A k-times expanded sparse array configuration antenna and a design method thereof

Abstract

The application discloses a kind of k Sparse array configuration antenna of N times expansion and its design method, comprising: determining the number of array elements and array element spacing of each sparse subarray;Design k Sparse array configuration of N times expansion and deduce array element position distribution;Deduce k Sparse array configuration of N times expansion in the continuous interval of difference coarray domain, sum coarray domain and sum difference coarray;Calculate k The degree of freedom of sparse array configuration of N times expansion;Calculate k The coarray redundancy rate of sparse array configuration of N times expansion.The application proposes a kind of k Sparse array configuration antenna of N times expansion and its design method, by introducing k N times expansion factor, reduce the number of overlapping array elements between sum coarray and difference coarray, while reducing coarray redundancy, ensure array degree of freedom.

Description

Technical Field

[0001] This invention belongs to the field of array antenna design, specifically relating to a... k Double-extended sparse array antenna and its design method. Background Technology

[0002] Compared to sparse array designs based on differential comatrix, sparse array designs based on summation-differential perspectives offer larger array apertures and comatrix degrees of freedom, improving angle measurement performance at the array design level and thus attracting widespread attention from researchers. However, in most existing array configurations, such as coprime arrays (CPA), nested arrays (NA), and differential summation coprime arrays with multiple periodic subarrays (DsCAMpS), there are a large number of overlapping elements between the summation comatrix and the differential comatrix. Only half of these overlapping elements can be used to expand the array degrees of freedom, resulting in low array utilization. Furthermore, most existing array configurations contain holes in their summation-differential comatrix, further hindering the improvement of array degrees of freedom. Summary of the Invention

[0003] This invention addresses the shortcomings of existing technologies by providing a [missing information]. k Double-extended sparse array antenna configuration and its design method, by introducing k The expansion factor is doubled to reduce the number of overlapping elements between the summation co-array and the difference co-array, thereby reducing the redundancy of the co-array while ensuring the array's degrees of freedom.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A sort of k A sparse array configuration antenna with a doubly extended shape, characterized in that the sparse array configuration includes two levels of sparse subarrays, namely... and ,according to Sequential array arrangement, subarray The number of array elements in the array is And the spacing between array elements is Pair array conduct k Double expansion yields subarray The number of array elements in the array is And the spacing between array elements is ,in , , The incident signal wavelength, the total number of array elements .

[0006] To optimize the above technical solution, the specific measures also include: Furthermore, the distribution of array element positions in the sparse array configuration satisfy ,as follows:

[0007] in, express k order expansion factor, k This represents the expansion coefficient, and its value is related to... and The value is irrelevant.

[0008] Furthermore, the summation difference comatrix of the sparse array configuration is symmetric about the origin, and the summation difference comatrix... Its positive part negative part , represented as:

[0009] in, Denotes the set of positive difference comatrixes. The set of positive summation common arrays is represented as:

[0010] Positive part of the difference comatrix The continuous interval of the difference comatrix is ; The positive part of the summation matrix The continuous interval of the summation matrix is: ; The continuous interval of the entire summation difference comatrix is .

[0011] Furthermore, the degrees of freedom of the sparse array configuration are: ; The co-array redundancy of the sparse array configuration is:

[0012] in, This represents the maximum value of the difference comatrix. This represents the minimum value of the largest continuous interval of the summation matrix.

[0013] The present invention also proposes a method k A method for designing a sparse array antenna with a doubly extended configuration, characterized by comprising the following steps: Step 1: Determine the number of array elements and the element spacing in each sparse subarray of the two-level sparse subarray; Step 2: Design based on the parameters set in Step 1. k The sparse array configuration with double expansion is derived and the element position distribution is deduced; Step 3: Based on the sparse array configuration designed in Step 2, calculate... k The doubly extended sparse array configuration is available in the continuous intervals of the differential coarray, the summation coarray, and the summation-differential coarray. Step 4: Based on the sparse array configuration designed in Step 2, and combined with the continuous intervals calculated in Step 3, calculate... k Degrees of freedom for sparse array configurations that are doubled; Step 5: Based on the sparse array configuration designed in Step 2, and combined with the degrees of freedom calculated in Step 4, calculate... k Co-array redundancy in a doubly expanded sparse array configuration.

[0014] Furthermore, in step 1, a sparse subarray is defined. and ,according to Sequential array arrangement, subarray The number of array elements in the array is And the spacing between array elements is Pair array conduct k Double expansion yields subarray The number of array elements in the array is And the spacing between array elements is ,in , , The incident signal wavelength, the total number of array elements .

[0015] Furthermore, in step 2, the distribution of array element positions in the sparse array configuration... satisfy ,as follows:

[0016] in, express k order expansion factor, k This represents the expansion coefficient, and its value is related to... and The value is irrelevant.

[0017] Furthermore, in step 3, the summation difference comatrix of the sparse array configuration is symmetric about the origin, and the summation difference comatrix... Its positive part negative part , is represented as:

[0018] in, Denotes the set of positive difference comatrixes. The set of positive summation common arrays is represented as:

[0019] Therefore, the positive part of the difference comatrix can be calculated. The continuous interval of the difference comatrix is ; The positive part of the summation matrix The continuous interval of the summation matrix is: ; The continuous interval of the entire summation difference comatrix is .

[0020] Furthermore, in step 4, k The degrees of freedom of the double-extended sparse array configuration are .

[0021] Furthermore, in step 5, k The co-array redundancy of the double-expanded sparse array configuration is:

[0022] in, This represents the maximum value of the difference comatrix. This represents the minimum value of the largest continuous interval of the summation matrix.

[0023] The beneficial effects of this invention are: unlike traditional array configuration designs based on summation difference co-matrix, this invention discloses a... k Double-extended sparse array antenna configuration and its design method, introducing k The expansion factor is doubled to reduce the number of overlapping elements between the summation co-array and the differential co-array, thereby reducing the redundancy of the co-array. The proposed array configuration has a hole-free summation differential co-array, and its array degrees of freedom are superior to most existing array configurations. Attached Figure Description

[0024] Figure 1 The present invention proposes k A schematic diagram of the design process for a sparse array antenna with a doubly extended configuration.

[0025] Figure 2 The sparse array antenna configuration proposed in this invention has different order factors. Q The following is a two-dimensional topological structure diagram.

[0026] Figure 3 This is a comparison diagram of the continuous degrees of freedom of the present invention, coprime array (CPA), super nested array (Super NA), and coprime nested array (Coprime NA) under the same array element number condition. Detailed Implementation

[0027] The invention will now be described in further detail with reference to the accompanying drawings.

[0028] In one embodiment, reference is made to Figure 1 This invention proposes a k The design methodology for sparse array antennas with doubly extended configurations includes: Step 1: Determine the number of elements and the spacing between elements in each sparse subarray, as follows: Define sparse subarrays and subarray The number of array elements in the array is And the spacing between array elements is Pair array conduct k Double expansion yields subarray The number of array elements in the array is And the spacing between array elements is in , , The incident signal wavelength, the total number of array elements .

[0029] Step 2: Based on the parameters set in Step 1, design... k The sparse array configuration with double expansion is shown below, and the element position distribution is derived as follows: Element position distribution in sparse array configuration satisfy ,Right now

[0030] in, express k order expansion factor, k This represents the expansion coefficient, and its value is related to... and The value is irrelevant. It only indicates that the value is taken within a range.

[0031] Step 3: Based on the array configuration designed in Step 2, derive... k The doubly extended sparse array configuration covers the continuous intervals of the differential co-array domain, the summation co-array domain, and the summation-differential co-array domain, as detailed below: Since the summation difference comatrix of a sparse array is symmetric about the origin, its positive value part negative part It can be represented as:

[0032] in, Denotes the set of positive difference comatrixes. Represents the set of positive summation common arrays, specifically:

[0033] therefore, k The summation difference comatrix of the doubly extended sparse array configuration can be expressed as: .

[0034] Based on the above calculation results, it can be seen that the positive part of the difference comatrix... The continuous interval of the difference comatrix is ; Find the positive part of the summation matrix The continuous interval of the summation matrix is: .

[0035] because ,and and If it is established, then This indicates that the difference comatrix can fill all the holes in the summation comatrix, and the continuous interval of the entire summation difference comatrix is... .

[0036] Step 4: Based on the array configuration designed in Step 2, calculate... k The degrees of freedom for the double-expanded sparse array configuration are as follows: According to the calculation results in step 3, we can see that k The degrees of freedom of the double-extended sparse array configuration are .

[0037] Step 5: Based on the array configuration designed in Step 2, calculate... k The co-array redundancy rate of the double-expanded sparse array configuration is as follows: k The co-array redundancy of the double-expanded sparse array configuration is:

[0038] in This represents the maximum value of the difference comatrix. This represents the minimum value of the largest continuous interval of the summation matrix.

[0039] Figure 2 This is a graph showing the co-array redundancy as a function of the number of array elements for three array configurations: the present invention, the nested array (NA), and the differential summation coprime array with multiple periodic subarrays (DsCAMpS). As shown in the graph, the co-array redundancy of NA increases with the number of array elements, eventually approaching 1; the proposed method... kThe co-array redundancy of the doubly extended sparse array configuration and DsCAMpS decreases with the increase of the number of array elements, eventually approaching 0; with the same number of array elements, the array configuration proposed in this invention has a lower array redundancy.

[0040] Figure 3 This is a graph showing the continuous degrees of freedom (DOF) as a function of the number of array elements for three array configurations: the present invention, coprime array (CPA), nested array (NA), and differential summation coprime array with multiple periodic subarrays (DsCAMpS). As can be seen from the graph, the DDF of all four array configurations increases with the number of array elements. With the same number of array elements, the array configuration proposed in this invention has more DDFs, and this advantage becomes more pronounced with increasing element count.

[0041] In another embodiment, the present invention also proposes a method proposed in the first embodiment. k The design method of sparse array antenna with double expansion k A sparse array configuration antenna with double expansion.

[0042] In summary, the present invention discloses a... k Double-extended sparse array antenna configuration and its design method, introducing k The expansion factor is doubled to reduce the number of overlapping elements between the summation co-array and the differential co-array, thereby reducing the redundancy of the co-array. The proposed array configuration has a hole-free summation differential co-array, and its array degrees of freedom are superior to most existing array configurations.

[0043] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A kind k A sparse array configuration antenna with a 100% expansion capability, characterized in that... The sparse array configuration includes two levels of sparse subarrays, namely... and ,according to Sequential array arrangement, subarray The number of array elements in the array is And the spacing between array elements is Pair array conduct k Double expansion yields subarray The number of array elements in the array is And the spacing between array elements is ,in , , The incident signal wavelength, the total number of array elements ; The distribution of array element positions in the sparse array configuration satisfy ,as follows: in, express k order expansion factor, k This represents the expansion coefficient, and its value is related to... and The value is irrelevant.

2. The one described in claim 1 k The sparse array configuration antenna with double expansion is characterized by: The summation difference comatrix of the sparse array configuration is symmetric about the origin. Its positive part negative part , represented as: in, Denotes the set of positive difference comatrixes. The set of positive summation common arrays is represented as: Positive part of the difference comatrix The continuous interval of the difference comatrix is ; Find the positive part of the summation matrix The continuous interval of the summation matrix is: ; The continuous interval of the entire summation difference comatrix is .

3. The one described in claim 2 k The sparse array configuration antenna with double expansion is characterized by: The degrees of freedom of the sparse array configuration are: ; The co-array redundancy of the sparse array configuration is: in, This represents the maximum value of the difference comatrix. This represents the minimum value of the largest continuous interval of the summation matrix.

4. A kind k A method for designing sparse array antennas with double-expansion, characterized in that, Includes the following steps: Step 1: Determine the number of elements and the element spacing in each sparse subarray of the two-level sparse subarray; in Step 1, the sparse subarray is defined. and ,according to Sequential array arrangement, subarray The number of array elements in the array is And the spacing between array elements is Pair array conduct k Double expansion yields subarray The number of array elements in the array is And the spacing between array elements is ,in , , The incident signal wavelength, the total number of array elements ; Step 2: Design based on the parameters set in Step 1. k The sparse array configuration is expanded by a factor of two, and the element position distribution is derived; in step 2, the element position distribution in the sparse array configuration is... satisfy ,as follows: in, express k order expansion factor, k This represents the expansion coefficient, and its value is related to... and The value is irrelevant; Step 3: Based on the sparse array configuration designed in Step 2, calculate... k The doubly extended sparse array configuration is available in the continuous intervals of the differential coarray, the summation coarray, and the summation-differential coarray. Step 4: Based on the sparse array configuration designed in Step 2, and combined with the continuous intervals calculated in Step 3, calculate... k Degrees of freedom for sparse array configurations that are doubled; Step 5: Based on the sparse array configuration designed in Step 2, and combined with the degrees of freedom calculated in Step 4, calculate... k Co-array redundancy in a doubly expanded sparse array configuration.

5. The one described in claim 4 k The method for designing sparse array antennas with double expansion is characterized by: In step 3, the summation difference comatrix of the sparse array configuration is symmetric about the origin. Its positive part negative part , represented as: in, Denotes the set of positive difference comatrixes. The set of positive summation common arrays is represented as: Therefore, the positive part of the difference comatrix can be calculated. The continuous interval of the difference comatrix is ; Find the positive part of the summation matrix The continuous interval of the summation matrix is: ; The continuous interval of the entire summation difference comatrix is .

6. The one described in claim 5 k The method for designing sparse array antennas with double expansion is characterized by: In step 4 k The degrees of freedom of the double-extended sparse array configuration are .

7. The one described in claim 6 k The method for designing sparse array antennas with double expansion is characterized by: In step 5 k The co-array redundancy of the double-expanded sparse array configuration is: in, This represents the maximum value of the difference comatrix. This represents the minimum value of the largest continuous interval of the summation matrix.

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