Method for acquiring low-peak side-lobe sparse array with array element position constraint

Abstract

The invention discloses a low-peak sidelobe sparse array acquisition method with array element position constraint, which comprises the following steps of: defining an optimization model for a uniformly arranged linear array, optimizing the position of an array element by optimizing the value of f, and enabling the maximum sidelobe level MSLL of a directional diagram of the optimized linear array to be minimum; meanwhile, the aperture of the sparse linear array needs to be unchanged. According to the method, under the condition that the low calculation amount is guaranteed and the array element position constraint is met, the sparse array without grating lobes and with the globally optimal solution and with the low peak side lobes can be rapidly obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of sparse arrays, and in particular to a method for obtaining a low peak sidelobe sparse array with element position constraints. Background Art

[0002] Sparse arrays can achieve a narrower scanning beam, higher resolution, etc. with fewer elements, thereby reducing production costs and being more and more widely used in fields such as radar and communication electronics. The peak sidelobe level of an array antenna is an important indicator for evaluating its performance. In addition, in some scenarios (such as multiple functions sharing an antenna), elements at certain positions (used for other functions) must be retained. Developing a low peak sidelobe sparse array synthesis algorithm with element position constraints has very important theoretical and practical significance.

[0003] Currently, the optimization method for sparse arrays is the exhaustive method, but the computational complexity of this method increases exponentially with the number of elements. Therefore, it is only applicable to the optimization design of small sparse arrays.

[0004] Intelligent algorithms based on genetic algorithms, simulated annealing, etc. are natural algorithms based on randomness. The processing flow is complex, the computational amount is large, and it takes a long operation time to obtain the final optimization result, and it is difficult to find the global optimal solution. In addition, the optimization result depends on the initial random seed.

[0005] In addition, the synthesis method of a low peak sidelobe sparse array that retains elements at specific positions has not been studied. Summary of the Invention

[0006] In view of this, the present invention provides a method for obtaining a low peak sidelobe sparse array with element position constraints.

[0007] The present invention discloses a method for obtaining a low peak sidelobe sparse array with element position constraints, which includes:

[0008] For a uniformly arranged linear array, an optimization model is defined. By optimizing the value of f, the positions of the elements are optimized so that the maximum sidelobe level MSLL of the optimized linear array pattern is minimized; at the same time, it is necessary to ensure that the aperture of the sparse linear array remains unchanged.

[0009] Further, use f m to represent whether there is an element at the position of the m-th element in the uniformly arranged linear array: f m =1 indicates that there is an element at the position of the m-th element; f m =0 indicates that there is no element at the position of the m-th element; the positions of q elements are constrained, that is, f q =1, q∈{2,…,M - 1}, q < N, M is the number of elements in the uniformly arranged linear array, N is the number of elements in the sparse array, that is, f m=1; then the maximum sidelobe level MSLL of the corresponding pattern F(θ) after optimization is expressed as:

[0010]

[0011] Where S represents the sidelobe interval of the pattern, Represents the azimuth of a uniformly spaced linear array.

[0012] Furthermore, the optimization model of the uniformly arranged linear array is defined as:

[0013]

[0014] Among them, f indicates whether there are array elements at all array element positions in the uniformly arranged linear array, and min indicates the minimum value function. By optimizing the value of f, the position of the array element is optimized so that the maximum sidelobe level MSLL of the optimized linear array radiation pattern is minimized.

[0015] Furthermore, during optimization, the constraint condition of the optimization model is that there are array elements at the array element positions at both ends of the uniformly arranged linear array, so as to ensure that the aperture of the sparse linear array obtained after optimization remains unchanged.

[0016] Furthermore, the optimizing the value of f to optimize the position of the array element so as to minimize the maximum sidelobe level MSLL of the optimized linear array pattern includes:

[0017] Step 1: Set the initial uniformly arranged linear array to {P0:f m =1,m=1,2,…,M}, that is, the initial array has M elements of 1;

[0018] Step 2: First loop, delete {P0:f m =1, m=1, 2, ..., M}, obtain multiple combination sets, and calculate the peak sidelobe levels PSL of the multiple combination sets, and select K combinations with the smallest peak sidelobe levels;

[0019] Step 3: In the p-th cycle, 2≤p≤MN, some array elements in the K combinations are deleted respectively, and the peak sidelobe levels PSL of the K combinations after deleting some arrays are calculated, and K combinations with the smallest peak sidelobe levels are selected from them, which is the optimized sparse linear array with N array elements.

[0020] Furthermore, the step 2 comprises:

[0021] In the first cycle, in {P0:f m =1,m=1,2,…,M}, delete the combination except f q=1,q∈{2,…,M-1}, we get M-3-Q combination sets, recorded as There are M-1 array elements in each combination. m is 1; respectively The peak sidelobe levels PSL of the M-3-Q combinations are selected, and the K combinations with the smallest peak sidelobe levels are selected from the peak sidelobe levels PSL of the M-3-Q combinations, and are recorded as {P1:P 11 ,P 12 ,…,P 1K}.

[0022] Furthermore, the step 3 comprises:

[0023] In the pth cycle, 2≤p≤MN, for the set P p-1 For the kth combination, 1≤k≤K, we sequentially divide f by q =1,q∈{2,…,M-1}, delete one array element, and get M-2-pQ combination sets, recorded as There are Mp array elements in each combination. m is 1, respectively The peak sidelobe levels PSL of the M-2-pQ combinations are calculated to obtain K(M-2-pQ) combinations PSL. The K combinations with the smallest peak sidelobe levels are selected from the K(M-2-pQ) combinations PSL, which are recorded as {P p :P p1 ,P p2 ,…,P pK}, after the MNth cycle is completed, the combination with the smallest side lobe is selected from the K combinations, which is the optimized sparse array with N array elements.

[0024] Furthermore, a sparse array of N array elements is obtained from a uniformly arranged linear array with M array elements. The method of gradually approximating the optimal solution is adopted. Each iteration cycle ensures that there are array elements at the constrained position, and finally the optimal solution of a sparse array with N array elements is obtained, where M is greater than N.

[0025] Due to the adoption of the above technical solution, the present invention has the following advantages: the present invention does not rely on randomness, but takes the regular array as the starting point of optimization to purposefully and gradually approach the optimal solution. Under the condition of ensuring low computational complexity and satisfying the constraints of array element positions, a sparse array with low peak side lobes without grating lobes and with a global optimal solution can be quickly obtained, solving the problem of large sparse array synthesis. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments described in the embodiments of the present invention. For those of ordinary skill in the art, other accompanying drawings can also be obtained based on these drawings.

[0027] Figure 1 It is a schematic flow diagram of optimizing the positions of the array elements in the embodiments of the present invention. Specific embodiments

[0028] The present invention will be further described in conjunction with the accompanying drawings and embodiments. The described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art shall fall within the scope of protection of the embodiments of the present invention.

[0029] See Figure 1 , the present invention provides an embodiment of a method for obtaining a low peak sidelobe sparse array with array element position constraints, which includes:

[0030] For a uniformly arranged linear array, an optimization model is defined. By optimizing the value of f, the positions of the array elements are optimized so that the maximum sidelobe level MSLL of the optimized linear array pattern is minimized; at the same time, it is necessary to ensure that the aperture of the thinned linear array remains unchanged.

[0031] In one embodiment, for a uniformly arranged linear array, f m is used to represent whether there is an array element at the position of the mth array element: f m =1 indicates that there is an array element at the position of the mth array element; f m =0 indicates that there is no array element at the position of the mth array element; the positions of q array elements are constrained, that is, f q =1, q ∈ {2,..., M - 1}, q < N, M is the number of array elements of the uniformly arranged linear array, and N is the number of array elements of the sparse array, that is, the number of f m =1; then the maximum sidelobe level MSLL of the corresponding optimized pattern F(θ) is expressed as:

[0032]

[0033] where S represents the sidelobe interval of the pattern, represents the azimuth angle of the uniformly arranged linear array.

[0034] In one embodiment, the optimization model of the uniformly arranged linear array is defined as:

[0035]

[0036] Among them, f indicates whether there are array elements at all array element positions in the uniformly arranged linear array, and min indicates the minimum value function. By optimizing the value of f, the position of the array element is optimized so that the maximum sidelobe level MSLL of the optimized linear array radiation pattern is minimized.

[0037] In one embodiment, during optimization, the constraint condition of the optimization model is that there are array elements at the array element positions at both ends of the uniformly arranged linear array, so as to ensure that the aperture of the sparse linear array obtained after optimization remains unchanged.

[0038] In one embodiment, optimizing the value of f to optimize the position of the array element so that the maximum sidelobe level MSLL of the optimized linear array pattern is minimized includes:

[0039] Step 1: Set the initial uniformly arranged linear array to {P0:f m =1,m=1,2,…,M}, that is, the initial array has M elements of 1;

[0040] Step 2: First loop, delete {P0:f m =1, m=1, 2, ..., M}, obtain multiple combination sets, and calculate the peak sidelobe levels PSL of the multiple combination sets, and select K combinations with the smallest peak sidelobe levels;

[0041] Step 3: In the p-th cycle, 2≤p≤MN, some array elements in the K combinations are deleted respectively, and the peak sidelobe levels PSL of the K combinations after deleting some arrays are calculated, and K combinations with the smallest peak sidelobe levels are selected from them, which is the optimized sparse linear array with N array elements.

[0042] In one embodiment, step 2 includes:

[0043] In the first cycle, in {P0:f m =1,m=1,2,…,M}, delete the combination except f q =1,q∈{2,…,M-1}, we get M-3-Q combination sets, recorded as There are M-1 array elements in each combination. m is 1; respectively The peak sidelobe levels PSL of the M-3-Q combinations are selected, and the K combinations with the smallest peak sidelobe levels are selected from the peak sidelobe levels PSL of the M-3-Q combinations, and are recorded as {P1:P 11 ,P 12 ,…,P 1K}.

[0044] In one embodiment, step 3 includes:

[0045] In the pth cycle, 2≤p≤MN, for the set P p-1 For the kth combination, 1≤k≤K, we sequentially divide f by q =1,q∈{2,…,M-1}, delete one array element, and get M-2-pQ combination sets, recorded as There are Mp array elements in each combination. m is 1, respectively The peak sidelobe levels PSL of the M-2-pQ combinations are calculated to obtain K(M-2-pQ) combinations PSL. The K combinations with the smallest peak sidelobe levels are selected from the K(M-2-pQ) combinations PSL, which are recorded as {P p :P p1 ,P p2 ,…,P pK}, after the MNth cycle is completed, the combination with the smallest side lobe is selected from the K combinations, which is the optimized sparse array with N array elements.

[0046] In one embodiment, a sparse array of N array elements is obtained from a uniformly arranged linear array of M array elements, and a method of gradually approaching the optimal solution (the solution obtained by minimizing MSLL) is adopted. Each iteration cycle ensures that there are array elements at the constrained position, and finally an optimal solution containing a sparse array of N array elements is obtained, where M is greater than N. Its deformation methods such as planar array or three-dimensional array synthesis are also included in the present invention.

[0047] In the simulation, the regular uniform array element M = 64 is taken as an example. The above method is used to solve the problem under different sparse array element numbers N = 50, and its peak sidelobe level performance is analyzed. The peak sidelobe level changes of the optimal array under each number of array elements when N is 32 to 63 are described. The fth element is specified. m =1, m = 1, 7, 13, 19, 23, 27, 31, that is, these array elements are retained. When N = 50, the PSL of the optimal sparse array reaches about -20.74 dB.

[0048] The present invention provides a new low-sidelobe sparse array optimization method with array element position constraints for, including but not limited to, sparse arrays. The technology has small computational complexity, obvious effects, and can quickly find the sparse array distribution with the optimal PSL. It is suitable for linear arrays, planar arrays, and three-dimensional arrays.

[0049] The present invention provides a fast and effective optimization method for optimizing a sparse array with element position constraints, and its variant forms are also included in the present invention.

[0050] The preferred embodiments of the invention are not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and modifications. However, any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

[0051] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A low peak sidelobe sparse array acquisition method with array element position constraints, It is characterized in that include: For uniformly arranged linear arrays, an optimization model is defined to optimize the position of the array elements by optimizing the value of f so that the maximum sidelobe level MSLL of the optimized linear array pattern is minimized; at the same time, the aperture of the linear array after sparse arrangement remains unchanged.

2. The method according to claim 1, It is characterized in that Use f m to indicate whether there is an array element at the position of the m-th array element in a uniformly arranged linear array: f m = 1 indicates that there is an array element at the position of the m-th array element; f m = 0 indicates that there is no array element at the position of the m-th array element; Constrain the positions of q array elements, that is, f q = 1, q ∈ {2, …, M - 1}, q < N, where M is the number of array elements in the uniformly arranged linear array and N is the number of array elements in the sparse array, that is, f m the number of = 1; Then the maximum sidelobe level MSLL of the corresponding radiation pattern F(θ) after optimization is expressed as: Where S represents the sidelobe interval of the pattern, Represents the azimuth of a uniformly spaced linear array.

3. The method according to claim 2, It is characterized in that The optimization model for defining a uniformly arranged linear array is: Among them, f indicates whether there are array elements at all array element positions in the uniformly arranged linear array, and min indicates the minimum value function. By optimizing the value of f, the position of the array element is optimized so that the maximum sidelobe level MSLL of the optimized linear array radiation pattern is minimized.

4. The method according to claim 3, It is characterized in that During optimization, the constraint condition of the optimization model is that there are array elements at the array element positions at both ends of the uniformly arranged linear array to ensure that the aperture of the sparse linear array obtained after optimization remains unchanged.

5. The method according to claim 3, It is characterized in that The step of optimizing the value of f to optimize the position of the array element so that the maximum sidelobe level MSLL of the optimized linear array pattern is minimized includes: Step 1: Set the initial uniformly arranged linear array as {P 0 :f m =1,m=1,2,…,M}, that is, the initial array has M elements of 1; Step 2: First loop, delete {P 0 :f m =1, m=1, 2, ..., M}, obtain multiple combination sets, and calculate the peak sidelobe levels PSL of the multiple combination sets, and select K combinations with the smallest peak sidelobe levels; Step 3: In the p-th cycle, 2≤p≤MN, some array elements in the K combinations are deleted respectively, and the peak sidelobe levels PSL of the K combinations after deleting some arrays are calculated, and K combinations with the smallest peak sidelobe levels are selected from them, which is the optimized sparse linear array with N array elements.

6. The method according to claim 5, It is characterized in that The step 2 comprises: In the first cycle, 0 :f m =1,m=1,2,…,M}, delete the combination except f q =1,q∈{2,…,M-1}, we get M-3-Q combination sets, recorded as There are M-1 array elements in each combination. m is 1; respectively The peak sidelobe levels PSL of the M-3-Q combinations are selected, and the K combinations with the smallest peak sidelobe levels are selected from the peak sidelobe levels PSL of the M-3-Q combinations, which are denoted as {P 1 :P 11 ,P 12 ,…,P 1K }.

7. The method according to claim 6, It is characterized in that The step 3 comprises: In the pth cycle, 2≤p≤MN, for the set P p-1 For the kth combination, 1≤k≤K, we sequentially divide f by q =1,q∈{2,…,M-1}, delete one array element, and get M-2-pQ combination sets, recorded as There are Mp array elements in each combination. m is 1, respectively The peak sidelobe levels PSL of the M-2-pQ combinations are calculated to obtain K(M-2-pQ) combinations PSL. The K combinations with the smallest peak sidelobe levels are selected from the K(M-2-pQ) combinations PSL, which are recorded as {P p :P p1 ,P p2 ,…,P pK }, after the MNth cycle is completed, the combination with the smallest side lobe is selected from the K combinations, which is the optimized sparse array with N array elements.

8. The method according to claim 5, It is characterized in that A sparse array of N elements is obtained from a uniformly arranged linear array of M elements. The method of gradually approximating the optimal solution is adopted. Each iteration cycle ensures that there are elements at the constrained position, and finally the optimal solution of a sparse array of N elements is obtained, where M is greater than N.

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