A sparse array configuration antenna with zero co-array redundancy and a design method thereof

Abstract

The application provides a sparse array configuration antenna with zero co-array redundancy and a design method thereof, and the implementation steps are as follows: a general array arrangement strategy of zero-redundant sparse array is designed; a design example of the zero-redundant sparse array configuration is given based on the strategy, including the number of sub-arrays, the number of array elements and the array element spacing, and an analytical expression of the array element position distribution is calculated; according to the designed array configuration, the continuous intervals of the sparse array in the difference co-array domain, the sum co-array domain and the sum-difference co-array domain are derived; and the maximum continuous degrees of freedom of the array are calculated. The application solves the problem of large number of overlapping array elements between virtual co-arrays and low array utilization in the existing array design, and improves the degrees of freedom of the array while realizing zero co-array redundancy.

Description

Technical Field

[0001] This invention belongs to the field of array antenna design, specifically relating to a sparse array antenna with zero co-array redundancy and its design method. Background Technology

[0002] Array design is a crucial aspect of array signal processing, as array performance directly impacts algorithm performance. Unlike traditional uniform arrays, sparse arrays employ specific rules for sparse array arrangement, overcoming the Nyquist sampling limitation and offering numerous advantages such as increased degrees of freedom, suppression of inter-element coupling, and expanded array aperture, attracting widespread attention from experts and scholars both domestically and internationally.

[0003] Based on the virtual co-array domain used, the configuration design of sparse arrays can be mainly divided into two categories: differential co-arrays and summation differential co-arrays. The limitation of the differential co-array-based array design method is that the number of degrees of freedom in the constructed virtual array cannot exceed twice the physical aperture. In contrast, the summation differential co-array-based array design method introduces the concept of a summation co-array, significantly increasing the array's degrees of freedom. However, for most existing array configuration designs, there are a large number of redundant array elements between the summation virtual array and the differential virtual array, limiting further increases in array degrees of freedom. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a sparse array configuration antenna with zero co-array redundancy and its design method. It reduces the number of overlapping array elements of differential co-array and summation co-array to zero, allowing all virtual array elements to be used to improve array degrees of freedom, thereby improving angle measurement performance from the array design level.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A sparse array configuration antenna with zero co-array redundancy is characterized in that the sparse array configuration satisfies the zero redundancy characteristic and includes a two-level sparse subarray with a total number of array elements N = N1 + N2. Among them, the first subarray It contains N1 array elements with an element spacing of N1d, where d represents the normalized element spacing. express The N1th element; the second subarray It contains N2 array elements with an element spacing of d. express The N2th element in the array, N2=2n, n≥2 and N2 / 2<N1≤N2; and The distribution of array element positions between them satisfies

[0007] To optimize the above technical solution, the specific measures also include:

[0008] Furthermore, the sparse array configuration satisfies the following condition:

[0009] For a virtual difference comatrix, the longest continuous interval satisfies in, Indicates non-negative difference subsets. Represents a set Continuous intervals;

[0010] For a virtual summation matrix, the longest continuous interval satisfies in, Represent the set of non-negative sums. This represents the summation operator. Represents a set Continuous intervals;

[0011] For a virtual summation difference comatrix, the longest continuous interval of the virtual difference comatrix is ​​seamlessly connected to the longest continuous interval of the virtual summation comatrix, and there are no overlapping virtual array elements or holes between them, satisfying the following condition:

[0012] Furthermore, in the sparse array configuration, and The location distributions are as follows:

[0013]

[0014]

[0015] In the formula, l p and l q They represent and The position index in the middle.

[0016] Furthermore, the sparse array configuration in the continuous intervals of the differential co-array domain, the summation co-array domain, and the summation-differential co-array domain is as follows:

[0017] The continuous interval within the difference comatrix domain is: (-S1, S1), where,

[0018] The continuous interval of the summation domain is (-S2, S3), where S2 = S1 + 1.

[0019] The continuous interval of the summation difference comatrix is ​​(-S3, S3).

[0020] Furthermore, the maximum number of consecutive degrees of freedom of the sparse array configuration is

[0021] Furthermore, this invention proposes a design method for a sparse array configuration antenna with zero co-array redundancy, characterized by comprising: defining a sparse array configuration satisfying zero redundancy characteristics, comprising a second-order sparse subarray with a total number of array elements N = N1 + N2. in, N1 represents the first subarray. Number of array elements included express The N1th array element; N2 represents the second subarray. Number of array elements included express The N2th element in the array, the element position distribution between the two subarrays satisfies

[0022] Furthermore, the sparse array configuration satisfies the following condition:

[0023] For a virtual difference comatrix, the longest continuous interval satisfies in, Indicates non-negative difference subsets. Represents a set Continuous intervals;

[0024] For a virtual summation matrix, the longest continuous interval satisfies in, Represent the set of non-negative sums. This represents the summation operator. Represents a set Continuous intervals;

[0025] For a virtual summation difference comatrix, the longest continuous interval of the virtual difference comatrix is ​​seamlessly connected to the longest continuous interval of the virtual summation comatrix, and there are no overlapping virtual array elements or holes between them, satisfying the following condition:

[0026] The beneficial effects of the present invention are as follows: The sparse array configuration antenna with zero co-array redundancy provided by the present invention reduces the number of overlapping array elements between the summation virtual array and the differential virtual array to zero during the implementation process, so that all virtual array elements are used to improve the array degrees of freedom, solving the problem of low array utilization in existing similar array design methods, and improving the direction finding performance from the array design level. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the design process of a sparse array configuration antenna with zero co-array redundancy provided by the present invention.

[0028] Figure 2This is a comparison diagram of virtual arrays of sparse arrays and nested arrays with zero co-array redundancy provided by the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0030] like Figure 1 As shown, the present invention provides a sparse array configuration antenna with zero co-array redundancy. The design method of the sparse array configuration includes the following steps.

[0031] Step 1: Design a general array layout strategy for zero-co-array redundancy sparse arrays.

[0032] Define a second-order sparse subarray containing N = N1 + N2 elements. in N1 represents the first subarray. The number of array elements contained, where p1 represents the subarray. The first element in the array, Subarray The N1th array element; N2 represents the second subarray. The number of array elements contained, where q1 represents the subarray. The first element in the array, Subarray The N2th element in the array, the element position distribution between the two subarrays satisfies

[0033] To ensure the zero redundancy characteristic of sparse arrays, the following must be satisfied:

[0034] 1) For a virtual difference comatrix, its longest continuous interval satisfies in, Indicates non-negative difference subsets. Represents a set Continuous intervals.

[0035] 2) For a virtual summation matrix, its longest continuous interval satisfies in Represent the set of non-negative sums. This represents the summation operator. Represents a set Continuous intervals.

[0036] 3) For the virtual sum-difference coarray, the longest continuous interval of the virtual difference coarray and the longest continuous interval of the virtual sum coarray are seamlessly connected, with no overlapping virtual array elements or holes between them, and their longest continuous interval satisfies

[0037] Step 2: Based on the strategy proposed in Step 1, a design example of a sparse array configuration antenna with zero coarray redundancy is provided, including: determining the number of subarrays, the number of array elements contained in each subarray, and the array element spacing; calculating the analytical expression of the array element position distribution.

[0038] 1) Determine the number of subarrays, the number of array elements contained in each subarray, and the array element spacing:

[0039] The sparse array configuration with zero coarray redundancy consists of two subarrays with a total number of array elements N = N1+N2. The first subarray contains N1 array elements with an array element spacing of N1d, and the second subarray contains N2 array elements with an array element spacing of d, where N2=2n, n≥2 and N2 / 2<N1≤N2, d represents the normalized array element spacing, which is half of the wavelength of the incident signal.

[0040] 2) Calculate the analytical expression of the array element position distribution:

[0041] The array element position distribution in the sparse array configuration satisfies: Subarray and subarray have their position distributions expressed as:

[0042]

[0043]

[0044] where l p and l q respectively represent the position indices in the subarray and .

[0045] Step 3: Based on the array configuration in Step 2, derive the continuous intervals in the difference coarray domain, the sum coarray domain, and the sum-difference coarray domain.

[0046] 1) Continuous interval of the difference coarray:

[0047] The sparse array proposed in this embodiment is continuous in the entire difference coarray domain, with a continuous interval of (-S1, S1), where

[0048] 2) Continuous interval of the sum coarray:

[0049] The sparse array proposed in this embodiment has a continuous interval of (-S2, S3) in the summation domain, where S2 = S1 + 1.

[0050] 3) Find the continuous intervals of the summation difference matrix:

[0051] Since the differential virtual array and the summation virtual array are seamlessly linked, the sparse array proposed in this embodiment is continuous throughout the differential co-array domain, with the continuous interval being (-S3, S3).

[0052] Step 4: Based on the results of Step 3, calculate the maximum continuous degrees of freedom of the array.

[0053] Calculate the continuous degrees of freedom of the summation difference virtual matrix:

[0054] Figure 2 This is a comparison diagram of the virtual arrays of the zero-redundancy sparse array and the nested array proposed in this embodiment when the number of array elements N=8. Figure 2 It can be seen that, under the same conditions, the nested array has 18 overlapping virtual array elements and a maximum continuous degree of freedom of 51; however, the sparse array with zero co-array redundancy proposed in this embodiment has 0 overlapping virtual array elements and a maximum continuous degree of freedom of 81. Therefore, it can be seen that the sparse array proposed in this embodiment has a significantly improved array degree of freedom.

[0055] In summary, the zero-co-array redundancy sparse array antenna proposed in this invention reduces the number of overlapping elements between the summation virtual array and the differential virtual array to zero during implementation. This allows all virtual elements to be used to enhance the array's degrees of freedom, solving the problem of large overlapping elements and low array utilization in existing array designs. It improves array degrees of freedom while achieving zero co-array redundancy, thus enhancing direction-finding performance from the array design level. Furthermore, the design method proposed in this invention is universal; antennas meeting various requirements can be designed based on the general deployment strategy of zero-co-array redundancy sparse arrays.

[0056] 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 sparse array antenna with zero co-array redundancy, characterized in that, The sparse array configuration satisfies the zero redundancy characteristic and contains a total number of array elements. Second-order sparse subarray The first subarray Include There are one array element and the spacing between the array elements is... , This represents the normalized element spacing. express The Middle The first array element; the second subarray Include There are one array element and the spacing between the array elements is... , express The Middle Each array element, , and , ; and The distribution of array element positions between them satisfies ; The sparse array configuration satisfies the following condition: For a virtual difference comatrix, the longest continuous interval satisfies ,in, Indicates non-negative difference subsets. Represents a set Continuous intervals; For a virtual summation matrix, the longest continuous interval satisfies ,in, Represent the set of non-negative sums. This represents the summation operator. Represents a set Continuous intervals; For a virtual summation difference comatrix, the longest continuous interval of the virtual difference comatrix is ​​seamlessly connected to the longest continuous interval of the virtual summation comatrix, and there are no overlapping virtual array elements or holes between them, satisfying the following condition: ; In the sparse array configuration and The location distributions are as follows: In the formula, and They represent and The position index in the middle.

2. The sparse array configuration antenna with zero co-array redundancy as described in claim 1, characterized in that: The sparse array configuration in the continuous intervals of the differential co-array domain, the summation co-array domain, and the summation-differential co-array domain is as follows: The continuous intervals within the differential codomain are: ,in, ; The continuous intervals within the summation domain are: ,in, , ; The continuous interval of the summation difference comatrix is: .

3. The sparse array configuration antenna with zero co-array redundancy as described in claim 2, characterized in that: The maximum continuous degree of freedom of the sparse array configuration is .

4. A design method for a sparse array antenna with zero co-array redundancy, characterized in that, include: A sparse array configuration that satisfies the zero redundancy property contains a total number of array elements. Second-order sparse subarray ,in, , Indicates the first subarray Number of array elements included express The Middle Each array element; , Indicates the second subarray Number of array elements included express The Middle The distribution of array elements between two subarrays satisfies the following conditions: ; The sparse array configuration satisfies the following condition: For a virtual difference comatrix, the longest continuous interval satisfies ,in, Indicates non-negative difference subsets. Represents a set Continuous intervals; For a virtual summation matrix, the longest continuous interval satisfies ,in, Represent the set of non-negative sums. This represents the summation operator. Represents a set Continuous intervals; For a virtual summation difference comatrix, the longest continuous interval of the virtual difference comatrix is ​​seamlessly connected to the longest continuous interval of the virtual summation comatrix, and there are no overlapping virtual array elements or holes between them, satisfying the following condition: .

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