A universal nested array configuration family antenna and a design method thereof

Abstract

The application relates to a universal nested array configuration family antenna and a design method thereof, and comprises the following steps: determining the number of array elements and the element spacing of a three-level sparse subarray; designing a universal nested array configuration family and deducing the element position distribution; analyzing the internal geometric characteristics of each subarray in each array configuration in the family from a two-dimensional perspective; deducing the analytical expression of the continuous degrees of freedom of each array configuration in the nested array configuration family under the differential common array domain, and analyzing the influence of the value of a sequence factor in the array configuration family on the degrees of freedom. The application introduces the concept of "family" into the design of a sparse array, and proposes a design method of the nested array configuration family antenna. Different from a certain fixed array configuration, each array in the family can be transformed into each other, and the flexibility of the array layout is significantly increased.

Description

Technical Field

[0001] This invention belongs to the field of array antenna design, specifically relating to a general nested array configuration family of antennas and its design method. Background Technology

[0002] Sparse arrays refer to array configurations in which the array elements of an antenna receiving array are sparsely arranged according to certain rules. Compared with traditional uniform arrays, they have many advantages such as expanded array aperture, increased degrees of freedom, and reduced mutual coupling effect between array elements.

[0003] Typical sparse array configurations include: minimum redundancy arrays, minimum aperture arrays, coprime arrays, and nested arrays. Based on these prototype arrays, researchers have proposed various derivative arrays, such as super-nested arrays and coprime nested arrays, which further expand the degrees of freedom and suppress mutual coupling between array elements. However, these sparse array configurations share a common problem: their good performance can only be guaranteed when the number and position of array elements are fixed. Once the position of one or more array elements changes, the resulting virtual array and degrees of freedom may be affected accordingly, resulting in low array flexibility and making them unsuitable for space-constrained practical applications. Summary of the Invention

[0004] This invention addresses the shortcomings of existing technologies by providing a universal nested array configuration family antenna and its design method. Unlike a single array configuration, the array configurations within the family can be interchanged, significantly improving array deployment flexibility. Furthermore, each array configuration within the family features aperture-free differential co-arraying, offering superior array freedom compared to most existing array configurations.

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

[0006] A family of general nested array configuration antennas, characterized in that the array configuration within the family consists of three levels of sparse subarrays, namely... and according to Sequential array arrangement; subarray The array has N1 array elements and an element spacing of d. (Subarray) The number of array elements in the array is Q and the element spacing is (N1+1)d, and the subarray... The number of array elements is N2-Q and the element spacing is N1d, where N1≤N2, d=λ / 2, Q is the order factor in the array configuration family and Q={1,…,N2-1}, λ is the wavelength of the incident signal, and the total number of array elements is N=N1+N2.

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

[0008] Furthermore, the array element positions are distributed in the array configuration. satisfy in

[0009]

[0010] Furthermore, in the two-dimensional representation space topology diagram of the array configuration, the subarrays The first array element falls into the subarray In the four neighborhoods of the last element in the array, the subarray The array elements are distributed along the main diagonal and parallel lines of the two-dimensional topology. The two-dimensional representation space topology of the array configuration is geometrically continuous and there are no isolated points.

[0011] Furthermore, the differential comatrix of the array configuration is symmetric about the origin, and the differential comatrix... Positive part and negative part Represented as:

[0012]

[0013]

[0014] in, Indicates differential diversity. To represent the difference subsets, specifically:

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] The continuous interval of the differential co-array is (-(N2+1)N1-Q+1, (N2+1)N1+Q-1), and the analytical expression for the continuous degrees of freedom of each array configuration within the family is DOF=2(N2+1)N1+2Q-1.

[0022] Furthermore, the continuous degrees of freedom increase with the increase of the order factor, and the DOF reaches its maximum value when Q = N²⁻¹. max =2(N2+1)N1+2N2-3.

[0023] This invention also proposes a general nested array configuration family antenna design method, wherein the array configuration within the family consists of three levels of sparse subarrays, characterized by the following steps:

[0024] Step 1: Determine the number of array elements and the spacing between array elements in each subarray of the three-level sparse subarray;

[0025] Step 2: Based on the parameters set in Step 1, design a general family of nested array configurations and derive the analytical expression for the distribution of array element positions;

[0026] Step 3: Based on the array configuration family designed in Step 2, analyze the intrinsic geometric characteristics between the subarrays of each array configuration within the family from a two-dimensional perspective;

[0027] Step 4: Based on the array configuration family designed in Step 2, calculate the analytical expressions for the continuous degrees of freedom of each array configuration in the family under the differential co-array domain.

[0028] Furthermore, in step 1, the three-level sparse subarrays are respectively and according to Sequential array arrangement; subarray The array has N1 array elements and the element spacing is d. The number of array elements in the array is Q and the element spacing is (N1+1)d, and the subarray... The number of array elements is N2-Q and the element spacing is N1d, where N1≤N2, d=λ / 2, Q is the order factor in the array configuration family and Q={1,…,N2-1}, λ is the wavelength of the incident signal, and the total number of array elements is N=N1+N2.

[0029] Furthermore, in step 2, the element position distribution P in the array configuration family satisfies in

[0030]

[0031] Furthermore, step 3 specifically includes the following steps:

[0032] Step 3.1: Construct a two-dimensional representation space topology diagram corresponding to each array configuration within the family;

[0033] Step 3.2: Design subarray The first array element falls into the subarray In the four neighborhoods of the last element in the array, the subarray The array elements are distributed along the main diagonal and parallel lines of the two-dimensional topology;

[0034] Step 3.3: Design the two-dimensional representation space topology of the entire array configuration to be geometrically continuous, with no isolated points.

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

[0036] Step 4.1: Calculate the difference covariance matrix The difference comatrix is ​​symmetric about the origin, and the positive part... and negative part Represented as:

[0037]

[0038]

[0039] in, Indicates differential diversity. To represent the difference subsets, specifically:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] Step 4.2: Based on the calculation results of the difference comatrix in Step 4.1, obtain...

[0047]

[0048]

[0049]

[0050] The continuous interval of the entire difference comatrix is ​​(-(N2+1)N1-Q+1, (N2+1)N1+Q-1). Therefore, the analytical expression for the continuous degrees of freedom of each array configuration in the nested array configuration family is DOF=2(N2+1)N1+2Q-1.

[0051] The continuous degrees of freedom increase with the increase of the order factor, and the DOF reaches its maximum value when Q = N²⁻¹. max =2(N2+1)N1+2N2-3.

[0052] The beneficial effects of this invention are as follows: Unlike the traditional single array configuration design, this invention discloses a general nested array configuration family antenna and its design method from a two-dimensional perspective, introducing the concept of "family" into sparse array design. The array configurations within the family can be converted to each other, significantly improving the array layout flexibility. Each array configuration within the family has a hole-free differential co-array, and the array degree of freedom is better than most existing array configurations. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating the general nested array configuration family antenna design method proposed in this invention.

[0054] Figures 2a to 2d The diagrams show the two-dimensional topology of the universal nested array configuration antenna proposed in this invention under Q=1, Q=2, Q=3 and Q=4.

[0055] Figure 3 This is a comparison diagram of the continuous degrees of freedom of the present invention, coprime array (CPA), super nested array (SuperNA), and coprime nested array (Coprime NA) under the same array element number condition. Detailed Implementation

[0056] The invention will now be described in further detail with reference to the accompanying drawings.

[0057] Reference Figure 1 In one embodiment, the present invention proposes a general nested array configuration family antenna design method, comprising:

[0058] Step 1: Determine the number of elements and the spacing between elements in the three-level sparse subarray, as follows:

[0059] Define a three-level sparse subarray and The entire sparse array consists of three levels of subarrays, the first level being... Level 2 and Level 3 Each level is a subarray, and the entire array is arranged in... Sequential array arrangement, subarray The array has N1 array elements and the element spacing is d. The number of array elements in the array is Q and the element spacing is (N1+1)d, and the subarray... The number of array elements is N2-Q and the element spacing is N1d, where N1≤N2, d=λ / 2, Q is the order factor in the array configuration family and Q={1,…,N2-1}, λ is the wavelength of the incident signal, and the total number of array elements is N=N1+N2.

[0060] Step 2: Based on the parameters set in Step 1, design a general family of nested array configurations and derive the analytical expression for the distribution of array element positions, as follows:

[0061] Distribution of array elements in sparse array configuration satisfy in,

[0062]

[0063] Step 3: Based on the array configuration family designed in Step 2, analyze the intrinsic geometric characteristics between subarrays of each array configuration within the family from a two-dimensional perspective, as follows:

[0064] Step 3.1: Construct the corresponding two-dimensional representation space topology graph

[0065] The two-dimensional representation here is a linear array topology, not a planar array. It is formed by stacking all sensor positions from bottom to top in the one-dimensional representation.

[0066] Step 3.2: Design the intrinsic geometric properties between subarrays for each array configuration within the family:

[0067] (1) Subarray The first array element falls into the subarray On the four neighboring domains of the last array element;

[0068] (2) Subarray The array elements are distributed along the main diagonal and parallel lines of the two-dimensional topology;

[0069] (3) The entire array configuration is geometrically continuous and there are no isolated points.

[0070] Step 4: Based on the array configuration family designed in Step 2, derive the analytical expressions for the continuous degrees of freedom of each array configuration within the nested array configuration family under the differential co-array domain, as follows:

[0071] Step 4.1: Calculate the difference covariance matrix

[0072] Since the difference comatrix is ​​symmetric about the origin, its positive part and negative part It can be represented as:

[0073]

[0074]

[0075] in, Indicates differential diversity. This indicates mutual difference diversity.

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] Therefore, the complete difference comatrix in the nested array configuration family can be expressed as:

[0083]

[0084] Step 4.2: Calculate the continuous degrees of freedom

[0085] According to the calculation results of the difference comatrix in step 4.1, we know that:

[0086]

[0087]

[0088]

[0089] The continuous interval of the entire difference coarray is (-(N2+1)N1-Q+1, (N2+1)N1+Q-1). Therefore, the analytical expression for the continuous degrees of freedom of each array configuration within the nested array configuration family is DOF=2(N2+1)N1+2Q-1.

[0090] Step 5: Based on the array configuration family designed in Step 2, analyze the influence of the order factor values ​​on the degrees of freedom in the array configuration family, as follows:

[0091] Calculate the partial derivatives of the degrees of freedom with respect to the order factor Q. The degrees of freedom increase with the increase of the order factor Q. When Q = N²⁻¹, the DOF… max =2(N2+1)N1+2N2-3.

[0092] In another embodiment, the present invention also proposes a general nested array configuration family antenna designed by the general nested array configuration family antenna design method proposed in the first embodiment.

[0093] Figures 2a to 2dThis invention presents a two-dimensional topology diagram of a general nested array configuration family of antennas under different order factors Q. As shown in the diagram, for different order factors Q, the two-dimensional topology diagram of the entire array configuration is geometrically continuous, with no isolated points; subarrays... The first array element falls into the subarray On the four neighborhoods of the last element in the array; subarray The array elements are distributed along the main diagonal and parallel lines of the two-dimensional topology.

[0094] Figure 3 This is a comparison diagram of the continuous degrees of freedom of the present invention, coprime arrays (CPA), super nested arrays (Super NA), and coprime nested arrays (Coprime NA) under the same number of array elements. As shown in the diagram, under the same number of array elements, the array configuration in the general nested array family proposed in this invention has a larger number of continuous degrees of freedom compared to CPA, Super NA, and Coprime NA. Furthermore, the array degrees of freedom increase with the increase of the order factor Q.

[0095] In summary, the present invention discloses a general nested array configuration family antenna and its design method, which introduces the concept of "family" into sparse array design. Unlike the traditional single array configuration design, the array configurations within the family can be converted to each other, significantly improving the array layout flexibility. Each array configuration within the family has aperture-free differential co-array, and the array degree of freedom is better than most existing array configurations.

[0096] 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 family of general nested array configuration antennas, characterized in that, The intra-family array configuration consists of three 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 subarray The number of array elements in the array is And the spacing between array elements is subarray The number of array elements in the array is And the spacing between array elements is ,in , , It is the order factor in the array configuration family and , The incident signal wavelength, the total number of array elements ; The array element position distribution in the array configuration satisfy ,in ； In the two-dimensional representation space topology diagram of the array configuration, the subarrays The first array element falls into the subarray In the four neighborhoods of the last element in the array, the subarray The array elements are distributed along the main diagonal and parallel lines of the two-dimensional topology. The two-dimensional representation space topology of the array configuration is geometrically continuous and there are no isolated points.

2. The general nested array configuration family of antennas as described in claim 1, characterized in that: The differential comatrix of the array configuration is symmetric about the origin. The current part and negative part Represented as: in, Indicates differential diversity. To represent the difference subsets, specifically: The continuous interval of the difference comatrix is The analytical expression for the continuous degrees of freedom of each array configuration within the family is: .

3. A family of general nested array antennas as described in claim 2, characterized in that: The continuous degrees of freedom increase with the increase of the order factor. hour, Get the maximum value .

4. A design method for a family of antennas with a general nested array configuration as described in claim 1, wherein the array configuration within the family consists of three levels of sparse subarrays, characterized in that, Includes the following steps: Step 1: Determine the number of array elements and the spacing between array elements in each subarray of the three-level sparse subarray; Step 2: Based on the parameters set in Step 1, design a general family of nested array configurations and derive the analytical expression for the distribution of array element positions; Step 3: Based on the array configuration family designed in Step 2, analyze the intrinsic geometric characteristics between the subarrays of each array configuration within the family from a two-dimensional perspective; Step 4: Based on the array configuration family designed in Step 2, calculate the analytical expressions for the continuous degrees of freedom of each array configuration in the family under the differential co-array domain.

5. The antenna design method for a general nested array configuration family as described in claim 4, characterized in that: Step 4 specifically includes the following steps: Step 4.1: Calculate the difference covariance matrix The difference comatrix is ​​symmetric about the origin, and the positive part... and negative part Represented as: in, Indicates differential diversity. To represent the difference subsets, specifically: Step 4.2: Based on the calculation results of the difference comatrix in Step 4.1, obtain... Then the continuous interval of the entire difference comatrix is Therefore, the analytical expression for the continuous degrees of freedom of each array configuration within the nested array configuration family is: ; Wherein, the continuous degrees of freedom increase with the increase of the order factor. hour, Get the maximum value .

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