Sparse planar array synthesis method

Abstract

The present invention relates to the field of array antenna synthesis, and in particular to a sparse planar array synthesis method. In the present invention, in order to balance the proportion of a development and exploration process, a nonlinear function is used to reconstruct an arithmetic optimization accelerator in an arithmetic optimization algorithm; the top three optimal individuals are used to replace the current optimal individual to perform exploration and development and an elite mutation strategy is introduced, so as to enhance the capability of the algorithm to escape a local optimum, and improve the convergence precision of the algorithm; and an adaptive matrix mapping rule is provided, the current array element distribution is determined, and if the current array element distribution does not meet the minimum array element spacing constraint, the current array element distribution is adjusted by means of an adjustment strategy, thereby guaranteeing the degree of freedom of array elements while avoiding an unfeasible solution.

Description

A Synthesis Method for Sparse Planar Arrays Technical Field

[0001] The present invention relates to the field of array antenna synthesis, and in particular to a sparse planar array synthesis method. Background Art

[0002] The array synthesis problem is a research focus in the field of array antennas. Its core is to determine the number of array elements and the excitation phase, excitation amplitude and position of each element according to the required array radiation characteristics. When each element in the array antenna adopts an isotropic radiating element, the uniformly weighted array synthesis can be simplified to the optimization of the position of each element in the array. At present, there are two main methods for optimizing the position of the array elements. One is the sparse array optimization that only allows the array element position to appear at a given grid point, and the other is the sparse array optimization in which each element is freely placed under the condition of satisfying the given array aperture and array element spacing constraints. Due to the high degree of freedom of the array elements of the sparse array, the desired radiation characteristics can usually be achieved with a smaller number of elements, which has obvious advantages over the sparse array.

[0003] The synthesis of sparse planar arrays has always been a difficult problem due to the minimum element spacing constraint. Existing methods for synthesizing sparse planar arrays adjust element positions to meet this constraint. While this can avoid infeasible solutions, it also forces adjustments to many array distributions that originally met the minimum element spacing constraint, limiting the elements' degrees of freedom and making it difficult to find some feasible solutions. Furthermore, existing intelligent optimization algorithms suffer from low search efficiency and insufficient convergence accuracy during array antenna optimization.

[0004] To address the above problems, the present invention proposes a sparse planar array synthesis method based on an improved arithmetic optimization algorithm, which can avoid infeasible solutions while ensuring the degree of freedom of array elements and improving optimization accuracy.

[0005] Summary of the Invention

[0006] In order to overcome the problems in the prior art, the present invention proposes a sparse planar array synthesis method.

[0007] The technical solution of the present invention to solve the above technical problems is as follows:

[0008] The present invention provides a method for synthesizing a sparse planar array, which specifically comprises the following steps:

[0009] Step 1. Assume that there is a rectangular sparse planar array with an array aperture of 2L×2H on the xoy plane, the number of array elements is 4N, and the array is symmetric about the x-axis and y-axis. Construct the initialization population matrix of the rectangular sparse planar array;

[0010] Step 2. Use the adaptive matrix mapping rule to map the individuals in the initialized population matrix to the actual positions of the array elements, and calculate the fitness of each individual;

[0011] Step 3. Calculate the value of the arithmetic optimization accelerator coefficient according to the current number of iterations;

[0012] Step 4. Select exploration update or development update according to the value of the arithmetic optimization accelerator coefficient;

[0013] Step 5. Perform elite mutation on the global optimal individual;

[0014] Step 6. If the maximum number of iterations is reached, output the optimization result and exit; otherwise, go to step 2.

[0015] Furthermore, step 1 includes: selecting a suitable optimized array matrix dimension according to the array aperture, and the optimized array matrix dimensions P and Q need to satisfy:

[0016] Among them, d c is the minimum element spacing.

[0017] Furthermore, the step 2 specifically includes the following steps:

[0018] Step 21. Initialize the population matrix to have m individuals, each of which has n dimensions, where n is 3P×Q; the first P×Q variables of each individual are the mapping matrix A∈R in the x direction. P×Q , the variable from P×Q+1 to 2P×Q is the mapping matrix B∈R in the y direction P×Q , and finally P×Q variables are the weight matrix W∈R P×Q ;

[0019] Step 22. According to the minimum element spacing d of the optimized array c , the array dimensions P, Q generate the fixed part matrix DX∈R in the x direction P×Q and the fixed part matrix DY∈R in the y direction P×Q ;

[0020] Step 23. Determine the actual position matrix X of the array elements in the x direction according to the mapping matrix A in the x direction, and determine the actual position matrix Y of the array elements in the y direction according to the mapping matrix B in the y direction;

[0021] Step 24. Based on the actual position of each array element, calculate the distance between array elements in different rows and columns; if the minimum array element spacing constraint is not met, adaptively adjust the array element position;

[0022] Step 25. Calculate the fitness of the current individual according to the actual position of the current array element.

[0023] The step 23 specifically includes the following steps:

[0024] Sort the elements of each row of the x-direction mapping matrix A from small to large to form the sorted x-direction mapping matrix A′, and combine it with the x-direction fixed part matrix DX to obtain the x-direction array element actual position matrix X;

[0025] The elements of each column of the mapping matrix B in the y direction are arranged from small to large to form the sorted mapping matrix B' in the y direction, and the sorted mapping matrix B' is combined with the fixed part matrix DY in the y direction to obtain the actual position matrix Y of the array elements in the y direction.

[0026] Furthermore, the step 24 specifically includes the following steps:

[0027] Generate the offset matrix B according to the mapping matrix B' in the y direction offset :

[0028] Among them, β i,max is the maximum value of each row in the mapping matrix B' in the y direction, β i,max Monotonically increasing; Represents the maximum value of row z in the sorted y-direction mapping matrix B';

[0029] like Further adjust the mapping matrix B' in the y direction and update the offset matrix B offset ;

[0030] Where, d c Indicates the minimum array element spacing;

[0031] After adjustment, the actual coordinate matrix Y of each array element in the y direction is: Y=B′+DY+B offset .

[0032] Furthermore, the step 3 specifically includes the following steps:

[0033] The mathematical model of the arithmetic optimization accelerator coefficient reconstructed by nonlinear function, the value of the arithmetic optimization accelerator coefficient is:

[0034] Among them, G is the current iteration number, G M is the maximum number of iterations, Max and Min are the maximum and minimum values ​​of the arithmetic optimization accelerator coefficient respectively.

[0035] Furthermore, the step 4 specifically includes the following steps:

[0036] Before updating, each individual generates a random number r uniformly distributed between [0,1]. When r>MOA(G), the development phase is selected, otherwise the exploration phase is selected, where G is the current iteration number.

[0037] During the exploration phase, the following update is used:

[0038] During the development phase, the following updates are used: leader=(gbest+best2+best3) / 3

[0039] Among them, p i,j Represents the element of the jth dimension of the i-th individual, LB j and UB j are the lower and upper bounds of the search space for the j-th dimension solution, μ is a constant used to control optimization; r2 and r3 are random numbers uniformly distributed between [0,1]; ε is a small constant used to prevent division by zero; gbest represents the current best individual, best2 represents the current second-best individual, and best3 represents the current third-best individual; MOP (Multi-Objective Programming) is a mathematical optimization probabilistic generator used to control the accuracy of exploration and development; the mathematical model of MOP is:

[0040] Among them, σ is the sensitivity coefficient, G 1 / σ is the current iteration number, G M 1 / σ is the maximum number of iterations.

[0041] Furthermore, the step 5 specifically includes the following steps:

[0042] Randomly select two individuals p from the population rd1 、p rd2 , perform elite mutation on the global optimal individual, elite mutation individual gbest * for:

[0043] Among them, p rd1 、p rd2 are two individuals randomly selected from the current population, F is the perturbation coefficient, r4 is a random number uniformly distributed between [0,1], and gbest represents the current best individual; calculate the elite variant individual gbest * If the fitness is better than the current gbest, gbest will be updated.

[0044] Compared with the prior art, the present invention has the following technical effects:

[0045] In order to balance the proportions of development and exploration processes, the present invention adopts nonlinear function reconstruction for the arithmetic optimization accelerator in the arithmetic optimization algorithm; the top three individuals are used to replace the current optimal individual for exploration and development, and an elite mutation strategy is introduced to enhance the algorithm's ability to escape local optimality and improve the algorithm's convergence accuracy; an adaptive matrix mapping rule is proposed to judge the current array element distribution. If it does not meet the minimum array element spacing constraint, it is adjusted through an adjustment strategy to avoid infeasible solutions while ensuring the freedom of the array elements. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions and advantages of the embodiments of the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0047] FIG1 is a flowchart of an improved arithmetic optimization algorithm of the present invention;

[0048] FIG2 is a convergence curve diagram of the present invention;

[0049] FIG3 is a diagram showing the optimal array element distribution in Experiment 1 of the present invention;

[0050] FIG4 is an experimental diagram of the present invention. Directional section diagram;

[0051] FIG5 is an experimental diagram of the present invention. Directional section diagram;

[0052] FIG6 is a three-dimensional directional diagram corresponding to the optimal array element distribution in Experiment 1 of the present invention;

[0053] FIG. 7 is a diagram of Experiment 2 of the present invention. Directional section diagram;

[0054] FIG8 is a diagram showing the optimal array element distribution in Experiment 2 of the present invention;

[0055] FIG9 is a three-dimensional directional diagram corresponding to the optimal array element distribution in Experiment 2 of the present invention. DETAILED DESCRIPTION

[0056] The present invention will be described in further detail below with reference to the accompanying drawings and embodiments.

[0057] To further illustrate the technical means and effects employed by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, describes in detail the specific implementations, structures, features, and effects of the technical solutions proposed by the present invention. Specific features, structures, or characteristics in one or more embodiments may be combined in any suitable manner. Unless otherwise defined, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention pertains.

[0058] This paper addresses the problems existing in the prior art and proposes an array antenna synthesis method based on an improved arithmetic optimization algorithm. First, to balance the development and exploration processes, the arithmetic optimization accelerator in the arithmetic optimization algorithm is reconstructed using nonlinear functions. Second, the top three individuals are used to replace the current optimal individual for exploration and development, and an elite mutation strategy is introduced to enhance the algorithm's ability to escape local optima and improve its convergence accuracy. Finally, an adaptive matrix mapping rule is proposed to determine the current array element distribution. If it does not meet the minimum element spacing constraint, it is adjusted through an adjustment strategy, avoiding infeasible solutions while maintaining the freedom of the array elements.

[0059] 1 , the present invention proposes a method for synthesizing a sparse planar array, which specifically includes the following steps:

[0060] Step 1. Assume that there is a rectangular sparse planar array with an array aperture of 2L×2H on the xoy plane, the number of array elements is 4N, and the array is symmetrical about the x-axis and y-axis. By optimizing the N array elements in the first quadrant, the array elements in other quadrants can be mirrored to construct the initialization population matrix of the rectangular sparse planar array.

[0061] Select the appropriate optimized array matrix dimensions based on the array aperture. The optimized array matrix dimensions P and Q need to satisfy the following requirements:

[0062] Among them, d c is the minimum element spacing.

[0063] To determine which elements are to be thinned out, a weight matrix W is constructed with dimensions P × Q, where N 1s represent the remaining elements and P × QN 0s represent the thinned-out elements. The upper bound UB and lower bound LB of the optimization variables are set based on the specific rectangular sparse planar array.

[0064] According to the upper bound UB and lower bound LB of the optimization variable, the population matrix P is randomly initialized, and its mathematical expression is as follows:

[0065] Among them, P is the initial population matrix, there are m individuals in the population, p m,n Represents the mth individual, the dimension of the individual is n, and the size of n is 3P×Q.

[0066] Step 2. Use the adaptive matrix mapping rule to map the individuals in the initialized population matrix into the actual positions of the array elements, and calculate the fitness of each individual.

[0067] This step specifically includes:

[0068] Step 21. Initialize the population matrix to have m individuals, each individual has n dimensions, and the size of n is 3P×Q; the optimized variable is an individual in the population, and the first P×Q variables of each individual are the mapping matrix A∈R in the x direction P×Q , the variable from P×Q+1 to 2P×Q is the mapping matrix B∈R in the y direction P×Q , and finally P×Q variables are the weight matrix W∈R P×Q , P is the number of array elements in each column of the mapping matrix, and Q is the number of array elements in each row of the mapping matrix;

[0069] Among them, α P,Q Represents the element of row P and column Q in the mapping matrix A in the x-direction, β P,Q Represents the element of row P and column Q in the mapping matrix B in the y direction. The element α in the mapping matrix A in the x direction is [0,S x ] interval, the element β in the y-direction mapping matrix B is [0,S y ] Random number in the interval; S x is the margin S of the array element in the x direction x =L-(Q-0.5)d c ;S y is the margin S of the array element in the y direction y =H-(P-0.5)d c , d c Indicates the minimum element spacing.

[0070] Step 22. According to the minimum element spacing d of the array to be optimized c , the array dimensions P, Q generate the fixed part matrix DX∈R in the x direction P×Q and the fixed part matrix DY∈R in the y direction P×Q The role of the fixed part matrix is ​​to ensure that the element spacing between two adjacent elements in the same row and column meets the constraints in the x and y directions.

[0071] Among them, the matrix DX∈R P×Q Represents the fixed part matrix in the x direction, matrix DY∈R P×Q Represents the fixed part matrix in the y direction.

[0072] Step 23: Determine the actual position matrix X of the array elements in the x direction according to the mapping matrix A in the x direction, and determine the actual position matrix Y of the array elements in the y direction according to the mapping matrix B in the y direction.

[0073] Sort the elements of each row of the x-direction mapping matrix A from small to large to form the sorted x-direction mapping matrix A′, and combine it with the x-direction fixed part matrix DX to obtain the x-direction array element actual position matrix X; X=A′+DX

[0074] In the above formula, X represents the actual position matrix of the array element in the x direction, A′ represents the sorted mapping matrix in the x direction, and DX represents the fixed part matrix in the x direction; α′ P,Q The elements of row P and column Q in the sorted x-direction mapping matrix, α' i,1 ≤α' i,2 ≤…≤α' i,Q , i represents the row, α' i,1 Represents the element in row i and column 1 of the sorted x-direction mapping matrix, α' i,Q Represents the element in row i and column Q of the sorted x-direction mapping matrix.

[0075] Arrange the elements of each column of the mapping matrix B in the y direction from small to large to form the sorted mapping matrix B' in the y direction, and combine it with the fixed part matrix DY in the y direction to obtain the actual position matrix Y of the array elements in the y direction; Y=B′+DY

[0076] In the above formula, Y represents the actual position matrix of the array element in the y direction, B' represents the mapping matrix in the y direction after sorting, DY represents the fixed part matrix in the y direction, β' P,Q The elements of row P and column Q in the sorted y-direction mapping matrix, j represents the column, β' 1,j Represents the element in row 1 and column j of the sorted y-direction mapping matrix, β' P,j Represents the element at row P and column j in the sorted y-direction mapping matrix.

[0077] Step 24. Based on the actual position of each array element, calculate the distance between the array element and array elements in different rows and columns; if the minimum array element spacing constraint is not met, adaptively adjust the array element position.

[0078] Generate the offset matrix B according to the mapping matrix B' in the y direction offset :

[0079] Among them, β i,max is the maximum value of each row in the sorted y-direction mapping matrix B', because each column of the matrix is ​​increasing, so as the row i increases, βi,max Monotonically increasing, It represents the cumulative sum of the maximum values ​​of each row of the mapping matrix B' in the y direction from the 1st row to the P-1th row.

[0080] like This indicates that direct adjustment of the P-th row array elements will not meet the array aperture requirements. It is necessary to further adjust the sorted y-direction mapping matrix B' and update the offset matrix B offset ;

[0081] After adjustment, the actual coordinate matrix Y of each array element in the y direction is: Y=B′+DY+B offset

[0082] The y-direction distance between any two adjacent rows of array elements is:

[0083] Among them, y i+1,m 、y i,n are the actual positions of the array element in the i+1th row and mth column and the array element in the ith row and nth column in the y direction, β' i+1,m ,β' i,n The elements of the i+1th row and mth column and the ith row and nth column in the mapping matrix B' in the y direction, β z,max , β i,max are the maximum values ​​of the zth and ith rows in the mapping matrix B' in the y direction respectively.

[0084] The x-direction distance between adjacent array elements in any row is: i,m+1 -x i,m =α' i,m+1 +(m+1-0.5)d c -α' i,m -(m-0.5)d c =α' i,m+1 -α' i,m +d c ≥d c

[0085] Among them, x i,m+1 、x i,m are the actual positions of the array element in the i-th row, m+1th column, and the array element in the i-th row, mth column in the x direction, α' i,m+1 is the x-direction margin of the element in the i-th row and the m+1-th column, α' i,m The x-direction margin of the element in the i-th row and the m-th column.

[0086] Since the distance between any array elements in two adjacent rows in the y direction and the distance between any array elements in each row in the x direction both meet the minimum array element spacing requirement, the distance between any two array elements in the array also meets the minimum array element spacing requirement.

[0087] The above adjustment strategy is aimed at the case where the average adjustment margin in the x direction is smaller than the average adjustment margin in the y direction, that is, S x / Q<S y / P, and vice versa.

[0088] Step 25. Calculate the fitness of the current individual according to the actual position of the current array element.

[0089] Step 3. Calculate the value of the arithmetic optimization accelerator coefficient MOA according to the current number of iterations.

[0090] The mathematical model of the arithmetic optimization accelerator coefficient MOA reconstructed by nonlinear function, the value of the arithmetic optimization accelerator coefficient MOA (Math Optimizer Accelerated) is:

[0091] Among them, G is the current iteration number, G M is the maximum number of iterations, Max and Min are the maximum and minimum values ​​of MOA respectively.

[0092] Step 4. Select exploration update or development update according to the value of the arithmetic optimization accelerator coefficient MOA.

[0093] Before updating, each individual generates a random number r uniformly distributed between [0,1]. When r>MOA(G), the development phase is selected, otherwise the exploration phase is selected, where G is the current iteration number.

[0094] During the exploration phase, the following update is used:

[0095] During the development phase, the following updates are used: leader=(gbest+best2+best3) / 3

[0096] Among them, p i,j represents the element of the jth dimension of the i-th individual, p j Represents the element of the j-th dimension, LB j and UB j are the lower and upper bounds of the search space for solutions in the jth dimension. μ is a constant used to control optimization, usually set to 0.499. r2 and r3 are random numbers uniformly distributed between [0,1]. ε is a small constant used to prevent division by zero. gbest represents the current best individual, best2 represents the current second-best individual, and best3 represents the current third-best individual. MOP (Multi-Objective Programming) is a mathematical optimization probabilistic machine. The mathematical model of MOP is:

[0097] Among them, σ is the sensitivity coefficient, which is usually set to 5. MOP is a value that decreases monotonically with the increase of the number of iterations and is used to control the accuracy of exploration and development; G 1 / σ is the 1 / σ power of the current iteration number G, G M 1 / σ is the current maximum number of iterations G M 1 / σ to the power of .

[0098] Step 5. Perform elite mutation on the global optimal individual.

[0099] To further improve the AOA algorithm's ability to escape local optima and prevent premature maturation, an elite mutation strategy is introduced. During each generation of population evolution, an elite mutation is performed on the currently optimal individual. In the early stages of the search, the elite individual relies on the mutation of other individuals in the population, making this mutation strategy relatively efficient. However, in the later stages of the search, when differences between individuals are minimal, this mutation strategy becomes less efficient.

[0100] In order to take into account the mutation efficiency in the early and late stages of the search, two individuals p are randomly selected from the population. rd1 、p rd2 , use the following formula for elite mutation:

[0101] Among them, p rd1 、p rd2 are two individuals randomly selected from the current population, F is the perturbation coefficient, and r4 is a random number uniformly distributed between [0,1]. Calculate the elite mutation individual gbest * If the fitness is better than the current gbest, gbest will be updated.

[0102] Step 6. If the maximum number of iterations is reached, output the optimization result and exit; otherwise, go to step 2.

[0103] The experimental conditions of the present invention are as follows: the array aperture of the sparse planar array is 2L×2H=9.5λ×4.5λ, the number of array elements is 4N=108, the minimum array element spacing is d0=0.5λ, the array is symmetrical about the x-axis and the y-axis, and the array element positions of the remaining quadrants can be obtained by mirroring by optimizing only the array element positions in the first quadrant, P is 4, and Q is 9. The population number of the optimization algorithm is set to 100, the maximum number of iterations is 1000, and 10 independent experiments are performed. The parameters Max and Min of the improved arithmetic optimization algorithm are set to 1 and 0.2 respectively, and σ, μ and F are set to 5, 0.499, and 0.03 respectively. The optimization goal is to make and The sum of the peak sidelobe levels on the two planes is minimum, and its fitness function is as follows:

[0104] in, is the array pattern function, θ represents the azimuth angle, Indicates the pitch angle, FF max is the main lobe peak, X is the actual position of the array element in the x-direction, Y is the actual position of the array element in the y-direction, and there are N 1s in the state matrix W representing the retained array elements.

[0105] Figure 2 is the convergence curve of the IAOA algorithm. The optimal value of fitness is -61.47dB. The peak sidelobe level on the plane is -34.78dB. The peak sidelobe level on the plane is -26.69dB, the worst value of fitness is -55.63dB, and the average value is -57.31dB. Figures 3 to 5 show the optimal array element distribution diagrams of different algorithms, Directional cross-section and Directional cross-section diagram. Figure 6 is the three-dimensional direction diagram corresponding to the optimal value of the proposed algorithm.

[0106] The conditions of the second experiment of the present invention are: the array size of the sparse planar array is 2L×2H=9.5λ×4.5λ, the number of array elements 4N=100, the minimum array element spacing is d0=0.5λ, the array is symmetrical about the x-axis and y-axis, P is 5, and Q is 9. The optimization goal is to minimize the peak sidelobe level while meeting the specific angle null depth on the specified plane. Two nulls are placed on the plane, located at θ = 15° and θ = 45°, with a desired null depth of -70 dB. The Nth element is not fixed. The optimization algorithm population size is set to 100, the maximum number of iterations is 1000, and 10 independent experiments are performed. The parameters Max and Min of the improved arithmetic optimization algorithm are set to 1 and 0.2, respectively, and σ, μ, and F are set to 5, 0.499, and 0.03, respectively. The fitness function is as follows:

[0107] Among them, FF max is the main lobe peak, M is the number of nulls placed, c and c i Is the weight coefficient, uniformly set to 1, Null d is the expected null depth, Null o is the actual zero sink depth.

[0108] The optimal peak sidelobe level obtained by the proposed improved algorithm is -32.68dB, the null depth obtained at θ = 15° is -70.21dB, and the null depth obtained at θ = 45° is -72.98dB. Figures 7 and 8 show the results of the above algorithm in Figure 9 is the 3D directional diagram corresponding to the optimal value of the proposed algorithm.

[0109] In summary, the method of this embodiment can effectively address the problems of current algorithms in sparse planar array synthesis, which reduce the degree of freedom of array elements to avoid infeasible solutions, resulting in low search efficiency and insufficient convergence accuracy. The improved arithmetic optimization algorithm of the present invention has a strong ability to escape local optimality and high convergence accuracy. The adaptive matrix mapping rule can avoid infeasible solutions while maintaining the degree of freedom of array elements. Compared with existing algorithms, the proposed method can effectively reduce the peak sidelobe level of sparse planar arrays by 0.75dB-3.07dB and improve the null depth by 0.2dB-2.97dB.

[0110] It should be understood that, although the various steps in the flowcharts involved in the various embodiments described above are displayed in sequence according to the instructions of the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified in the present invention, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the various embodiments described above may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of steps or stages in other steps.

[0111] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention, and should all be included in the scope of protection of the present invention.

Claims

1. A method for synthesizing a sparse planar array, characterized in that: The specific steps include: Step 1. Assume that there is a rectangular sparse planar array with an array aperture of 2L×2H on the xoy plane, the number of array elements is 4N, and the array is symmetric about the x-axis and the y-axis. Construct the initialization population matrix of the rectangular sparse planar array; Step 2. Use the adaptive matrix mapping rule to map the individuals in the initialized population matrix into the actual positions of the array elements, and calculate the fitness of each individual; Step 3. Calculate the value of the arithmetic optimization accelerator coefficient according to the current number of iterations; Step 4. Select exploration update or development update according to the value of the arithmetic optimization accelerator coefficient; Step 5. Perform elite mutation on the global optimal individual; Step 6. If the maximum number of iterations is reached, output the optimization result and exit, otherwise transfer to step 2.

2. A sparse planar array synthesis method according to claim 1, characterized in that: The step 1 includes: selecting a suitable optimized array matrix dimension according to the array aperture, and the optimized array matrix dimensions P and Q need to satisfy: Among them, d c is the minimum array element spacing.

3. A sparse planar array synthesis method according to claim 2, characterized in that: The step 2 specifically includes the following steps: Step 21. Initialize the population matrix to have m individuals, each of which has n dimensions, where n is 3P×Q; the first P×Q variables of each individual are the mapping matrix A∈R in the x direction P×Q , the variable from P×Q+1 to 2P×Q is the mapping matrix B∈R in the y direction P×Q , and finally P×Q variables are the weight matrix W∈R P×Q ; Step 22. According to the minimum array element spacing d of the optimized array c , the array dimensions P, Q generate the fixed partial matrix DX∈R in the x direction P×Q and the fixed part matrix DY∈R in the y direction P×Q ; Step 23. Determine the actual position matrix X of the array elements in the x direction according to the mapping matrix A in the x direction, and determine the actual position matrix Y of the array elements in the y direction according to the mapping matrix B in the y direction; Step 24. According to the actual position of each array element, the distance between array elements in different rows and columns is calculated; if the minimum array element spacing constraint is not met, the array element position is adaptively adjusted; Step 25. Calculate the fitness of the current individual according to the actual position of the current array element.

4. A sparse planar array synthesis method according to claim 3, characterized in that: The step 23 specifically includes the following steps: The elements of each row of the mapping matrix A in the x direction are sorted from small to large to form a sorted mapping matrix A′ in the x direction, and the sorted mapping matrix A′ in the x direction is combined with the x-direction fixed part matrix DX to obtain the x-direction array element actual position matrix X; Each column element of the mapping matrix B in the y direction is arranged from small to large to form a sorted mapping matrix B' in the y direction, and it is combined with the fixed part matrix DY in the y direction to obtain the actual position matrix Y of the array elements in the y direction.

5. A method for synthesizing a sparse planar array according to claim 4, characterized in that: The step 24 specifically includes the following steps: Generate the offset matrix B according to the mapping matrix B' in the y direction offset : Among them, β i,max is the maximum value of each row in the mapping matrix B' in the y direction, β i,max Monotonically increasing; Represents the maximum value of row z in the sorted y-direction mapping matrix B'; like Further adjust the mapping matrix B' in the y direction and update the offset matrix B offset ; Where, d c Indicates the minimum array element spacing; After adjustment, the actual coordinate matrix Y of each array element in the y direction is: Y=B′+DY+B offset 。 6. A sparse planar array synthesis method according to claim 1, characterized in that: The step 3 specifically comprises the following steps: The mathematical model of the arithmetic optimization accelerator coefficient reconstructed by nonlinear function, the value of the arithmetic optimization accelerator coefficient is: Among them, G is the current iteration number, G M is the maximum number of iterations, Max and Min are the maximum and minimum values ​​of the arithmetic optimization accelerator coefficient respectively.

7. A method for synthesizing a sparse planar array according to claim 6, characterized in that: The step 4 specifically comprises the following steps: Before updating, each individual generates a random number r uniformly distributed between [0,1]. When r>MOA(G), the development phase is selected, otherwise the exploration phase is selected, where G is the current iteration number; During the exploration phase, the following update is used: During the development phase, the following updates are used: leader=(gbest+best2+best3) / 3 Among them, p i,j represents the element of the jth dimension of the i-th individual, p j Represents the element of the j-th dimension, LB j and UB j are the lower and upper bounds of the search space for the j-th dimension solution, μ is a constant used to control optimization; r2 and r3 are random numbers uniformly distributed between [0,1]; ε is a very small constant used to prevent division by 0; gbest represents the current best individual, best2 represents the current second-best individual, and best3 represents the current third-best individual; MOP is a mathematical optimization probabilist used to control the accuracy of exploration and development; the mathematical model of MOP is: Among them, σ is the sensitivity coefficient, G 1 / σ is the current iteration number, G M 1 / σ is the maximum number of iterations.

8. A method for synthesizing a sparse planar array according to claim 1, characterized in that: The step 5 specifically comprises the following steps: Randomly select two individuals p from the population rd1 、p rd2 , perform elite mutation on the global optimal individual, the elite mutation individual gbest * for: Among them, p rd1 、p rd2 are two individuals randomly selected from the current population, F is the perturbation coefficient, r4 is a random number uniformly distributed between [0,1], and gbest represents the current best individual; calculate the elite variant individual gbest * If the fitness is better than the current gbest, gbest will be updated.

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