, including a feed network, a coupling slot, and two layers of radiation patches and a floor. The designed antenna unit works at 17.7-21.2GHz, with a relative bandwidth of 18.0%, and a unit size of 7.0mm×7.0mm; the polarization mode is switchable between left-handed and right-handed circular polarization.

[0152] Using the antenna unit according to Figure 1 to Figure 5 The arrangement shown in the figure establishes a 3*3 sparse subarray, and performs full-wave simulation to obtain the scattering matrix of the sparse subarray. In the beam synthesis optimization, the equivalent subarray strategy is used to obtain the scattering matrix of the 8*8 sparse array, and its radiation field is calculated according to formula (8). The distribution diagram of the sparse array unit after optimization is shown in Figure 5 As shown in the figure, there are 41 antenna units in total, and the sparsity rate is 64%. Fig.10 The figure shows the convergence performance curve. It can be seen that after 293 generations of iteration, the fitness value tends to be stable. Figure 11-12The figure shows the comparison of the normalized directivity patterns of the E-plane and H-plane of the sparse array and the uniform array at 19.5GHz. The peak sidelobe level of the sparse array is -20.57dB, and the minimum gain is 19.84dB. The sparse sidelobe level and gain meet the design index requirements. Compared with the uniform full array, the gain of the sparse array is only reduced by 2.07dB, while the sidelobe is reduced by 5.33dB, indicating that the sparse array has the advantage of low sidelobe.

[0153] according to Fig. 9 The sparse array unit arrangement shown is modeled and simulated using HFSS software. Figure 13-14 The E-plane and H-plane radiation patterns obtained by simulation software, the classical pattern superposition method and the method of the present invention are compared. The simulation results are basically consistent with the method of the present invention in the main lobe, the first and second side lobes. The gain obtained by the simulation software is 19.08dB, which is 2.75dB lower than the gain of the classical pattern superposition method. This comparison shows that the method of the present invention can effectively complete the sparse array beam synthesis under the condition of considering mutual coupling and realize accurate sparse array antenna design.

[0154] Those skilled in the art will appreciate that the embodiments described are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to the embodiments described. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A sparse array beam synthesis method based on equivalent subarray strategy, characterized in that: The following steps are involved: Step 1: According to the index requirements of the sparse array radiation pattern, determine the parameters of the sparse array antenna: specifically including antenna unit design, subarray scale and antenna unit spacing; wherein the subarray scale includes the upper limit M of the number of antenna unit rows, the upper limit N of the number of antenna unit columns and the total number T of antenna units in the sparse array antenna, T∈[1,MN-1]; the direction of the antenna unit row is recorded as the x-axis direction, the direction of the antenna unit column is recorded as the y-axis direction, and the direction perpendicular to the xoy plane of the sparse array antenna and facing outward is recorded as the z-axis direction; the distance between the center points of the antenna units in two adjacent rows is recorded as , the distance between the center points of two adjacent columns of antenna units is recorded as ; Step 2, construct multiple small-scale sparse subarray models, and calculate the scattering field of each small-scale sparse subarray model according to the antenna unit design; Step 3, create a sparse array initial population, each individual in the population represents a sparse array beam synthesis scheme; set the maximum number of iterations and the fitness value threshold; Step 4: Based on the current population, a new population of the same size is generated using the differential evolution method, and the new population is mixed with the current population; Step 5, according to the scattering fields corresponding to various small-scale sparse subarray models, combined with the equivalent subarray strategy, calculate the radiation field of the sparse array antenna corresponding to each individual in the mixed population; Step 6, based on the radiation field of the sparse array antenna corresponding to each individual in the mixed population, calculate the fitness value corresponding to each individual, sort the individuals in order from small to large fitness values, and retain half of the individuals with small fitness values; Step 7: For the retained individuals, perform the selection, crossover, and mutation operations of the genetic algorithm to generate a new generation of population; Step 8, calculate the fitness value of each individual in the new generation population, and record the individual corresponding to the minimum fitness value as the optimal individual. If the fitness value of the optimal individual in the current iteration process is less than the fitness value threshold, or the maximum number of iterations has been reached, the sparse array beam synthesis scheme corresponding to the optimal individual in the current iteration process is used as the sparse array beam synthesis scheme outputted finally. Otherwise, execute step 4 based on the new generation population to proceed to the next round of iteration.

2. A sparse array beam synthesis method based on equivalent subarray strategy according to claim 1, characterized in that: The specific method of step 2 is: Construct multiple 3*3 sparse subarray models: Specifically, the spacing between two adjacent rows of antenna units in each 3*3 sparse subarray model is The spacing between two adjacent columns of antenna units is ; An antenna unit is set at the center position of each 3*3 sparse subarray model. According to whether there are antenna units at the first row and second column, the second row and first column, the second row and third column, and the third row and second column of the 3*3 sparse subarray model, 16 3*3 sparse subarray models are constructed, and their corresponding scattering fields are calculated according to the antenna unit design.

3. The sparse array beam synthesis method based on equivalent subarray strategy according to claim 2, characterized in that: The specific method of creating the sparse array initial population in step 3 is: Step 301, setting the population size P; Step 302, randomly sorting T 1s and MN-T 0s, so as to construct a sparse array matrix with M rows and N columns; wherein 1 indicates that an antenna unit is provided at the corresponding position of the sparse array antenna, and 0 indicates that there is no antenna unit at the corresponding position of the sparse array antenna; Step 303, repeating step 302 until P different M-row and N-column sparse array matrices are generated; Step 304 , for each sparse array matrix with M rows and N columns, extract each row of data in turn, and splice them in order to obtain a binary chromosome with a length of MN, which is recorded as an individual in the sparse array initial population.

4. The sparse array beam synthesis method based on equivalent subarray strategy according to claim 3, characterized in that: The specific method of step 4 is: Step 401, randomly select three individuals in the current population, then randomly select two individuals from the selected three individuals, calculate the vector difference between the two individuals and sum the vector difference with the third individual, thereby generating a new individual; Among them, in the process of calculating the vector difference of two individuals and the sum of the vector difference and the third individual, the corresponding bit data are calculated separately. For the summed individuals, if a bit data is 2, it is updated to 1, and if a bit data is -1, it is updated to 0; Step 402, judging the newly generated individual: if the number of 1s in its binary chromosome is greater than T, randomly select some 1s in the binary chromosome and change them to 0s, so that the number of 1s in the binary chromosome remains T; If the number of 1s in the binary chromosome is less than T, some 0s in the binary chromosome are randomly selected and changed to 1s so that the number of 1s in the binary chromosome remains T; If the number of 1s contained in its binary chromosome is exactly T, no change is made; Step 403, repeating steps 401 and 402 until a new population of size P is generated, and the new population is mixed with the current population.

5. The sparse array beam synthesis method based on equivalent subarray strategy according to claim 4, characterized in that: The specific method of step 5 is: Step 501, for each individual in the mixed population, obtain its corresponding sparse array matrix. If the value at the position of the mth row and the nth column in the sparse array matrix is ​​1, then according to the values ​​of the four adjacent upper, lower, left and right positions, m=1,2,3,...,M, n=1,2,3,...,N, a certain 3*3 sparse subarray model is matched, and the scattering field of the matched 3*3 sparse subarray model is recorded as the scattering field corresponding to the current position. ; If the value at the position of the mth row and nth column in the sparse array matrix is ​​0, then the scattering field corresponding to the current position is recorded as =0; Among them, for the values ​​of the first row, Mth row, first column, and Nth column in the sparse array matrix, if they do not have values ​​in any of the four adjacent upper, lower, left, and right positions, the values ​​of the corresponding missing adjacent upper, lower, left, and right positions are recorded as 0, and the 3*3 sparse subarray model is matched accordingly; Step 502, based on the scattering field corresponding to each position in the sparse array matrix, calculate the radiation field E of the corresponding sparse array antenna: ； in, is the radiation field of the antenna unit when excited by a unit voltage source, is the wave number, ; is the wavelength; is the incident voltage of the antenna unit at the position of the mth row and the nth column in the sparse array antenna. If there is no antenna unit at the position of the mth row and the nth column in the sparse array antenna, then ; j represents the imaginary unit, is the angle between the beam direction and the z-axis direction of the sparse array, It is the angle between the projection of the beam direction on the xoy plane and the x-axis.

6. The sparse array beam synthesis method based on equivalent subarray strategy according to claim 5, characterized in that: The specific method for calculating the fitness value corresponding to each individual in step 6 is: Step 601, for the radiation field E of the current individual, calculate its corresponding directivity pattern, and further calculate the maximum sidelobe level of the sparse array antenna corresponding to the current individual And gain ; Step 602: Calculate the fitness value corresponding to the current individual : ； in, is a coefficient, the value range is 0~1, and it satisfies ; is the target sidelobe level in the specification requirements of the sparse array pattern, is the target gain in the specification requirement for the sparse array pattern.

7. The sparse array beam synthesis method based on equivalent subarray strategy according to claim 6, characterized in that: The specific method of step 7 is: Step 701, sort all the retained individuals in order of fitness value from small to large, and select Q individuals with small fitness values, 1<Q<P-1; Step 702, randomly select q individuals from the selected Q individuals, and record the individual with the smallest fitness value among the q individuals as a parent individual, 1<q<Q-1; Step 703, repeating step 702 until 2P parent individuals are obtained, grouping the 2P parent individuals into groups of two, performing a crossover operation on each group of parent individuals, and obtaining P offspring individuals; Step 704, performing a mutation operation on the P offspring individuals after the crossover to obtain P mutated offspring individuals; Step 705, for each mutated offspring individual, a judgment is made: if the number of 1s in its binary chromosome is greater than T, some 1s in the binary chromosome are randomly selected and changed to 0s, so that the number of 1s in the binary chromosome remains at T; If the number of 1s in the binary chromosome is less than T, some 0s in the binary chromosome are randomly selected and changed to 1s so that the number of 1s in the binary chromosome remains T; If the number of 1s contained in its binary chromosome is exactly T, no change will be made; thus a new generation of population is generated.

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