A Sparse Array Beam Synthesis Method Based on the Equivalent Subarray Strategy

Abstract

The present invention discloses a sparse array beam synthesis method based on an equivalent subarray strategy, which relates to the technical field of array antenna beam synthesis. First, according to the equivalent subarray strategy, the scattered field of a large-scale sparse array is equivalently deduced by using the scattered field of a small-scale sparse subarray; then, the relationship between the scattering matrix and the radiation field of the sparse array is theoretically deduced to realize the calculation of the radiation field of the large-scale sparse array; finally, the HyGADE algorithm is used to optimize the sparse array pattern synthesis, and the radiation field of the large-scale sparse array is introduced into the fitness function of the algorithm to realize the sparse array beam synthesis based on the equivalent subarray strategy. The present invention takes into account the mutual coupling effect between antenna elements to realize the precise design of the sparse array.

Description

Technical Field

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

[0002] A sparse array antenna sparsely arranges antenna elements on a certain aperture. Compared with a uniform array, a sparse array can achieve the antenna radiation characteristics with fewer array elements, which can not only simplify the antenna feeding structure, reduce the weight of the antenna system, but also reduce the cost of the antenna. Sparse arrays have been widely used in the fields of wireless communication, radar, navigation, etc.

[0003] The sparse array beam synthesis technology is the core and difficult problem in the research of sparse array antennas. The traditional sparse array synthesis method usually adopts the pattern multiplication theorem and combines it with an intelligent optimization algorithm for optimization calculation. This method regards all antenna elements as completely identical and independent elements that do not affect each other, ignoring the mutual coupling effect between antenna elements, resulting in a certain difference between the design result and the actual situation. Moreover, 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 considering 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. This method realizes the equivalent derivation of the scattering field of a large-scale sparse array by using the scattering field of a small-scale sparse subarray, and further realizes the sparse array beam synthesis under the condition of considering mutual coupling.

[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, comprising the following steps:

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

[0008] Step 2, construct multiple small-scale sparse sub-array models, and calculate the scattering fields of each small-scale sparse sub-array model according to the antenna element design;

[0009] Step 3, create an initial population of sparse arrays, where 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, use the differential evolution method to generate a new population of the same scale, and mix the new population with the current population;

[0011] Step 5, according to the scattering fields corresponding to multiple small-scale sparse sub-array models, combine the equivalent sub-array strategy to calculate the radiation fields of the sparse arrays corresponding to each individual in the mixed population;

[0012] Step 6, based on the radiation fields of the sparse arrays corresponding to each individual in the mixed population, calculate the fitness value corresponding to each individual, sort the individuals in ascending order of the fitness value, and retain the first half of the individuals with smaller 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 of population, 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, then use the sparse array beam synthesis scheme corresponding to the optimal individual in the current iteration process as the finally output sparse array beam synthesis scheme. Otherwise, based on the new generation of population, execute Step 4 for the next iteration process.

[0015] Further, the specific method of Step 2 is as follows:

[0016] Construct multiple 3*3 sparse sub-array models: Specifically, the spacing between adjacent rows of antenna elements in each 3*3 sparse sub-array model is , and the spacing between adjacent columns of antenna elements is ; an antenna element is provided at the center position of each 3*3 sparse sub-array model. According to whether there are antenna elements at the four positions of the first row and second column, second row and first column, second row and third column, and third row and second column of the 3*3 sparse sub-array model, construct 16 3*3 sparse sub-array models, and calculate their corresponding scattering fields according to the antenna element design respectively.

[0017] Further, the specific method of creating the initial population of sparse arrays in Step 3 is as follows:

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

[0019] Step 302: Randomly sort T 1s and MN - T 0s to construct an M-row and N-column sparse array matrix. Here, 1 indicates that an antenna element is provided at the corresponding position of the sparse array antenna, and 0 indicates that no antenna element is provided at the corresponding position of the sparse array antenna.

[0020] Step 303: Repeat Step 302 until P different M-row and N-column sparse array matrices are generated.

[0021] Step 304: For each M-row and N-column sparse array matrix, sequentially extract the data of each row and splice them in order to obtain a binary chromosome of length MN, denoted as an individual in the initial population of the sparse array.

[0022] Furthermore, the specific manner of Step 4 is as follows:

[0023] Step 401: Randomly select three individuals from the current population, then arbitrarily select two individuals from the three selected individuals, calculate the vector difference between the two individuals and sum the vector difference with the third individual to generate a new individual.

[0024] Among them, in the calculation process of the vector difference between the two individuals and the sum of the vector difference and the third individual, the calculations are all performed for the corresponding bit data. For the individual after summation, if a certain bit data is 2, it is updated to 1, and if a certain bit data is -1, it is updated to 0.

[0025] Step 402: Make a judgment on 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 to become 0 so that the number of 1s in the binary chromosome remains T.

[0026] If the number of 1s in its binary chromosome is less than T, randomly select some 0s in the binary chromosome to become 1 so that the number of 1s in the binary chromosome remains T.

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

[0028] Step 403: Repeat Step 401 and Step 402 until a new population of size P is generated and mix the new population with the current population.

[0029] Furthermore, the specific manner of Step 5 is as follows:

[0030] Step 501: For each individual in the mixed population, obtain its corresponding sparse array matrix. If the value at the m-th row and n-th column position in the sparse array matrix is 1, then based on whether the values at its adjacent top, bottom, left, and right positions are 1 or 0, where m = 1, 2, 3, ……, M and n = 1, 2, 3, ……, N, match a certain 3×3 sparse sub-array model, and record the scattering field of the matched 3×3 sparse sub-array model as the scattering field corresponding to the current position. If the value at the m-th row and n-th column position in the sparse array matrix is 0, then record the scattering field corresponding to the current position = 0;

[0031] Among them, for the values at the first row, the M-th row, the first column, and the N-th column in the sparse array matrix, if there is no value at a certain position among its adjacent top, bottom, left, and right positions, record the missing values at the corresponding adjacent top, bottom, left, and right positions as 0, and perform the matching of the 3×3 sparse sub-array model accordingly;

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

[0033] ;

[0034] Among them, is the radiation field of the antenna element under the excitation of a unit voltage source, is the wave number, ; is the wavelength; is the incident voltage of the antenna element at the m-th row and n-th column position in the sparse array antenna. If there is no antenna element at the m-th row and n-th column position 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, is the angle between the projection of the beam direction on the xoy plane and the x-axis.

[0035] Furthermore, the specific method for calculating the fitness value corresponding to each individual in Step 6 is as follows:

[0036] Step 601: For the radiation field E of the current individual, calculate its corresponding radiation pattern, and further calculate the maximum sidelobe level and the gain ;

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

[0038] ;

[0039] Among them, is a coefficient, and its value range is all from 0 to 1, and satisfies ; is the target sidelobe level in the index requirements of the sparse array pattern, is the target gain in the index requirements of the sparse array pattern.

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

[0041] Step 701: For all the remaining individuals, sort them in ascending order according to the fitness value, and select Q individuals with smaller fitness values, where 1 < Q < P - 1;

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

[0043] Step 703: Repeat step 702 until 2P parent individuals are obtained. Group the 2P parent individuals into groups of two, and perform crossover operations on each group of parent individuals to obtain P offspring individuals;

[0044] Step 704: Perform mutation operations on the P offspring individuals after crossover to obtain P mutated offspring individuals;

[0045] Step 705: Make a judgment for each mutated offspring 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 0 so that the number of 1s in the binary chromosome remains T;

[0046] If the number of 1s in its binary chromosome is less than T, randomly select some 0s in the binary chromosome and change them to 1 so that the number of 1s in the binary chromosome remains T;

[0047] If the number of 1s in its binary chromosome is exactly T, no change is 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 as follows:

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

[0050] 2. The present invention improves the intelligent optimization algorithm used in beam synthesis. This algorithm combines the genetic algorithm with the differential evolution algorithm and improves the operators of the algorithm, effectively enhancing the performance of the optimization algorithm. This method can perform sparse array beam synthesis under the consideration of mutual coupling conditions, achieving the precise design of sparse array antennas and having certain engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0052] Figure 2 It is a schematic diagram of a 3×3 sparse subarray model corresponding to 2 adjacent units of the central unit in an embodiment of the present invention.

[0053] Figure 3 It is a schematic diagram of a 3×3 sparse subarray model corresponding to 3 adjacent units of the central unit in an embodiment of the present invention.

[0054] Figure 4 It is a schematic diagram of a 3×3 sparse subarray model corresponding to 4 adjacent units of the central unit in an embodiment of the present invention.

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

[0056] Figure 6 It is a schematic diagram of an equivalent subarray strategy in an embodiment of the present invention.

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

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

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

[0060] Figure 10 It is a schematic diagram of a convergence performance curve in an embodiment of the present invention.

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

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

[0063] Figure 13 The E-plane sparse array pattern obtained by using simulation software, the classical pattern superposition method, and the method of the present invention in the embodiments of the present invention.

[0064] Figure 14 The H-plane sparse array pattern obtained by using simulation software, the classical pattern superposition method, and the method of the present invention in the embodiments of the present invention. Specific embodiments

[0065] The content of 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 includes the following steps:

[0067] Step 1, according to the index requirements of the sparse array pattern, determine the parameters of its sparse array antenna: specifically including antenna element design, subarray scale, and antenna element spacing; wherein, the subarray scale includes the upper limit M of the number of antenna element rows, the upper limit N of the number of antenna element columns, and the total number T of antenna elements in the sparse array antenna, T ∈ [1, MN - 1]; denote the antenna element row direction as the x-axis direction, the antenna element column direction as the y-axis direction, and the direction perpendicular to the xy plane of the sparse array antenna and facing outward as the z-axis direction; denote the center point spacing between antenna elements in adjacent two rows of antenna elements as and the center point spacing between antenna elements in adjacent two columns of antenna elements as ; Both and

[0068] are greater than the element size of the antenna element;

[0069] Step 2, construct multiple small-scale sparse subarray models, and calculate the scattering fields of each small-scale sparse subarray model according to the antenna element design;

[0070] Step 3, create an initial population of the sparse array, where each individual in the population represents a sparse array beam synthesis scheme; set the maximum number of iterations and the fitness value threshold;

[0071] Step 4, based on the current population, use the differential evolution method to generate a new population of the same scale, and mix the new population with the current population;

[0072] Step 5, according to the scattering fields corresponding to multiple small-scale sparse subarray models, calculate the radiation fields of the sparse array antennas corresponding to each individual in the mixed population in combination with the equivalent subarray strategy;

[0073] Step 7: For the remaining individuals, perform 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 of 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 iteration number has been reached, then use the sparse array beam synthesis scheme corresponding to the optimal individual in the current iteration process as the finally output sparse array beam synthesis scheme; otherwise, based on the new generation of population, perform Step 4 for the next iteration process.

[0075] Furthermore, the specific method of Step 2 is as follows:

[0076] Construct multiple 3×3 sparse subarray models: Specifically, the spacing between adjacent rows of antenna elements in each 3×3 sparse subarray model is , and the spacing between adjacent columns of antenna elements is ; An antenna element is provided at the center position of each 3×3 sparse subarray model. According to whether there are antenna elements at the four positions of the first row and second column, second row and first column, second row and third column, and third row and second column of the 3×3 sparse subarray model, construct 16 kinds of 3×3 sparse subarray models, and calculate their corresponding scattering fields respectively according to the antenna element design.

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

[0078] Step 301: Set the population size P.

[0079] Step 302: Randomly sort T 1s and MN−T 0s to construct an M×N sparse array matrix; where, 1 indicates that there is an antenna element at the corresponding position of the sparse array antenna, and 0 indicates that there is no antenna element at the corresponding position of the sparse array antenna.

[0080] Step 303: Repeat Step 302 until P different M×N sparse array matrices are generated.

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

[0082] Furthermore, the specific method of Step 4 is as follows:

[0083] Step 401: Randomly select three individuals in the current population, then arbitrarily select two individuals from the three selected individuals, calculate the vector difference between the two individuals and sum the vector difference with the third individual to generate a new individual.

[0084] Among them, in the calculation process of the vector difference between two individuals and the summation of the vector difference and the third individual, the calculations are respectively performed on the corresponding bit data. For the individual after summation, if a certain bit data is 2, it is updated to 1; if a certain bit data is -1, it is updated to 0.

[0085] Specifically, the vector difference between two individuals is the difference of the corresponding gene codes, and the summation of the vector difference and the third individual is the sum value of the corresponding gene codes, 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: Judge 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 to become 0s so that the number of 1s in the binary chromosome remains T.

[0087] If the number of 1s in its binary chromosome is less than T, randomly select some 0s in the binary chromosome to become 1s so that the number of 1s in the binary chromosome remains T.

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

[0089] Step 403: Repeat Step 401 and Step 402 until a new population of size P is generated, and mix the new population with the current population.

[0090] Furthermore, the specific method of Step 5 is as follows:

[0091] Step 501: For each individual in the mixed population, obtain its corresponding sparse array matrix. If the value at the position of the m-th row and the n-th column in the sparse array matrix is 1, then according to whether the values at its adjacent four positions (up, down, left, and right) are 1 or 0, m = 1, 2, 3, ……, M, n = 1, 2, 3, ……, N, match a certain 3*3 sparse sub-matrix model, and record the scattering field of the matched 3*3 sparse sub-matrix model as the scattering field corresponding to the current position ; if the value at the position of the m-th row and the n-th column in the sparse array matrix is 0, record the scattering field corresponding to the current position = 0;

[0092] Among them, for the values in the first row, the M-th row, the first column, and the N-th column of the sparse array matrix, if there is no value at a certain position among its adjacent four positions (up, down, left, and right), record the values at the corresponding missing adjacent four positions as 0, and perform the matching of the 3*3 sparse sub-matrix model accordingly;

[0093] Step 502: Calculate the radiation field E of the sparse array antenna corresponding to it based on the scattered fields corresponding to each position in the sparse array matrix:

[0094] ;

[0095] where, is the radiation field of the antenna element under the excitation of a unit voltage source, is the wave number, ; is the wavelength; is the incident voltage of the antenna element at the position of the m-th row and n-th column in the sparse array antenna. If there is no antenna element at the position of the m-th row and n-th 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, is the angle between the projection of the beam direction on the xoy plane and the x-axis.

[0096] Furthermore, the specific method for calculating the fitness value corresponding to each individual in Step 6 is as follows:

[0097] Step 601: For the radiation field E of the current individual, calculate its corresponding radiation pattern, and further calculate the maximum sidelobe level and the gain ;

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

[0099] ;

[0100] where, are coefficients, and their value ranges are all from 0 to 1 and satisfy ; is the target sidelobe level in the index requirements of the sparse array radiation pattern, is the target gain in the index requirements of the sparse array radiation pattern.

[0101] Furthermore, the specific method for Step 7 is as follows:

[0102] Step 701: For all the remaining individuals, sort them in ascending order according to the fitness value, and select Q individuals with smaller fitness values, where 1 < Q < P - 1;

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

[0104] Step 703: Repeat Step 702 until 2P parental individuals are obtained. Group the 2P parental individuals into pairs, and perform crossover operations on each pair of parental individuals respectively to obtain P offspring individuals;

[0105] Step 704: Perform mutation operations on the P offspring individuals after crossover to obtain P mutated offspring individuals;

[0106] Step 705: Make a judgment for each mutated offspring 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 to keep the number of 1s in the binary chromosome as T;

[0107] If the number of 1s in its binary chromosome is less than T, randomly select some 0s in the binary chromosome and change them to 1s to keep the number of 1s in the binary chromosome as T;

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

[0109] Specifically, in a sparse array, due to the random arrangement of antenna elements, it is impossible to use a single sparse subarray to generalize the scattering field of the sparse array. Therefore, it is necessary to analyze the scattering fields of sparse subarrays with different arrangements. In the mutual coupling analysis of a sparse array, to simplify the calculation, only the influence brought by the four antenna elements closest to a specific antenna element in the array needs to be considered. As Figures 1 to 5 shown, they are 3×3 sparse subarrays with different arrangements, where the red represents the central unit of the subarray, and the yellow represents the edge units of the subarray. It includes one unit around, two units around, three units around, four units around, and no unit around. The scattering matrix of the sparse subarray can be obtained using simulation software. As Figure 6 shown, it is a schematic diagram of the equivalent subarray strategy for equivalently deriving the scattering field of a 5×5 sparse array using a 3×3 sparse subarray. In the target sparse array to be solved, according to the Figures 1 to 5 subarray arrangement shown, judge the arrangement form of the sparse subarray corresponding to each unit in turn and perform equivalent substitution, then it is possible to equivalently derive the scattering field of a large-scale sparse array using the scattering field of a small-scale sparse subarray, and finally obtain the scattering matrix of the large-scale sparse array.

[0110] Among them, for the antenna element in the first column of the second row as Figure 6 shown, mark the antenna element on its left as none. For the antenna element in the fifth column of the first row, mark the antenna elements above, on the left, and on the right as none. For the antenna element in the fifth column of the fifth row, mark the antenna elements on the left, on the right, and below as none, and perform the Figures 1 to 5 equivalent substitution of the 3×3 sparse subarray as shown.

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

[0112] Generally, we consider that the total radiation field of an array is equal to the superposition of the radiation fields of all the elements in the array. Among them, the definition of the element radiation field is: in the array environment, when only this element is excited by a unit source and all other elements are connected with matching loads, the radiation field of the array is called the active element radiation pattern. A sparse array can be regarded as obtained by removing some elements from a uniform array. Therefore, the sparse array can be studied starting from the uniform array. As Figure 7 shown, for a uniform linear array of N elements, it can be regarded as an N-port network. Assuming that all elements are excited by voltage sources, the incident voltage waves of each antenna element in the array are successively , ,..., , and the reflected voltage waves are successively , ,..., , 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] Among them, is the scattering matrix.

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

[0118] (3)

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

[0120] (4)

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

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

[0123] (5)

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

[0125] (6)

[0126] The above calculation method of the array antenna pattern is also applicable to the uniform planar array antenna, except that the calculation formula of the array factor of the linear array antenna needs to be replaced by the calculation formula of the planar 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 element spacing is , the number of units in the y-axis direction is N, and the element 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 in the following form:

[0129] (8)

[0130] Since the sparse array is regarded as obtained by removing some units from the uniform array, the above conclusion of the uniform planar array is extended to the planar sparse array. If the units of the sparse array are all excited by unit voltage sources, the retained units , the discarded units , and the relationship between the scattering matrix and the radiation field of the sparse array can be obtained by using this method.

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

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

[0133] Step 2: Use the differential evolution algorithm to generate a new population 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 a new individual. Repeating this process multiple times can generate a new population of the same size as the original population.

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

[0135] Step 4: Execute genetic algorithm operators (selection, crossover, mutation) to generate the next generation of population. Among them, the selection operator is improved based on the traditional random competition strategy, and its steps are as follows: First, select Q individuals with better fitness in the population, then randomly select q individuals from them, and finally select the optimal individual among these q individuals as the parent for the next crossover operation.

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

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

[0138] (9)

[0139] Among them, is a coefficient, and its value range is 0 to 1, and it satisfies ; is the target sidelobe level; is the actual maximum sidelobe level; is the target gain; is the actual gain.

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

[0141] Step 1: According to the index requirements of the desired sparse array pattern, determine the parameters of its sparse subarray (element design, subarray scale, element spacing, etc.);

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

[0143] Step 3: Use the equivalent subarray strategy to equivalently deduce the scattering field of the large-scale sparse array according to the scattering field of the sparse subarray;

[0144] Step 4: Deduce 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 for 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] Use the HyHGADE algorithm for sparse array beam synthesis to design a high-gain, low-sidelobe sparse array considering mutual coupling. The array size of the sparse array is 8×8, and the center operating frequency is 19.5 GHz. To achieve better optimization results, there is no requirement for the sparsity rate of the sparse array, and the sparsity rate of the sparse array is restricted by the gain index during optimization. The design objectives of the sparse array are as follows: sidelobe level ≤ -20 dB, gain ≥ 19 dB.

[0149] First, set the parameters of the optimization algorithm. The population size is 50, the maximum number of iterations is 500, and the element spacing . The binary coding method is adopted, where 0 represents no antenna element here, and 1 represents an antenna element here. The fitness function is shown in Equation (9).

[0150] (9)

[0151] As Figure 8 shown is the designed Ka-band antenna element. This antenna element selects a multilayer microstrip antenna and uses a multilayer dual-feed circularly polarized patch as the basic model. In terms of bandwidth design, a double-layer patch form is adopted to expand the antenna bandwidth. At the same time, a coupling slot is used as the feeding structure, which can further expand the antenna bandwidth. The lower-layer patch of the antenna is a dual-feed circularly polarized patch, and the upper-layer patch is a parasitic patch. By optimizing the design, the two patches resonate at different frequencies to broaden the antenna bandwidth. In terms of the implementation of polarization mode design, dual feeds are used to achieve broadband circular polarization. Different excitation phases are adopted on the dual feeds to achieve left-handed or right-handed circular polarization respectively, and at the same time, the compact design requirements in terms of physical size can be met. The antenna structure has a total of 5 printed circuit boards, including a feeder network, a coupling slot, and two layers of radiation patches and a ground plane. The designed antenna element operates at 17.7 - 21.2 GHz, with a relative bandwidth of 18.0%, and the element size is 7.0 mm × 7.0 mm; the polarization mode is left-handed and right-handed circular polarization switchable.

[0152] Use this antenna element to establish a 3×3 sparse subarray according to the arrangement shown in Figures 1 to 5 , and perform full-wave simulation to obtain the scattering matrix of the sparse subarray. In the beam synthesis optimization, use the equivalent subarray strategy to obtain the scattering matrix of the 8×8 sparse array, and calculate its radiation field according to Equation (8). After optimization, the sparse array element distribution diagram is as shown in Figure 5 . There are 41 antenna elements in the figure, and the sparsity rate is 64%. As shown in Figure 10 is the convergence performance curve. It can be seen from the figure that after iterating to the 293rd generation, the fitness value tends to be stable. As shown in Figures 11 to 12The following shows the comparison of the E-plane and H-plane normalized radiation patterns of the sparse array and the uniform array at 19.5 GHz. The peak sidelobe level of the sparse array is -20.57 dB, and the minimum gain is 19.84 dB. Both the sidelobe level and the gain of the sparse array meet the requirements of the design specifications. Compared with the uniform full array, the gain of the sparse array only decreases by 2.07 dB, while the sidelobe decreases by 5.33 dB, indicating that the sparse array has the advantage of low sidelobes.

[0153] According to Figure 9 the arrangement of the sparse array elements shown, the HFSS software is used for modeling and simulation analysis. Figures 13 to 14 The E-plane and H-plane radiation patterns obtained by the simulation software, the classical pattern superposition method, and the method of the present invention are compared. The simulation results are basically consistent with those of the method of the present invention in the main lobe, the first and the second sidelobes. The gain obtained by the simulation software is 19.08 dB, which is 2.75 dB lower than that of the classical pattern superposition method. This comparison shows that the method of the present invention can effectively complete the beam synthesis of the sparse array and realize the precise design of the sparse array antenna under the condition of considering mutual coupling.

[0154] Those skilled in the art will realize that the described embodiments are to help readers understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to the described embodiments. For those skilled in the art, various changes and modifications can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within 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; specifically: 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 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; 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 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.

3. The sparse array beam synthesis method based on equivalent subarray strategy according to claim 2, 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.

4. The sparse array beam synthesis method based on equivalent subarray strategy according to claim 3, 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.

5. The sparse array beam synthesis method based on equivalent subarray strategy according to claim 4, 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.

6. The sparse array beam synthesis method based on equivalent subarray strategy according to claim 5, 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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