Spare rectangular planar array antenna synthesis method, program, device and storage medium

Abstract

The invention belongs to the technical field of array antenna synthesis, and particularly relates to a thin cloth rectangular planar array antenna synthesis method, a program, equipment and a storage medium. According to the method, a thin cloth rectangular planar array antenna comprehensive method is converted into an optimization problem of an array element position in a quadrant, an improved sparrow algorithm is adopted, Kent mapping population initialization is introduced, and diversity of an initialized population is enhanced; the idea of a sine and cosine algorithm is fused in a position updating strategy of a discoverer, and a nonlinear sine learning factor is introduced to enhance all search capabilities; and finally, a crisscross strategy is introduced into a sparrow algorithm, and the optimization precision is improved by improving a search mode of a supervisor.

Description

Technical Field

[0001] This invention belongs to the field of array antenna synthesis technology, specifically relating to the synthesis method, program, equipment and storage medium of sparsely distributed rectangular planar array antennas. Background Technology

[0002] Array synthesis is a key research area in the field of array antennas. Its core is determining the number of array elements and the excitation phase, amplitude, and position of each element according to the required array radiation characteristics. When each element in the array antenna is an isotropic radiating element, the synthesis of a uniformly weighted array can be simplified to optimizing the position of each element in the array. Currently, the optimization of element positions mainly falls into two categories: sparse array optimization, which only allows element positions to appear at given grid points, and sparse array optimization, which allows each element to be freely placed under given array aperture and element spacing constraints. Because sparse arrays have higher element freedom, the desired radiation characteristics can usually be achieved with fewer elements, giving them a significant advantage over sparse arrays.

[0003] Synthesis of sparse planar arrays has always been a challenging problem due to the minimum element spacing constraint. Existing methods for synthesizing sparse planar arrays adjust the element positions to satisfy the minimum element spacing constraint. While this avoids infeasible solutions, it also forces adjustments to many array distributions that originally met the minimum element spacing constraint, limiting the degrees of freedom of the elements and causing some feasible solutions to be unsearchable. Furthermore, existing intelligent optimization algorithms suffer from low search efficiency and insufficient convergence accuracy during array antenna optimization. Summary of the Invention

[0004] The purpose of this invention is to provide a method, program, device and storage medium for synthesizing sparsely distributed rectangular planar array antennas, which can ensure the degree of freedom of array elements and improve optimization accuracy while avoiding infeasible solutions.

[0005] A synthesis method for sparsely distributed rectangular planar array antennas is proposed. For a sparsely distributed rectangular planar array with an array aperture of 2L×2H on the xoy plane, the number of array elements is 4N. The array is symmetrical about the origin. The method optimizes N array elements in the first quadrant, and the other three quadrants are obtained by symmetry from the first quadrant.

[0006] An improved sparrow algorithm is used to optimize the solution of the positions of N array elements in the first quadrant, including the following steps:

[0007] Step 1: Set the total number of sparrows in the population (NP), the proportion of discoverers (PD), the proportion of monitors (SD), and the maximum number of iterations in the sparrow algorithm; use Kent mapping to initialize the population; calculate the fitness value corresponding to the position of each sparrow in the initial population, and take the position with the largest corresponding fitness value as the optimal position of the discoverer;

[0008] Step 2: Mark the top PD×NP sparrows with the highest corresponding fitness values ​​in the population as discoverers, and mark the remaining sparrows as followers;

[0009] Step 3: Update the positions of all sparrows in the population according to the discoverer position update strategy and the follower position update strategy respectively; integrate the idea of ​​sine and cosine algorithm into the discoverer position update strategy and introduce a non-linear sine learning factor to enhance the global search capability;

[0010] Step 4: Randomly select SD×NP sparrow individuals from the population as monitors, and update the positions of the monitors using a cross-hatching strategy;

[0011] Step 5: Calculate the fitness value corresponding to the position of each sparrow in the updated population. If there is a fitness value greater than that corresponding to the optimal position of the discoverer, then update the optimal position of the discoverer.

[0012] Step 6: If the maximum number of iterations has not been reached, return to step 2; otherwise, output the arrangement of the N array elements in the first quadrant of the sparse rectangular planar array corresponding to the optimal position of the discoverer.

[0013] Furthermore, the method for population initialization using Kent mapping in step 1 is specifically as follows:

[0014] Step 1.1: Determine the dimensions P and Q of the array element position matrix;

[0015]

[0016] Where (L, H) are the position coordinates of the Nth element of the sparsely distributed rectangular planar array in the first quadrant; d c The minimum element spacing;

[0017] Step 1.2: Generate the mapping matrix X1∈R in the x-direction using the Kent mapping. P×Q The mapping matrix Y1∈R in the y-direction P ×Q ;

[0018] Step 1.2.1: Randomly initialize the first column elements [x] of the generated matrix. 1,1 ,...,x P,1 ] and [y 1,1 ,...,y P,1 ];

[0019] Step 1.2.2: Initially obtain matrix X′∈R based on the iterative formula. P×Q and Y′∈R P×Q ;

[0020]

[0021] Where, x i,j Let y be the element in the i-th row and j-th column of matrix X′, where i = 1, ..., P, j = 1, ..., Q, k = 1, ..., Q-1; i,j Let be the element in the i-th row and j-th column of matrix Y′; μ is a preset constant; S x S represents the margin of the array element in the x-direction. x =L-(Q-0.5)d c S y S represents the margin of the array element in the y-direction. y =H-(P-0.5)d c ;

[0022] Step 1.2.3: Normalize the elements in matrices X′ and Y′ to obtain X1∈R P×Q and Y1∈R P×Q ;

[0023]

[0024] in, Let be the element in the i-th row and j-th column of matrix X1, where j = 1, ..., Q; Let Y be the element in the i-th row and j-th column of matrix Y1;

[0025] Step 1.3: Generate the state matrix S using a Blackman window weighting method; determine the element position distribution matrix T based on the state matrix S. N ;

[0026]

[0027] Among them, s i,j m is the element in the i-th row and j-th column of the state matrix S; i n represents the weight value generated by the Blackman window at each element position in the i-th row of matrix X1; j The weight value generated by the Blackman window at each element position in the j-th column of matrix Y1;

[0028] Due to the constraint of the array aperture, the array element in the P-th row and Q-th column is preserved, i.e.

[0029]

[0030] Step 1.4: Based on the minimum element spacing d of the array to be optimized c Dimensions P and Q generate a fixed matrix X2∈R in the x-direction. P×Q And a fixed matrix Y2∈R in the y-direction P×QEnsure that the element spacing between two adjacent array elements in the same row and column satisfies the minimum spacing d in both the x and y directions. c constraint;

[0031]

[0032] Step 1.5: Sort each row of the x-direction mapping matrix X1 in ascending order to form the sorted x-direction mapping matrix X'1, and then combine it with the x-direction fixed matrix X2 and the position distribution matrix T. N The combination yields the actual position matrix X of the x-direction array elements, X = (X'1 + X2) * T N ;

[0033] Arrange the elements of each column of the mapping matrix Y1 in the y-direction from smallest to largest to form the sorted mapping matrix Y1′ in the y-direction. Then, combine this sorted matrix with the fixed y-direction matrix Y2 and the position distribution matrix T. N The combination yields the actual position matrix Y of the y-direction array elements, Y = (Y1' + Y2) * T N ;

[0034] Step 1.6: Take the actual position matrix X of the array elements in the x-direction as the real part and the actual position matrix Y of the array elements in the y-direction as the imaginary part to generate a complex matrix as the initial population matrix.

[0035] Furthermore, the formula for updating the discoverer's location in step 3 is:

[0036]

[0037] in, This represents the position of the sparrow individual corresponding to the α-th discoverer before the update in the current t-th iteration. This indicates the updated α = 1, ..., PD × NP; express The d-th dimension component, d = 1,...,Q; ω is the nonlinear learning factor, ω = ω min +(ω max -ω min )·sin(tπ / MaxCycle), ω min and ω max These are the upper and lower bounds of the non-linear learning factor, respectively; X best The optimal position for the discoverer; MaxCycle is the maximum number of iterations; R2(α,d) is the warning value within the range of [0,1]; ST(α,d) is the safety value within the range of [0.5,1]; r1 is a random number within the range of [0,2π], and r2 is a random number within the range of [0,2].

[0038] Furthermore, the follower position update strategy in step 3 is specifically as follows:

[0039] Follower individuals update their position by imitating the discoverer individual with the highest fitness, using the following formula:

[0040]

[0041] in, This represents the position of the sparrow corresponding to the β-th follower before the update in the current t-th iteration. This indicates that after the update, β = 1,...,(1-PD)×NP; express The d-th dimension component, d = 1,...,Q; X best The optimal position for the discoverer; X worst The position corresponding to the minimum global fitness; A + =A T (AA T ) -1 A is a 1×Q-dimensional random binary column vector whose elements are randomly assigned the value 1 or -1, and D is a 1×Q-dimensional column vector whose elements are all 1.

[0042] Furthermore, the specific steps in step 4, where the position of the monitor is updated using a cross-sectional strategy, are as follows:

[0043] Step 4.1: Select any two monitors as parent individuals and perform a horizontal cross operation in each dimension;

[0044]

[0045]

[0046] in, and The positions of the supervisors are respectively and The d-th dimension individual is generated through horizontal crossover; r1 and r2 are random numbers in the range [0,1]; c1 and c2 are random numbers in the range [-1,1].

[0047] The new individuals generated by horizontal crossover are compared with the parent individuals, and those with higher fitness are selected for retention.

[0048] Step 4.2: Perform a vertical cross operation on all dimensions of the individual monitor;

[0049]

[0050] in, It is determined by the position of the inspector The offspring individuals are generated by vertical crossover of the d1st and d2nd dimensions; r is a random number in [0,1].

[0051] The new individuals generated by vertical crossover are compared with the parent individuals, and individuals with high fitness are selected for retention.

[0052] A computer device / apparatus / system includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described sparsely distributed rectangular planar array antenna synthesis method.

[0053] A computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the above-described method for synthesizing sparsely distributed rectangular planar array antennas.

[0054] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the above-described sparsely distributed rectangular planar array antenna synthesis method.

[0055] The beneficial effects of this invention are as follows:

[0056] This invention transforms the synthesis method of sparsely distributed rectangular planar array antennas into an optimization problem of the position of array elements in one quadrant. It adopts an improved sparrow algorithm, introduces Kent mapping population initialization, and enhances the diversity of the initialization population. The idea of ​​sine and cosine algorithms is integrated into the position update strategy of the discoverer, and a nonlinear sine learning factor is introduced to enhance the overall search capability. Finally, the cross-hatching strategy is introduced into the sparrow algorithm to improve the optimization accuracy by improving the search method of the monitor. Attached Figure Description

[0057] Figure 1 This is a flowchart of the improved sparrow optimization algorithm in this invention.

[0058] Figure 2 In Embodiment 1 of the present invention Directional cross-section diagram.

[0059] Figure 3 In Embodiment 1 of the present invention Directional cross-section diagram.

[0060] Figure 4 This is the optimal array element distribution diagram in Embodiment 1 of the present invention.

[0061] Figure 5 This is a three-dimensional orientation pattern corresponding to the optimal array element distribution in Embodiment 1 of the present invention.

[0062] Figure 6 In Embodiment 2 of the present invention Directional cross-section diagram.

[0063] Figure 7 This is the optimal array element distribution diagram in Embodiment 2 of the present invention.

[0064] Figure 8 This is a three-dimensional orientation pattern corresponding to the optimal array element distribution in Embodiment 2 of the present invention. Detailed Implementation

[0065] The present invention will now be further described with reference to the accompanying drawings.

[0066] This invention addresses the problems existing in the prior art by proposing an array antenna synthesis method based on an improved arithmetic optimization algorithm. An improved sparrow algorithm for rectangular planar arrays is proposed. First, a Blackman window weighting method is used to generate the position distribution matrix. Then, the sparrow optimization algorithm is improved by introducing Kent mapping population initialization to enhance the diversity of the initialization population. Second, the idea of ​​the sine-cosine algorithm (SCA) is integrated into the position update strategy of the discoverer, and a nonlinear sine learning factor is introduced to enhance the global search capability. Finally, the cross-hatching strategy is introduced into the sparrow algorithm to improve the optimization accuracy by refining the search method of the observer.

[0067] Reference Figure 1 This invention proposes a sparsely distributed planar array synthesis method. There is a sparsely distributed rectangular planar array with an array aperture of 2L×2H on the xoy plane. The number of array elements is 4N. The array is symmetrical about the origin. The N array elements in the first quadrant are optimized. The other three quadrants can be obtained symmetrically from the first quadrant to construct the initial population matrix of the rectangular sparsely distributed planar array.

[0068] Select appropriate element position vectors based on the array aperture size, and transform the element position vectors into element position matrices. The dimensions P and Q of the element position matrix must satisfy the following:

[0069]

[0070] Where N is the number of array elements in the first quadrant, (L, H) are the position coordinates of the Nth array element in the first quadrant, and d c This represents the minimum array element spacing.

[0071] Kent mapping is used for population initialization to enhance the diversity of the initial population and generate a mapping matrix X1∈R in the x-direction. P×Q The mapping matrix Y1∈R in the y-direction P×Q The specific steps are as follows:

[0072] Step 1: Randomly initialize the first column elements of the generated matrix [x 1,1 ,...,x P,1 ] and [y 1,1,...,y P,1 ];

[0073] Step 2: Initially obtain matrix X′∈R based on the iterative formula. P×Q and Y′∈R P×Q ;

[0074]

[0075] Where, x i,j Let y be the element in the i-th row and j-th column of matrix X′, where i = 1, ..., P, j = 1, ..., Q, k = 1, ..., Q-1; i,j Let be the element in the i-th row and j-th column of matrix Y′; μ is a preset constant; S x S represents the margin of the array element in the x-direction. x =L-(Q-0.5)d c S y S represents the margin of the array element in the y-direction. y =H-(P-0.5)d c ;

[0076] Step 3: Normalize the elements in matrices X′ and Y′ to obtain X1∈R P×Q and Y1∈R P×Q ;

[0077]

[0078] in, Let be the element in the i-th row and j-th column of matrix X1, where j = 1, ..., Q; Let Y be the element in the i-th row and j-th column of matrix Y1;

[0079] The initial population matrix contains i individuals, each with dimensions j, where j is 2P×Q in size. The variable to be optimized is an individual in the population, and the first P×Q variables of each individual are the mapping matrix X1∈R in the x-direction. P×Q The variable from P×Q+1 to 2P×Q is the mapping matrix Y1∈R in the y-direction. P×Q ;

[0080] Based on the actual position of each array element, a state matrix S is generated through a Blackman window to determine which array elements need to be retained and which elements need to be sparsified.

[0081] The elements of the state matrix S can be obtained from the following formula:

[0082]

[0083] Where: m iLet n be the weight value generated by the Blackman window for each element position in the i-th row of the element position matrix X1. j Let be the weight value generated by the Blackman window at each element position in the j-th column of the element position matrix Y1, and let be the time-domain expression of the Blackman window. The position distribution matrix T of the array is determined by the state matrix. N Due to the constraint of the array aperture, the array element in the P-th row and Q-th column is retained, i.e.

[0084]

[0085] Using the element position distribution matrix T N By sparsely arranging the array, a sparse array with N array elements is obtained.

[0086] Based on the minimum element spacing d of the array to be optimized c The array dimensions P and Q generate a fixed matrix X2∈R in the x-direction. P×Q And a fixed matrix Y2∈R in the y-direction P×Q This ensures that the element spacing between two adjacent array elements in the same row and column satisfies the minimum spacing d in both the x and y directions. c constraint.

[0087]

[0088] Where, matrix X2∈R P×Q A fixed matrix representing the x-direction, matrix Y2∈R P×Q The fixed portion of the matrix represents the y-direction.

[0089] Sort each row of the mapping matrix X1 in the x-direction in ascending order to form the sorted mapping matrix X'1 in the x-direction, and then combine it with the fixed matrix X2 in the x-direction and the position distribution matrix T. N The combination yields the actual position matrix X of the x-direction array elements, X = (X'1 + X2) * T N ;

[0090] Arrange the elements of each column of the mapping matrix Y1 in the y-direction from smallest to largest to form the sorted mapping matrix Y1′ in the y-direction. Then, combine this sorted matrix with the fixed y-direction matrix Y2 and the position distribution matrix T. N The combination yields the actual position matrix Y of the y-direction array elements, Y = (Y1' + Y2) * T N ;

[0091] Using the actual position matrix X of the array elements in the x-direction as the real part and the actual position matrix Y of the array elements in the y-direction as the imaginary part, a complex matrix L is generated as the initial population matrix.

[0092] This paper incorporates the Sine-Cosine Algorithm (SCA) into the position update strategy for sparrow population discoverers, and introduces a nonlinear sinusoidal learning factor. Using the mathematical model of the nonlinear sinusoidal learning factor, the Sine-Cosine Algorithm (SCA) is integrated into the discoverer position update strategy. The formulas for the nonlinear sinusoidal learning factor and the improved discoverer position formula are as follows:

[0093]

[0094] in, This represents the position of the sparrow individual corresponding to the α-th discoverer before the update in the current t-th iteration. This indicates the updated α = 1, ..., PD × NP; express The d-th dimension component, d = 1,...,Q; ω is the nonlinear learning factor, ω = ω min +(ω max -ω min )·sin(tπ / MaxCycle), ω min and ω max These are the upper and lower bounds of the non-linear learning factor, respectively; X best The optimal position for the discoverer; MaxCycle is the maximum number of iterations; R2(α,d) is the warning value within the range of [0,1]; ST(α,d) is the safety value within the range of [0.5,1]; r1 is a random number within the range of [0,2π], and r2 is a random number within the range of [0,2].

[0095] Follower individuals update their position by imitating the discoverer individual with the highest fitness, using the following formula:

[0096]

[0097] in, This represents the position of the sparrow corresponding to the β-th follower before the update in the current t-th iteration. This indicates that after the update, β = 1,...,(1-PD)×NP; express The d-th dimension component, d = 1,...,Q; X best The optimal position for the discoverer; X worst The position corresponding to the minimum global fitness; A + =A T (AA T ) -1 A is a 1×Q-dimensional random binary column vector whose elements are randomly assigned the value 1 or -1, and D is a 1×Q-dimensional column vector whose elements are all 1.

[0098] To improve the global search capability of the Sparrow Search algorithm, a lateral crossover operation is applied to update the position of the monitor. Before updating each individual, its parent individuals are randomly paired, and a crossover operation is performed in the d-th dimension, as shown below:

[0099]

[0100] in, and respectively by the supervisor and The d-th dimension individual is generated through horizontal crossover. r1 and r2 are random numbers in the range [0,1], and c1 and c2 are random numbers in the range [-1,1]. Horizontal crossover expands the algorithm's search space and improves its global search capability. The solutions generated by horizontal crossover are compared with the parent individuals, and individuals with higher fitness are selected for retention. Therefore, the algorithm's development capability is enhanced through horizontal crossover.

[0101] To avoid premature convergence, a vertical crossover operation is performed on the individuals after the horizontal crossover operation to improve the algorithm's ability to avoid getting trapped in local optima. Unlike the horizontal crossover, the vertical crossover operation is performed across all dimensions of the newly generated individuals.

[0102] Assuming individual When the vertical intersection occurs between the d1-th and d2-th dimensions, the following equation applies:

[0103]

[0104] in, It is an individual The offspring individuals generated through vertical crossover in dimensions d1 and d2 are random numbers in the range r ∈ [0,1]. Similar to the horizontal crossover operation, the offspring individuals generated by the vertical crossover operation need to compete with their parents, and individuals with higher fitness are selected for preservation. Through this selection mechanism, the sparrows participating in the crossover do not lose certain valuable dimensional information; on the contrary, it can improve population diversity and continuously improve the quality of the solution. After performing vertical crossover, individuals that have fallen into local optima can make full use of the useful information in each dimension, thus having the opportunity to escape local optima.

[0105] In summary, the improved sparrow algorithm used in this invention is applied to the optimization problem of finding the positions of N array elements in the first quadrant, and includes the following steps:

[0106] Step 1: Set the total number of sparrows in the population (NP), the proportion of discoverers (PD), the proportion of monitors (SD), and the maximum number of iterations in the sparrow algorithm; use Kent mapping to initialize the population; calculate the fitness value corresponding to the position of each sparrow in the initial population, and take the position with the largest corresponding fitness value as the optimal position of the discoverer;

[0107] Step 1.1: Determine the dimensions P and Q of the array element position matrix;

[0108] Step 1.2: Generate the mapping matrix X1∈R in the x-direction using the Kent mapping. P×Q The mapping matrix Y1∈R in the y-direction P ×Q ;

[0109] Step 1.3: Generate the state matrix S using a Blackman window weighting method; determine the element position distribution matrix T based on the state matrix S. N ;

[0110] Step 1.4: Based on the minimum element spacing d of the array to be optimized c Dimensions P and Q generate a fixed matrix X2∈R in the x-direction. P×Q And a fixed matrix Y2∈R in the y-direction P×Q Ensure that the element spacing between two adjacent array elements in the same row and column satisfies the minimum spacing d in both the x and y directions. c constraint;

[0111] Step 1.5: Sort each row of the x-direction mapping matrix X1 in ascending order to form the sorted x-direction mapping matrix X'1, and then combine it with the x-direction fixed matrix X2 and the position distribution matrix T. N The combination yields the actual position matrix X of the x-direction array elements, X = (X'1 + X2) * T N ;

[0112] Arrange the elements of each column of the mapping matrix Y1 in the y-direction from smallest to largest to form the sorted mapping matrix Y1′ in the y-direction. Then, combine this sorted matrix with the fixed y-direction matrix Y2 and the position distribution matrix T. N The combination yields the actual position matrix Y of the y-direction array elements, Y = (Y1' + Y2) * T N ;

[0113] Step 1.6: Take the actual position matrix X of the array elements in the x-direction as the real part and the actual position matrix Y of the array elements in the y-direction as the imaginary part to generate a complex matrix as the initial population matrix;

[0114] Step 2: Mark the top PD×NP sparrows with the highest corresponding fitness values ​​in the population as discoverers, and mark the remaining sparrows as followers;

[0115] Step 3: Update the positions of all sparrows in the population according to the discoverer position update strategy and the follower position update strategy respectively; integrate the idea of ​​sine and cosine algorithm into the discoverer position update strategy and introduce a non-linear sine learning factor to enhance the global search capability;

[0116] Step 4: Randomly select SD×NP sparrow individuals from the population as monitors, and update the positions of the monitors using a cross-hatching strategy;

[0117] Step 5: Calculate the fitness value corresponding to the position of each sparrow in the updated population. If there is a fitness value greater than that corresponding to the optimal position of the discoverer, then update the optimal position of the discoverer.

[0118] Step 6: If the maximum number of iterations has not been reached, return to step 2; otherwise, output the arrangement of the N array elements in the first quadrant of the sparse rectangular planar array corresponding to the optimal position of the discoverer.

[0119] This invention introduces Kent mapping population initialization to enhance the diversity of the initial population; it integrates the idea of ​​the Sine-Cosine Algorithm (SCA) into the discoverer's position update strategy and introduces a nonlinear sine learning factor to enhance the overall search capability; finally, it introduces the cross-hatching strategy into the sparrow algorithm to improve the optimization accuracy by refining the search method of the monitor. This invention improves the generation method of the state matrix S by using the Blackman window weighted algorithm to generate the array position distribution matrix, and then performs array sparse distribution optimization using the improved sparrow optimization algorithm.

[0120] Example 1:

[0121] The experimental conditions for this invention are as follows: the array aperture of the sparsely distributed planar array is 2L×2H=9.5λ×4.5λ, the number of array elements is 4N=108, the minimum element spacing is d0=0.5λ, the array is symmetrical about the origin, and the element positions in the first quadrant are obtained. The other three quadrants can be obtained symmetrically from the first quadrant. P is 4, and Q is 9. The population size of the optimization algorithm is set to 200, and the maximum number of iterations is 1000. The parameters of the improved sparrow optimization algorithm are set as follows: PD=20%, SD=10%, ST=0.8, ω max =1,ω min =0.4. Make and The fitness function can be defined as follows: The sum of the maximum sidelobe levels on both planes is minimized.

[0122]

[0123] in, Here, θ represents the radiation pattern function of the array antenna. FF represents the pitch angle.max The main lobe peak value is used. X represents the actual position of the array element in the x-direction, and Y represents the actual position of the array element in the y-direction. The state matrix S is generated by weighting through a Blackman window to determine the array elements to be retained and the array elements to be sparsified. The state matrix S is then replaced with the array element position distribution matrix T. N for:

[0124]

[0125] Figure 2 for A cross-sectional view of the direction, in which the highest sidelobe level of the improved sparrow algorithm is -28.7204dB. Figure 3 In order to be in A cross-sectional view of the direction, in which the highest sidelobe level of the improved sparrow algorithm is -34.6584dB. Figures 4 to 5 The distribution map of array element positions and the three-dimensional orientation map corresponding to the optimal value of the proposed algorithm are given respectively.

[0126] Example 2:

[0127] The sparsely distributed planar array has an array size of 2L×2H=9.5λ×4.5λ, a number of elements of 4N=100, and a minimum element spacing of d0=0.5λ. The array is symmetrical about the origin, obtaining the element positions in the first quadrant. The other three quadrants can be obtained symmetrically from the first quadrant. P is set to 4, and Q is set to 9. The population size of the optimization algorithm is set to 200, and the maximum number of iterations is set to 1000. The parameters of the improved sparrow optimization algorithm are set as follows: PD=20%, SD=10%, ST=0.8, ω max =1,ω min =0.4. In order to suppress interference signals, in Nulls are placed on the plane, with nulls set within the range of θ between 30° and 35°, and the desired null depth is -80dB. The weighting coefficients c1 and c2 are set to 0.3 and 0.7, respectively. The fitness function is as follows:

[0128]

[0129] in, Here, θ represents the radiation pattern function of the array antenna. Indicates pitch angle, FF max This represents the main lobe peak value, N represents the number of nulls, and ζ... i c represents the difference between the i-th actual null depth and the expected null depth. i This represents the weighting coefficient and must satisfy the following conditions:

[0130] The optimal peak sidelobe level obtained by the improved sparrow optimization algorithm is -26.2888dB, the deepest null is -79.3458dB, and the null width is 7.5209°. Figure 6 The above algorithm is given in A cross-sectional view of the direction. Figure 7 A diagram showing the distribution of array elements is provided. Figure 8 It is the three-dimensional orientation pattern corresponding to the optimal value.

[0131] In summary, this invention demonstrates superior performance in both sidelobe level suppression and null synthesis for sparsely distributed planar arrays, effectively reducing sidelobe levels and nulls. This invention generates the position distribution matrix using a Blackman window weighting method, an improvement over the random assignment method, simplifying the calculation process and improving optimization efficiency. Furthermore, an improved sparrow optimization technique is employed to optimize the element positions, making the optimization results closer to the ideal element position distribution. Compared to existing algorithms, the proposed method effectively reduces the peak sidelobe level of sparsely distributed planar arrays by 1.67 dB–3.43 dB and improves the null depth by 0.2 dB–2.88 dB.

[0132] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for synthesizing a sparse rectangular planar array antenna, characterized in that: For a sparse rectangular planar array with an array aperture of 2L×2H on the xoy plane, the number of array elements is 4N, the array is symmetrical about the origin of the coordinate system, and the N array elements in the first quadrant are optimized, and the other three quadrants are obtained by symmetry of the first quadrant; The improved sparrow algorithm is used to optimize the position of N array elements in the first quadrant, including the following steps: Step 1: Set the total number of sparrow individuals NP, the proportion of discoverers PD, the proportion of supervisors SD, and the maximum number of iterations in the sparrow algorithm; use Kent mapping to initialize the population; calculate the fitness value corresponding to the position of each sparrow individual in the initial population, and take the position with the largest corresponding fitness value as the optimal position of the discoverer; Step 2: Mark the first PD×NP sparrow individuals with the largest corresponding fitness value in the population as discoverers, and mark the remaining sparrow individuals as followers; Step 3: Update the positions of all sparrow individuals in the population according to the discoverer position update strategy and the follower position update strategy respectively; integrate the idea of ​​sine-cosine algorithm into the discoverer position update strategy, and introduce a nonlinear sine learning factor to enhance the global search capability; Step 4: Randomly select SD×NP sparrow individuals from the population as supervisors, and use the vertical and horizontal cross strategy to update the position of the supervisor; Step 5: Calculate the fitness value corresponding to the position of each sparrow individual in the updated population. If there is a fitness value greater than the fitness value corresponding to the optimal position of the discoverer, update the optimal position of the discoverer. Step 6: If the maximum number of iterations has not been reached, return to step 2; Otherwise, the arrangement scheme of the N array element positions in the first quadrant of the sparse rectangular planar array corresponding to the finder's optimal position is output.

2. The method for synthesizing a sparse rectangular planar array antenna according to claim 1, characterized in that: The method of using Kent mapping to initialize the population in step 1 is specifically as follows: Step 1.1: Determine the dimensions P and Q of the array element position matrix; s.t.P×Q≥N,P,Q∈Z + P≤P max ,Q≤Q max Where (L, H) is the position coordinate of the Nth array element in the first quadrant of the sparse rectangular planar array; d c is the minimum array element spacing; Step 1.2: Use Kent mapping to generate the mapping matrix X1∈R in the x direction P×Q and the mapping matrix Y1∈R in the y direction P×Q ; Step 1.2.1: Randomly initialize the first column of the generated matrix [x 1,1 ,...,x P,1 ] and [y 1,1 ,...,y P,1 ]; Step 1.2.2: According to the iterative formula, the matrix X′∈R is initially obtained P×Q and Y′∈R P×Q ; Among them, x i,j is the element in the i-th row and j-th column of the matrix X′, i=1,...,P, j=1,...,Q, k=1,...,Q-1; y i,j is the element in the i-th row and j-th column of the matrix Y′; μ is a preset constant; S x is the margin of the array element in the x direction, S x =L-(Q-0.5)d c ; S y is the margin of the array element in the y direction, S y =H-(P-0.5)d c ; Step 1.2.3: Normalize the elements in matrices X′ and Y′ to obtain X1∈R P×Q and Y1∈R P×Q ; in, is the element in the i-th row and j-th column of the matrix X1, j=1,...,Q; is the element in the i-th row and j-th column of matrix Y1; Step 1.3: Generate the state matrix S through the Blackman window weighting; determine the array element position distribution matrix T according to the state matrix S N ; Among them, s i,j is the element in the i-th row and j-th column of the state matrix S; m i is the weight value generated by the Blackman window at each array element position in the i-th row of the matrix X1; n j is the weight value generated by the Blackman window at each array element position in the jth column of the matrix Y1; Due to the constraints of the array aperture, the array elements in the Pth row and Qth column of the array are retained, that is, Step 1.4: According to the minimum element spacing d of the array to be optimized c , dimensions P and Q generate a fixed matrix X2∈R in the x direction P×Q and the fixed matrix Y2∈R in the y direction P×Q , ensuring that the distance between two adjacent array elements in the same row and column in the x and y directions meets the minimum distance d c constraint; Step 1.5: Sort the elements of each row of the x-direction mapping matrix X1 from small to large to form the sorted x-direction mapping matrix X1', and combine it with the x-direction fixed matrix X2 and the position distribution matrix T N The actual position matrix X of the array element in the x direction is obtained by combining, X = (X1' + X2) * T N ; Arrange the elements of each column of the y-direction mapping matrix Y1 from small to large to form the sorted y-direction mapping matrix Y1′, and combine it with the y-direction fixed matrix Y2 and the position distribution matrix T N The actual position matrix Y of the array element in the y direction is obtained by combining, Y = (Y1' + Y2) * T N ; Step 1.6: Use the actual position matrix X of the array elements in the x direction as the real part and the actual position matrix Y of the array elements in the y direction as the imaginary part to generate a complex matrix as the initial population matrix.

3. The method for synthesizing a sparse rectangular planar array antenna according to claim 1, characterized in that: The update formula of the discoverer position in step 3 is: in, represents the position of the sparrow individual corresponding to the αth discoverer before updating in the current tth iteration, represents the updated,α=1,...,PD×NP;, express The d-th dimension component of is, d = 1, ..., Q; ω is the nonlinear learning factor, ω = ω min +(ω max -ω min )·sin(tπ / MaxCycle),ω min and ω max are the upper and lower limits of the nonlinear learning factor respectively; X best is the optimal position of the finder; MaxCycle is the maximum number of iterations; R2(α,d) is the warning value within [0,1]; ST(α,d) is the safety value within [0.5,1]; r1 is a random number within [0,2π], and r2 is a random number within [0,2].

4. The method for synthesizing a sparse rectangular planar array antenna according to claim 1, characterized in that: The follower position update strategy in step 3 is specifically as follows: The follower individual updates its position by imitating the discoverer individual with the highest fitness. The update formula is: in, represents the position of the sparrow individual corresponding to the βth follower before updating in the current tth iteration, represents the updated, β=1,...,(1-PD)×NP; express The d-th dimension component of X, d = 1, ..., Q; best is the optimal position of the finder; X worst is the position corresponding to the minimum global fitness; A + =A T (AA T ) -1 , A is a 1×Q-dimensional random binary column vector whose elements are randomly assigned to 1 or -1, and D is a 1×Q-dimensional column vector whose all elements are 1.

5. The method for synthesizing a sparse rectangular planar array antenna according to claim 1, characterized in that: In step 4, the vertical and horizontal cross strategy is used to update the position of the supervisor: Step 4.1: Select any two supervisors as parent individuals to pair, and perform a horizontal crossover operation in each dimension; in, and The position of the supervisor and The d-dimensional individual is generated by horizontal crossover; r1 and r2 are random numbers in [0,1]; c1 and c2 are random numbers in [-1,1]; The new individuals generated by horizontal crossover are compared with the parent individuals, and the individuals with high fitness are selected for retention; Step 4.2: Conduct longitudinal cross-operation on all dimensions of the individual monitors; in, The position of the supervisor The offspring individuals are generated by vertical crossover in the d1th dimension and the d2th dimension; r is a random number in [0,1]; The new individuals generated by vertical crossover are compared with the parent individuals, and the individuals with high fitness are selected and retained.

6. A computer device / equipment / system comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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