A method for designing a sparse wire array in two dimensions along an array axis and normal to the array axis

Abstract

The application discloses a design method for a linear array along an array axis and an array axis normal direction, and the method comprises the following steps: expanding the array element random distribution area from the array axis direction to the array axis normal direction, adding the normal dimension to the array element position optimization, and constituting a linear array model along the array axis and the array axis normal direction; based on the linear array model along the array axis and the array axis normal direction, adopting nested optimization to determine the position of each array element. The linear array model proposed in the application expands the array element distribution area to the array axis normal direction, adds the normal optimization dimension to the array element position parameter optimization, and can obtain better performance in suppressing the grating lobe compared to the scheme of only optimizing the array element position arrangement in the array axis direction, and can weaken the coupling effect between the array elements.

Description

Technical Field

[0001] This invention belongs to the field of optimized array design technology in sparse array radar, and particularly relates to a two-dimensional sparse line array design method along the array axis and the array axis normal. Background Technology

[0002] Research in this field mainly falls into three technical paths: analytical methods, optimization models for low-sidelobe sparse linear arrays, and optimization models based on beam pattern reconstruction. Analytical methods include typical minimum redundancy matrices, coprime matrices, and nested matrices, as well as optimization methods based on combinations of these three. Other methods include Taylor's method based on Ishinaru theory, exponential matrices, raised cosine matrices, and Chebyshev matrices. The optimization model research approach for low-sidelobe sparse linear arrays includes heuristic optimization methods such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Neural Networks, and simulated annealing; optimization methods based on Fourier transforms; and methods that transform the problem into a convex optimization problem by constructing an objective function and constraining the desired beam characteristics. In the optimization model research approach based on beam pattern reconstruction, matrix decomposition and compressed sensing are representative examples. The main purpose of matrix decomposition-based design algorithms is to extract important features of the matrix; therefore, many sparse linear array design algorithms can reduce the number of array elements through matrix decomposition. Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. Traditional compressed sensing algorithms and sparse constraint optimization algorithms can both design sparse linear arrays that meet the requirements.

[0003] When the intra-array phase difference between antenna elements is balanced with the spatial phase difference, that is, when the phase provided by the intra-array phase shifting module can completely compensate for the phase difference caused by spatial propagation (the two phases are the same, but the signs are opposite), the maximum value of the linear array antenna pattern is obtained.

[0004] In scanning mode, the beam scans to θ max The condition that no grid lobes appear is:

[0005]

[0006] θ max This represents the maximum angle of the desired direction within the scanning range.

[0007] In recent years, research on sparse array and sparse array design methods has shown that these methods can effectively suppress the grating lobe phenomenon in uniform arrays, while also having significant advantages in saving costs and reducing system complexity.

[0008] All the studies conducted through the aforementioned approaches are based on a processing model where array elements are arranged along the array axis. They only focus on the algorithmic level, improving the algorithm in conventional dimensions. Regarding the coupling between array elements, previous methods did not improve the average spatial distance between elements, and therefore could not effectively mitigate the coupling effect between array elements. Summary of the Invention

[0009] The purpose of this invention is to further improve the effect of suppressing grating lobes. A new model is proposed, which is a design method for a two-dimensional sparse wire array along the array axis and the array axis normal.

[0010] To achieve the above objectives, this invention proposes a two-dimensional sparse wire array design method along the array axis and the array axis normal, the method comprising:

[0011] The area where array elements are randomly distributed is expanded from along the array axis to the array axis normal, adding a normal dimension to the array element position optimization, thus forming a two-dimensional sparse wire array model along the array axis and the array axis normal.

[0012] Based on a two-dimensional sparse wire array model along the array axis and the array axis normal, nested optimization is used to determine the position of each array element.

[0013] As an improvement to the above method, there are N array elements in total, the array aperture is L, and the array elements are not uniformly distributed.

[0014] As an improvement to the above method, the nested optimization is a GA_PSO nested optimization that employs the standard genetic algorithm and the particle swarm optimization algorithm in the axial and normal directions, respectively, specifically including:

[0015] Step 1) Initialize the population along the axial and normal directions;

[0016] Step 2) converts the distance interval along the axial direction and the change in the normal direction;

[0017] Step 3) Perform fitness calculation;

[0018] Step 4) Substitute the current array element distribution as the initial value into the nested normal link h_PSO algorithm to obtain the global optimal result of this link as the global local optimal result of the normal. Compare it with the fitness value before this round of optimization. If there is no improvement, do not update. Otherwise, update the global local optimal result of the normal to the global global optimal result of the normal, and update the global fitness function value.

[0019] Step 5) Determine whether the stopping condition is met based on the fitness value. If not, proceed to step 6); otherwise, proceed to step 7.

[0020] Step 6) After performing selection, crossover, and mutation operations on the positions of array elements along the axis, sort the individual genes, convert them into distance intervals, and then proceed to step 3).

[0021] Step 7) Output the optimal individual, determine the position of each array element, and the optimization process ends.

[0022] As an improvement to the above method, step 1) includes:

[0023] The number of populations along the axial direction and the normal direction is NP, and both populations are initialized.

[0024] As an improvement to the above method, step 3) includes:

[0025] The pattern function is calculated using the following formula:

[0026]

[0027] Where, d m It is represented as the distance between the m-th array element and the first array element, θ0 is the direction of the main beam, N is the number of array elements, ω=2f, and f is the operating frequency;

[0028] The fitness PSLL is calculated using the following formula:

[0029]

[0030] Where max() represents the function to find the maximum value, F dB (θ) represents the normalized radiation pattern function, S represents the sidelobe interval of the radiation pattern, and if the zero-power point of the main lobe of the radiation pattern is... but

[0031]

[0032] Where, θ min θ max These are the minimum and maximum angles for the desired direction within the scanning range, respectively.

[0033] As an improvement to the above method, step 4) substitutes the current array element distribution as an initial value into the nested normal vector stage h_PSO algorithm to obtain the global optimal result of this stage as the global-local optimal result value of the normal vector. Specifically, this includes:

[0034] Step 4-1) Input the current array element distribution;

[0035] Step 4-2) Use the current distribution of array elements as the initial position of the particle swarm and initialize the particle velocities;

[0036] Step 4-3) Perform fitness calculation;

[0037] Step 4-4) Determine whether the stopping condition is met based on the fitness value. If not, proceed to step 4-5); otherwise, proceed to step 4-6.

[0038] Steps 4-5) compare the particle fitness function values, update the local optimum of this step; update the global optimum of this step: including fitness function value and particle position; then update the particle velocity, update the particle position, handle the out-of-bounds situation and convert it into normal change, and go to step 4-3).

[0039] Steps 4-6) Obtain the global optimal result of this step as the numerical value of the global local optimal result of the normal direction.

[0040] As an improvement to the above method, steps 4-5) sequentially update particle velocity, update particle position, handle boundary overflow cases, and convert them into normal changes, specifically including:

[0041] Based on the number of array elements N when optimizing the distribution of the pairwise axes and normals, the dimension of the optimization problem to be solved is set to N, and the particle swarm size is NP. i =(x i1 ,x i2 ,…,x iN ) represents the position of the array element corresponding to the i-th particle; υ i =(υ i1 υ i2 , ..., v iN ) represents the velocity of the i-th particle, p i =(p i1 p i2 , ..., p iN Let g = (g1, g2, ..., g2) represent the best position found by the i-th particle. N () indicates the best location found by the entire group;

[0042] The following iterative equations are used to update the particle velocity and particle position:

[0043] v id (t+1)=ω·v id (t)+c1r1(p id (t)-x id (t))+c2r2(g d (t)-x id (t))

[0044] x id (t+1)=x id (t)+v id (t+1)

[0045] Where i = 1, 2, ..., NP; d = 1, 2, ..., N; d is the number of array elements, c1 and c2 are learning factors, t represents the number of iterations, and r1 and r2 are random numbers that follow a uniform distribution on [0, 1].

[0046] v max and -v max The upper and lower boundaries of particle velocity are set. Particle velocities exceeding the boundaries are set as boundary values. If a particle's position exceeds the boundaries after an update, it is confined to the boundaries.

[0047] As an improvement to the above method, step 6) involves sorting the individual genes of the array element positions along the axis after selection, crossover, and mutation operations, converting them into distance intervals. Specifically, this includes:

[0048] The axial array element positions are selected using a roulette wheel selection method, which uses the proportion of fitness of each individual to determine the probability of its offspring being retained.

[0049] Pair the selected odd-numbered individuals with even-numbered individuals, and use a single-point crossover method for each pair of individuals, with a crossover probability P. c Exchange some of their genes;

[0050] In the population after crossover, from j = 1 to N, i = 1 to NP, generate a random number r in the interval [0, 1]. If r < P m P m Let represent the mutation probability. Then, the (j, i)th gene is selected as the mutated gene, and then replaced with a parameter from the randomly generated value range.

[0051] As an improvement to the above method, the nested optimization is a PSO_PSO nested optimization that uses particle swarm optimization in both the axial and normal directions, specifically including:

[0052] Step 1) Initialize the population along the axial and normal directions;

[0053] Step 2) converts the distance interval along the axial direction and the change in the normal direction;

[0054] Step 3) Perform fitness calculation;

[0055] Step 4) Substitute the current array element distribution as the initial value into the nested h_PSO algorithm to obtain the global optimal result of this step as the normal global local optimal result value, and compare it with the fitness value before this round of optimization. If there is no improvement, do not update; otherwise, update the normal global local optimal result to the global optimal result, and update the global fitness function value.

[0056] Step 5) Determine if the stopping condition is met. If not, proceed to step 6); otherwise, proceed to step 7.

[0057] Step 6) After updating the particle velocity and particle position of the array elements along the axis, handle the out-of-bounds situation, convert it into a distance interval, and then proceed to step 3).

[0058] Step 7) Output the optimal individual, determine the position of each array element, and the optimization process ends.

[0059] Compared with the prior art, the advantages of the present invention are:

[0060] 1. The processing model proposed in this application extends the distribution area of ​​array elements to the array axis normal, adding a normal optimization dimension to the optimization of array element position parameters. Under this model, only the single optimization parameter of array element position is considered. By making full use of the added normal optimization dimension, various optimization frameworks can be designed, such as nested optimization, alternating optimization, or weighted optimization.

[0061] 2. The linear array dual-dimensional optimization scheme proposed in this application can achieve better performance in suppressing grid lobes compared with the scheme that only optimizes the array element position arrangement in the array axis direction, and can also reduce the coupling effect between array elements. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the array element optimization in the model, where Figure 1 (a) in the diagram is a one-dimensional uniform linear array. Figure 1 (b) in the diagram represents the optimization of a sparse wire array along a single dimension of the array axis. Figure 1 (c) in this application is the sparse wire array dual-dimensional optimized linear array;

[0063] Figure 2 This is a diagram of the model array signal processing structure of the present invention;

[0064] Figure 3 It describes the time delay of various spatial relationships between adjacent array elements;

[0065] Figure 4 This is a flowchart of the GA_PSO optimization process in Embodiment 1 of the present invention;

[0066] Figure 5 This is a flowchart of the PSO_PSO optimization process in Embodiment 2 of the present invention;

[0067] Figures 6(a) and 6(b) show the results of the existing standard genetic algorithm, where Figure 6(a) is the beam pattern and Figure 6(b) is the array element factor. Polar coordinate beam pattern at time;

[0068] Figures 7(a) and 7(b) show the results of the basic particle swarm optimization algorithm in the prior art, where Figure 7(a) is the beam pattern and Figure 7(b) is the array element factor. Polar coordinate beam pattern at time;

[0069] Figures 8(a) and 8(b) show the GA_PSO nesting optimization results of Embodiment 1 of the present invention, where Figure 8(a) is the beam pattern and Figure 8(b) is the array element factor. Polar coordinate beam pattern at time;

[0070] Figures 9(a) and 9(b) show the PSO_PSO nesting optimization results of Embodiment 2 of the present invention, where Figure 9(a) is the beam pattern and Figure 9(b) is the array element factor. Polar coordinate beam pattern at time;

[0071] Figures 10(a) to 10(d) These are the statistical results of the spatial distance between array elements. Figure 10(a) shows the MISD statistics of the prior art GA optimization, Figure 10(b) shows the MISD statistics of the prior art PSO optimization, Figure 10(c) shows the MISD statistics of GA_PSO optimization in Embodiment 1 of the present invention, and Figure 10(d) shows the MISD statistics of PSO_PSO optimization in Embodiment 2 of the present invention. Detailed Implementation

[0072] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0073] Technical solution:

[0074] 1) Two-dimensional linear array model

[0075] Depend on Figure 1 As shown, from left to right, they are (a) a one-dimensional uniform linear array, (b) a sparse linear array optimized along the array axis in a single dimension, and (c) a sparse linear array optimized in two dimensions as proposed in this application.

[0076] In (c), the distribution of array elements is based on the random distribution along the array axis in (b). In the region where the array axis normal is not coplanar (specifically, in plane B in (c), plane B is perpendicular to plane A), the normal direction is also randomly optimized. This means that at this stage, the activity strategy of the array elements is to start from the position after the random distribution along the array axis and move up and down along the normal direction of the array axis in plane B.

[0077] That is, the area where the array elements are randomly distributed is expanded from along the array axis to the array axis normal, adding a normal dimension to the optimization of the array element position, thus forming a two-dimensional sparse wire array model along the array axis and the array axis normal;

[0078] Based on a two-dimensional sparse wire array model along the array axis and the array axis normal, nested optimization is used to determine the position of each array element.

[0079] 2) Nested optimization

[0080] This includes GA_PSO, which uses the standard genetic algorithm in the axial direction and the particle swarm algorithm in the normal direction, and PSO_PSO, which uses the particle swarm algorithm in both directions.

[0081] The specific steps include:

[0082] Step 1) Initialize the population along the axial and normal directions;

[0083] Step 2) converts the distance interval along the axial direction and the change in the normal direction;

[0084] Step 3) Perform fitness calculation;

[0085] Step 4) Substitute the current array element distribution as the initial value into the nested normal link h_PSO algorithm to obtain the global optimal result of this link as the global local optimal result of the normal. Compare it with the fitness value before this round of optimization. If there is no improvement, do not update. Otherwise, update the global local optimal result of the normal to the global global optimal result of the normal, and update the global fitness function value.

[0086] Step 5) Determine whether the stopping condition is met based on the fitness value. If not, proceed to step 6); otherwise, proceed to step 7.

[0087] Step 6) The axial array elements can be optimized using GA or PSO algorithms, converted into distance intervals, and then proceeded to step 3);

[0088] Step 7) Output the optimal individual, determine the position of each array element, and the optimization process ends.

[0089] Array Synthesis:

[0090] First, a model of a non-uniformly arranged linear array is established, with an array aperture of L. It consists of N antenna elements with unequal spacing, d... m Let θ be the distance between the m-th array element and the first array element, where i ≤ N. Let the main beam pointing direction be θ0. Therefore, its pattern function expression can be expressed as:

[0091]

[0092] In the expression of phased array radiation pattern, the compensation between inter-array phase difference and spatial phase difference is usually used, but it is essentially a compensation between time differences, as shown in the above formula, where ω=2πf, f is the operating frequency.

[0093] Fitness function:

[0094] According to the definition of the maximum sidelobe level of the radiation pattern, the formula for calculating PSLL can be expressed as follows:

[0095]

[0096] In the formula, max represents the function for finding the maximum value, F dB(θ) represents the normalized pattern function, and S represents the sidelobe interval of the pattern. If the zero-power point of the main lobe of the pattern is... but

[0097]

[0098] This formula considers determining the PSLL within the scan range when no grating lobes appear. When grating lobes appear, the location of the main lobe needs to be determined first, and then the side lobes need to be found to avoid confusion with the grating lobes. In subsequent optimization processes, the location of the grating lobes will gradually change to side lobes with larger normalized gain. Therefore, only the peak points within the side lobe interval are calculated, reducing the computational burden caused by conventional methods that calculate all sampling points in the side lobe interval.

[0099] Standard genetic algorithm PSO:

[0100] (i) Population initialization

[0101] Here, a population of NP individuals, each with a dimension of L, is used as an intermediate population. Each individual in the population is sorted in ascending order to obtain the true distance interval population d, and d(1) = 0 and d(end) = L for each individual to ensure that the array aperture remains unchanged.

[0102] (ii) Select operation

[0103] The "roulette wheel" selection method is used, which determines the likelihood of offspring retention based on the proportion of fitness of each individual.

[0104] (iii) Cross operation

[0105] Pair the selected odd-numbered individuals with even-numbered individuals, and for each pair of individuals, use a crossover probability P. c They exchange some genes. Here, a single-point crossover method is used.

[0106] (iv) Mutation operations

[0107] In the population after crossover, from j = 1 to N, i = 1 to NP, generate a random number r in the interval [0, 1]. If r < P m P m Let represent the mutation probability. Then, the (j, i)th gene is selected as the mutated gene, and then it is replaced with a parameter from the randomly generated value range.

[0108] Basic Particle Swarm Optimization (PSO) Algorithm:

[0109] Let the dimension of the optimization problem to be solved be N, and the particle swarm size be NP. In the particle swarm optimization algorithm, x i =(x i1 xi2 , ..., x iN ) represents the position of the i-th particle; υ i =(υ i1 υ i2 , ..., v iN ) represents the velocity of the i-th particle; p i =(p i1 p i2 , ..., p iN ) represents the best position found by the i-th particle; g = (g1, g2, ..., g...) N () indicates the best location found by the entire group.

[0110] The basic PSO uses the following iterative equations to update velocity and position:

[0111] v id (t+1)=ω·v id (t)+c1r1(p id (t)-x id (t))+c2r2(g d (t)-x id (t))

[0112] x id (t+1)=x id (t)+v id (t+1)

[0113] Where i = 1, 2, ..., NP; d = 1, 2, ..., N; c1 and c2 are learning factors; t represents the number of iterations; r1 and r2 are random numbers that follow a uniform distribution on [0, 1].

[0114] v max and -v max These are set as the upper and lower boundaries for particle velocities; particle velocities exceeding these boundaries are set as boundary values. If a particle's position exceeds these boundaries after an update, it will be confined to the boundaries.

[0115] The algorithm described above is called the global version of the particle swarm optimization algorithm. For the sparse wire array design problem, the number of array elements corresponds to the problem dimension, and the position of the i-th particle is the array element distribution corresponding to the i-th particle.

[0116] Based on the array structure proposed in this paper, the time delay between array elements needs to be rewritten.

[0117] The first element at the left end of the array is used as the reference element. Figure 2 This is a diagram of the model array signal processing structure of the present invention; based on geometric relationships, by Figure 2 The structure can be summarized as follows: the time delay of any adjacent array elements is:

[0118]

[0119] This formula is correct. Figure 2 The same applies to various sub-cases. Figure 3 (a), (b), (c), and (d) are four sub-cases of time delay between adjacent array elements.

[0120] In addition, based on the rules of array element spacing and inter-array element coupling, the above model has a larger array element spatial distance compared to the scheme that only optimizes the array element position arrangement within the array aperture range along the array axis, which helps to reduce the inter-array element coupling effect.

[0121] In conventional array element location random distribution, the algorithm's search area is within the array aperture along the array axis. Based on the array structure proposed in this application, the optimization of array element locations adds a normal dimension, thus expanding the search area.

[0122] Therefore, nested optimization algorithms are considered along the array axis and the array axis normal to achieve iterative approximation optimization.

[0123] Example 1

[0124] like Figure 4 As shown, Embodiment 1 of the present invention proposes a two-dimensional sparse wire array design method along the array axis and the array axis normal. Specifically, it includes:

[0125] Step 1) Initialize the population along the axial and normal directions;

[0126] Step 2) converts the distance interval along the axial direction and the change in the normal direction;

[0127] Step 3) Perform fitness calculation;

[0128] Step 4) Substitute the current array element distribution as the initial value into the nested normal path h_PSO algorithm to obtain the global optimal result of this step as the global local optimal result of the normal path. Compare this result with the fitness value before this round of optimization. If there is no improvement, do not update; otherwise, update the global local optimal result of the normal path to the global optimal result of the normal path, and update the global fitness function value. Specifically:

[0129] Step 4-1) Input the current array element distribution;

[0130] Step 4-2) Use the current distribution of array elements as the initial position of the particle swarm and initialize the particle velocities;

[0131] Step 4-3) Perform fitness calculation;

[0132] Step 4-4) Determine whether the stopping condition is met based on the fitness value. If not, proceed to step 4-5); otherwise, proceed to step 4-6.

[0133] Steps 4-5) compare the particle fitness function values, update the local optimum of this step; update the global optimum of this step: including fitness function value and particle position; then update the particle velocity, update the particle position, handle the out-of-bounds situation and convert it into normal change, and go to step 4-3).

[0134] In this context, based on the number of array elements N when optimizing the distribution of the pairwise axes normals, the dimension of the optimization problem to be solved is set to N, and the particle swarm size is NP. i =(x i1 x i2 , ..., x iN ) represents the position of the array element corresponding to the i-th particle; v i =(v i1 v i2 , ..., v iN ) represents the velocity of the i-th particle, p i =(p i1 p i2 , ..., p iN Let g = (g1, g2, ..., g2) represent the best position found by the i-th particle. N () indicates the best location found by the entire group;

[0135] The following iterative equations are used to update the particle velocity and particle position:

[0136] v id (t+1)=ω·v id (t)+c1r1(p id (t)-x id (t))+c2r2(g d (t)-x id (t))

[0137] x id (t+1)=x id (t)+v id (t+1)

[0138] Where i = 1, 2, ..., NP; d = 1, 2, ..., N; c1 and c2 are learning factors, t represents the number of iterations, and r1 and r2 are random numbers that follow a uniform distribution on [0, 1].

[0139] v max and -v max The upper and lower boundaries of particle velocity are set. Particle velocities exceeding the boundaries are set as boundary values. If a particle's position exceeds the boundaries after an update, it is confined to the boundaries.

[0140] Steps 4-6) Obtain the global optimal result of this step as the numerical value of the global local optimal result of the normal direction.

[0141] Step 5) Determine whether the stopping condition is met based on the fitness value. If not, proceed to step 6); otherwise, proceed to step 7.

[0142] Step 6) After performing selection, crossover, and mutation operations on the positions of array elements along the axis, sort the individual genes, convert them into distance intervals, and then proceed to step 3); specifically:

[0143] The axial array element positions are selected using a roulette wheel selection method, which uses the proportion of fitness of each individual to determine the probability of its offspring being retained.

[0144] Pair the selected odd-numbered individuals with even-numbered individuals, and use a single-point crossover method for each pair of individuals, with a crossover probability P. c Exchange some of their genes;

[0145] In the population after crossover, from j = 1 to N, i = 1 to NP, generate a random number r in the interval [0, 1]. If r < P m P m Let represent the mutation probability. Then, the (j, i)th gene is selected as the mutated gene, and then replaced with a parameter from the randomly generated value range.

[0146] Step 7) Output the optimal individual, determine the position of each array element, and the optimization process ends.

[0147] Example 2

[0148] like Figure 5 As shown, Embodiment 2 of the present invention proposes a two-dimensional sparse wire array design method along the array axis and the array axis normal. Specifically, it includes:

[0149] Step 1) Initialize the population along the axial and normal directions;

[0150] Step 2) converts the distance interval along the axial direction and the change in the normal direction;

[0151] Step 3) Perform fitness calculation;

[0152] Step 4) Substitute the current array element distribution as the initial value into the nested h_PSO algorithm to obtain the global optimal result of this step as the normal global local optimal result value, and compare it with the fitness value before this round of optimization. If there is no improvement, do not update; otherwise, update the normal global local optimal result to the global optimal result, and update the global fitness function value.

[0153] Step 5) Determine if the stopping condition is met. If not, proceed to step 6); otherwise, proceed to step 7.

[0154] Step 6) After updating the particle velocity and particle position of the array elements along the axis, handle the out-of-bounds situation, convert it into a distance interval, and then proceed to step 3).

[0155] Step 7) Output the optimal individual, determine the position of each array element, and the optimization process ends.

[0156] Innovation points:

[0157] Under this model, considering only the single optimization parameter of the array element position, various optimization frameworks can be designed by making full use of the added normal optimization dimension, such as nested optimization, alternating optimization, or weighted optimization.

[0158] Beneficial effects of this invention:

[0159] Taking the array axis using a genetic algorithm and the array axis normal using a particle swarm algorithm, as well as the array axis and array axis normal both using a particle swarm algorithm, as examples, we demonstrate the performance improvement brought by using this model.

[0160] Figures 6(a) and 6(b) show the results of the existing standard genetic algorithm, where Figure 6(a) is the beam pattern and Figure 6(b) is the array element factor. Polar coordinate beam pattern at time;

[0161] After optimization using the GA method, the grating lobe was suppressed to some extent, and the peak sidelobe level (PSLL) optimization result was -11.07dB. The main lobe width was not widened compared to the uniform array.

[0162] Figures 7(a) and 7(b) show the results of the basic particle swarm optimization algorithm in the prior art, where Figure 7(a) is the beam pattern and Figure 7(b) is the array element factor. Polar coordinate beam pattern at time;

[0163] After optimization using the PSO method, PSLL finally converged at -14.40dB, but the main lobe width was widened. If the range of -3dB attenuation of the peak gain of the middle main lobe is taken as the main lobe width, this scheme is widened by about 4.3° compared with the uniform array.

[0164] Figures 8(a) and 8(b) show the nested optimization results of GA_PSO in Embodiment 1 of the present invention, where Figure 8(a) is the beam pattern and Figure 8(b) is the array element factor. Polar coordinate beam pattern at time;

[0165] No grating lobes appeared in the beam pattern after optimization of the array element position using the GA_PSO nested scheme. The final PSLL optimization converged at -12.59dB, which is 1.52dB better than the standard GA result.

[0166] Figures 9(a) and 9(b) show the PSO_PSO nesting optimization results of Embodiment 2 of the present invention, where Figure 9(a) is the beam pattern and Figure 9(b) is the array element factor. Polar coordinate beam pattern at time;

[0167] The optimization of PSLL using the PSO_PSO nested scheme converged at -16.76 dB, an improvement of 2.36 dB over the basic particle swarm optimization algorithm. The -3 dB main lobe width broadened by approximately 1.9° compared to the uniform array, an improvement of 2.4° over the basic particle swarm optimization algorithm.

[0168] Figures 10(a) to 10(d) These are the statistical results of the spatial distance between array elements. Figure 10(a) is the MISD statistics of the prior art GA optimization, Figure 10(b) is the MISD statistics of the prior art PSO optimization, Figure 10(c) is the MISD statistics of the GA_PSO optimization of Embodiment 1 of the present invention, and Figure 10(d) is the MISD statistics of the PSO_PSO optimization of Embodiment 2 of the present invention.

[0169] The average element spacing optimized using standard GA and basic PSO is 1.3λ, while the MISD optimized using GA_PSO and PSO_PSO schemes are 1.54λ and 1.43λ, respectively. Based on the relationship between element spacing and element coupling, it can be seen that since the elements move along the array axis normal, the MISD is larger, which helps reduce the element coupling effect.

[0170] In summary, the proposed two-dimensional optimization scheme for linear arrays achieves better performance in suppressing grating lobes compared to schemes that only optimize the element placement along the array axis, while also reducing coupling effects between elements. The optimization framework is versatile, and combined with various algorithmic improvements proposed in recent years, even better results can be achieved.

[0171] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for designing a two-dimensional sparse wire array along an array axis and a normal to the array axis, the method comprising: The randomly distributed region of array elements is expanded from along the array axis to the normal direction of the array axis, adding a normal dimension to the optimization of array element positions, thus forming a two-dimensional sparse wire array model along the array axis and in the normal direction of the array axis; the array elements have a total of N 1, array aperture is L The array elements are not uniformly distributed; the time delay between any two adjacent array elements is... for: in, This represents the projection distance between two adjacent array elements along the array axis. At the speed of light, Beam pointing angle, This represents the height difference between two adjacent array elements along the array axis normal. Based on a two-dimensional sparse wire array model along the array axis and the array axis normal, nested optimization is used to determine the position of each array element; the nested optimization is either GA_PSO nested optimization or PSO_PSO nested optimization.

2. The method for designing a two-dimensional sparse wire array along the array axis and the normal direction of the array axis according to claim 1, characterized in that, The nested optimization is a GA_PSO nested optimization, specifically including: Step 1) Initialize the population along the axial and normal directions; Step 2) converts the distance interval along the axial direction and the change in the normal direction; Step 3) Perform fitness calculation; Step 4) Substitute the current array element distribution as the initial value into the nested normal link h_PSO algorithm to obtain the global optimal result of this link as the global local optimal result of the normal. Compare it with the fitness value before this round of optimization. If there is no improvement, do not update. Otherwise, update the global local optimal result of the normal to the global global optimal result of the normal, and update the global fitness function value. Step 5) Determine whether the stopping condition is met based on the fitness value. If not, proceed to step 6; otherwise, proceed to step 7. Step 6) After performing selection, crossover, and mutation operations on the positions of array elements along the axis, sort the individual genes, convert them into distance intervals, and then proceed to step 3). Step 7) Output the optimal individual, determine the position of each array element, and the optimization process ends.

3. The method for designing a two-dimensional sparse wire array along the array axis and the normal direction of the array axis according to claim 2, characterized in that, Step 1) includes: The population size along the axial direction and the normal direction are both NP Each population is initialized.

4. The method for designing a two-dimensional sparse wire array along the array axis and the normal direction of the array axis according to claim 3, characterized in that, Step 3) includes: The pattern function is calculated using the following formula: in, Represented as the first The distance between each array element and the first array element. The direction of the main beam. N The number of array elements , For operating frequency, j It is the imaginary part; Fitness is calculated using the following formula. PSLL : in, max () represents the function to find the maximum value. This represents the normalized pattern function. This represents the sidelobe interval of the radiation pattern. If the zero-power point of the main lobe of the radiation pattern is... ,but in, , These are the minimum and maximum angles for the desired direction within the scanning range, respectively.

5. The method for designing a two-dimensional sparse wire array along the array axis and the normal direction of the array axis according to claim 3, characterized in that, Step 4) involves substituting the current array element distribution as an initial value into the nested normal vector stage h_PSO algorithm to obtain the global optimal result of this stage as the global-local optimal result value of the normal vector. Specifically, this includes: Step 4-1) Input the current array element distribution; Step 4-2) Use the current distribution of array elements as the initial position of the particle swarm and initialize the particle velocities; Step 4-3) Perform fitness calculation; Step 4-4) Determine whether the stopping condition is met based on the fitness value. If not, proceed to step 4-5; otherwise, proceed to step 4-6. Steps 4-5) Compare particle fitness function values ​​and update the local optimum for this step; update the global optimum for this step, including fitness function value and particle position; then update particle velocity and particle position sequentially, handle out-of-bounds cases and convert them into normal changes, and return to step 4-3). Steps 4-6) Obtain the global optimal result of this step as the numerical value of the global local optimal result of the normal direction.

6. The method for designing a two-dimensional sparse wire array along the array axis and the normal direction of the array axis according to claim 5, characterized in that, Steps 4-5) sequentially update particle velocity, update particle position, handle boundary overflow cases, and convert them into normal changes, specifically including: Optimize the number of array elements based on the normal distribution of the pair axis. N Let the dimension of the optimization problem to be solved be... N The particle swarm size is , Indicates the first The position of the array element corresponding to each particle; Indicates the first The speed of each particle Indicates the first The best position found by each particle. This indicates the best location found by the entire group; The following iterative equations are used to update the particle velocity and particle position: in, d The number of array elements and As a learning factor, Indicates the number of iterations. and Is The above are random numbers that follow a uniform distribution; Will and The upper and lower boundaries of particle velocity are set. Particle velocities exceeding the boundaries are set as boundary values. If a particle's position exceeds the boundaries after an update, it is confined to the boundaries.

7. The method for designing a two-dimensional sparse wire array along the array axis and the normal direction of the array axis according to claim 2, characterized in that, Step 6) involves sorting the individual genes of the array elements along the axis after selection, crossover, and mutation operations, converting them into distance intervals. Specifically, this includes: The axial array element positions are selected using a roulette wheel selection method, which uses the proportion of fitness of each individual to determine the probability of its offspring being retained. Pair the selected odd-numbered individuals with even-numbered individuals, and use a single-point crossover method for each pair of individuals, with the crossover probability... Exchange some of their genes; In the population after crossover, from , In the interval Generate a random number ,if , Let represent the mutation probability, then the th A gene is selected as the gene to be mutated, and then replaced with a parameter from a randomly generated range of values.

8. The method for designing a two-dimensional sparse wire array along the array axis and the normal direction of the array axis according to claim 1, characterized in that, The nested optimization method is specifically PSO_PSO nested optimization, which includes: Step 1) Initialize the population along the axial and normal directions; Step 2) converts the distance interval along the axial direction and the change in the normal direction; Step 3) Perform fitness calculation; Step 4) Substitute the current array element distribution as the initial value into the nested h_PSO algorithm to obtain the global optimal result of this step as the normal global local optimal result value, and compare it with the fitness value before this round of optimization. If there is no improvement, do not update; otherwise, update the normal global local optimal result to the global optimal result, and update the global fitness function value. Step 5) Determine if the stopping condition is met; if not, proceed to step 6); otherwise, proceed to step 7). Step 6) After updating particle velocity and particle position along the axial array element positions, handle out-of-bounds cases, convert them into distance intervals, and then proceed to step 3). Step 7) Output the optimal individual, determine the position of each array element, and the optimization process ends.

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