CN115693183A - K-time expansion sparse array configuration antenna and design method thereof - Google Patents

K-time expansion sparse array configuration antenna and design method thereof Download PDF

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CN115693183A
CN115693183A CN202211283237.6A CN202211283237A CN115693183A CN 115693183 A CN115693183 A CN 115693183A CN 202211283237 A CN202211283237 A CN 202211283237A CN 115693183 A CN115693183 A CN 115693183A
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array
sparse
array configuration
common
configuration
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赵嫔姣
胡国兵
杨娟
王利伟
陈恺
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Jinling Institute of Technology
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Abstract

The invention discloses akThe sparse array configuration antenna of the multiple expansion and its design method, including: determining the number of array elements and the spacing of the array elements of each sparse subarray; design ofkConstructing a double-expanded sparse array and deducing the position distribution of array elements; derivation ofkThe doubly-expanded sparse array configuration is in a continuous interval of a difference common array domain, a summation common array domain and a summation difference common array domain; computingkA degree of freedom of a doubly extended sparse array configuration; computingkCo-array redundancy ratio of a double extended sparse array configuration. The invention provides a method for calculating a sum-difference domain view anglekThe antenna with multiple extended sparse array configuration and its design method are introducedkThe multiple expansion factors reduce the number of overlapping array elements between the summation common array and the differential common array, and the array freedom degree is ensured while the common array redundancy is reduced.

Description

K-time expansion sparse array configuration antenna and design method thereof
Technical Field
The invention belongs to the field of array antenna design, and particularly relates to a k-time expansion sparse array configuration antenna and a design method thereof.
Background
Compared with the sparse array design based on the difference common array, the sparse array design based on the summation difference visual angle has larger array aperture and common array freedom degree, and the angle measurement performance can be improved from the array design level, so that the sparse array design based on the summation difference visual angle is widely concerned by students. However, most of the existing array configurations, such as relatively prime arrays (CPAs), nested Arrays (NAs), and differential sum relatively prime arrays (dscampss) with multi-period subarrays, have a large number of overlapping array elements between the sum and differential commons, and only half of the overlapping array elements can be used to extend the array freedom, resulting in low array utilization. In addition, for most existing array configurations, holes exist in the sum-difference common array, and the array freedom degree needs to be further improved.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a k-time expansion sparse array configuration antenna and a design method thereof, and by introducing k-time expansion factors, the number of overlapped array elements between a summation common array and a difference common array is reduced, and the array freedom degree is ensured while the common array redundancy is reduced.
In order to achieve the purpose, the invention adopts the following technical scheme:
a k-time expansion sparse array configuration antenna is characterized in that the sparse array configuration comprises two levels of sparse sub-arrays which are respectively
Figure BDA0003897992820000011
And
Figure BDA0003897992820000012
according to the following
Figure BDA0003897992820000013
In a sequential arrangement of sub-arrays
Figure BDA0003897992820000014
In the array element number is N 1 And the array element interval is N 1 d, pair subarrays
Figure BDA0003897992820000015
Performing k times expansion to obtain
Figure BDA0003897992820000016
Sub-array
Figure BDA0003897992820000017
In which the number of array elements is N 2 And the array element spacing is d, wherein 2 < N 1 ≤N 2 D = λ/2, λ is the incident signal wavelength, and the total array element number N = kN 1 +N 2 。
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, the array element position distribution in the sparse array configuration
Figure BDA0003897992820000018
Satisfy the requirement of
Figure BDA0003897992820000019
The following were used:
Figure BDA00038979928200000110
wherein, K level (. H) denotes a spreading factor of order k, k denotes a spreading factor and this value is related to N 1 And N 2 The value is irrelevant.
Further, the sum and difference common array of the sparse array configuration is symmetrical about the origin, and the sum and difference common array is symmetrical about the origin
Figure BDA0003897992820000021
Positive part thereof
Figure BDA0003897992820000022
Negative part
Figure BDA0003897992820000023
Expressed as:
Figure BDA0003897992820000024
Figure BDA0003897992820000025
wherein the content of the first and second substances,
Figure BDA0003897992820000026
a set of positive differential co-arrays is represented,
Figure BDA0003897992820000027
represents a positive sum co-array set, expressed as:
Figure BDA0003897992820000028
Figure BDA0003897992820000029
Figure BDA00038979928200000210
Figure BDA00038979928200000211
Figure BDA00038979928200000212
Figure BDA00038979928200000213
positive part of differential common matrix
Figure BDA00038979928200000214
The continuous interval of the differential common matrix is
Figure BDA00038979928200000215
Positive part of summation array
Figure BDA00038979928200000216
The successive intervals of the summation array are
Figure BDA00038979928200000217
The whole summation difference common array has a continuous interval of
Figure BDA00038979928200000218
Further, the degrees of freedom of the sparse array configuration are:
Figure BDA00038979928200000219
the common array redundancy of the sparse array configuration is as follows:
Figure BDA00038979928200000220
wherein D is diff Representing the maximum value of the differential common matrix, D sum Representing the minimum of the largest continuous interval of the sum co-matrix.
The invention also provides a k-time expansion sparse array configuration antenna design method, which is characterized by comprising the following steps of:
step 1: determining the array element number and the array element spacing of each sparse subarray in the two levels of sparse subarrays;
step 2: designing a k-time expanded sparse array configuration and deducing array element position distribution according to the parameters set in the step 1;
and step 3: based on the sparse array configuration designed in the step 2, calculating continuous intervals of the k-time expanded sparse array configuration in a differential common array domain, a summation common array domain and a summation differential common array domain;
and 4, step 4: calculating the degree of freedom of the sparse array configuration expanded by k times based on the sparse array configuration designed in the step 2 and by combining each continuous interval calculated in the step 3;
and 5: and (4) calculating the degree of freedom of the sparse array configuration with k times of expansion based on the sparse array configuration designed in the step (2) and in combination with the degree of freedom calculated in the step (4).
Further, in step 1, a sparse sub-array is defined
Figure BDA0003897992820000031
And
Figure BDA0003897992820000032
according to
Figure BDA0003897992820000033
In a sequential arrangement of sub-arrays
Figure BDA0003897992820000034
In the array element number is N 1 And the array element interval is N 1 d, pair subarrays
Figure BDA0003897992820000035
Performing k times expansion to obtain
Figure BDA0003897992820000036
Sub-array
Figure BDA0003897992820000037
In the array element number is N 2 And the array element spacing is d, wherein 2 < N 1 ≤N 2 D = λ/2, λ is the incident signal wavelength, and the total array element number N = kN 1 +N 2 。
Further, in the step 2, the array element positions in the sparse array configuration are distributed
Figure BDA00038979928200000323
Satisfy the requirement of
Figure BDA0003897992820000038
The following were used:
Figure BDA0003897992820000039
wherein, kl evel (. Cndot.) denotes a spreading factor of order k, k denotes a spreading factor and this value is related to N 1 And N 2 The value is irrelevant.
Further, in the step 3, the sum and difference common array of the sparse array configuration is symmetrical about the origin, and the sum and difference common array
Figure BDA00038979928200000310
Positive part thereof
Figure BDA00038979928200000311
Negative part
Figure BDA00038979928200000312
Expressed as:
Figure BDA00038979928200000313
Figure BDA00038979928200000314
wherein the content of the first and second substances,
Figure BDA00038979928200000315
a set of positive differential common arrays is represented,
Figure BDA00038979928200000316
represents a positive sum co-array set, expressed as:
Figure BDA00038979928200000317
Figure BDA00038979928200000318
Figure BDA00038979928200000319
Figure BDA00038979928200000320
Figure BDA00038979928200000321
Figure BDA00038979928200000322
calculated from this, the positive part of the differential common matrix
Figure BDA0003897992820000041
The continuous interval of the differential common matrix is
Figure BDA0003897992820000042
Positive part of summation array
Figure BDA0003897992820000043
The successive intervals of the summation array are
Figure BDA0003897992820000044
The whole summation difference common array has a continuous interval of
Figure BDA0003897992820000045
Further, in the step 4, the degree of freedom of the k-fold expansion sparse array configuration is
Figure BDA0003897992820000046
Further, in the step 5, the common array redundancy of the k-fold expanded sparse array configuration is as follows:
Figure BDA0003897992820000047
wherein D is diff Representing the maximum value of the differential common matrix, D sum Representing the minimum of the largest continuous interval of the sum co-matrix.
The invention has the beneficial effects that: different from the traditional array configuration design based on the sum and difference common array, the invention discloses a k-time expansion sparse array configuration antenna and a design method thereof, wherein k-time expansion factors are introduced, the number of overlapped array elements between the sum common array and the difference common array is reduced, and the redundancy of the common array is reduced; the array configuration has a non-hole sum difference common array, and the array freedom degree is superior to most existing array configurations.
Drawings
Fig. 1 is a schematic flow chart of a k-fold expansion sparse array configuration antenna design method provided by the present invention.
Fig. 2 is a two-dimensional topological structure diagram of the sparse array configuration antenna provided by the invention under different sequence factors Q.
FIG. 3 is a continuous degree of freedom contrast diagram of the co-prime array (CPA), super nested array (SuperNA) and co-prime nested array (Coprime NA) of the present invention under the same array element number.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
In an embodiment, referring to fig. 1, the present invention provides a method for designing a k-fold extended sparse array configuration antenna, including:
step 1: determining the array element number and the array element interval of each sparse subarray, which comprises the following steps:
defining sparse subarrays
Figure BDA0003897992820000048
And
Figure BDA0003897992820000049
sub-array
Figure BDA00038979928200000410
In the array element number is N 1 And the array element interval is N 1 d, pair of subarrays
Figure BDA00038979928200000411
Performing k times expansion to obtain
Figure BDA00038979928200000412
Sub-array
Figure BDA00038979928200000413
In the array element number is N 2 And the array element spacing is d, wherein 2 < N 1 ≤N 2 D = λ/2, λ is the incident signal wavelength, and the total array element number N = kN 1 +N 2 。
Step 2: based on the parameters set in the step 1, designing a k-fold-expanded sparse array configuration and deducing array element position distribution, specifically as follows:
array element position distribution in sparse array configuration
Figure BDA0003897992820000051
Satisfy the requirement of
Figure BDA0003897992820000052
Namely, it is
Figure BDA0003897992820000053
Wherein, K level (. H) denotes a spreading factor of order k, k denotes a spreading factor and this value is related to N 1 And N 2 The values are irrelevant, and p only indicates that the value is within the range.
And step 3: deducing continuous intervals of the k-time expanded sparse array configuration in the differential common array domain, the summation common array domain and the summation differential common array domain according to the array configuration designed in the step 2, wherein the continuous intervals are as follows:
since the sum-difference co-array of the sparse array is symmetric about the origin, its positive part
Figure BDA0003897992820000054
Negative part
Figure BDA0003897992820000055
Can be expressed as:
Figure BDA0003897992820000056
Figure BDA0003897992820000057
wherein the content of the first and second substances,
Figure BDA0003897992820000058
a set of positive differential co-arrays is represented,
Figure BDA0003897992820000059
representing a positive summation common array set, specifically:
Figure BDA00038979928200000510
Figure BDA00038979928200000511
Figure BDA00038979928200000512
Figure BDA00038979928200000513
Figure BDA00038979928200000514
Figure BDA00038979928200000515
thus, a sum-difference co-array of k-fold expanded sparse array configurations can be represented as
Figure BDA00038979928200000516
From the above calculation results, the positive part of the differential common matrix is found
Figure BDA00038979928200000517
The continuous interval of the differential common matrix is
Figure BDA00038979928200000518
Positive part of the summing matrix
Figure BDA00038979928200000519
The successive intervals of the summation array are
Figure BDA0003897992820000061
Since 2 < N 1 ≤N 2 And is and
Figure BDA0003897992820000062
and
Figure BDA0003897992820000063
is established, then
Figure BDA0003897992820000064
The differential common array can be filled in all holes in the summation common array, and the continuous interval of the whole summation differential common array is
Figure BDA0003897992820000065
And 4, step 4: based on the array configuration designed in the step 2, the degree of freedom of the sparse array configuration expanded by k times is calculated, which is specifically as follows:
according to the calculation result in the step 3, the degree of freedom of the k-time expansion sparse array configuration is
Figure BDA0003897992820000066
And 5: based on the array configuration designed in the step 2, calculating the common array redundancy rate of the k-time expansion sparse array configuration, which is specifically as follows:
the common array redundancy of the k-time expansion sparse array configuration is as follows:
Figure BDA0003897992820000067
wherein D diff Representing the maximum value of the differential common matrix, D sum Representing the minimum of the largest continuous interval of the sum co-matrix.
FIG. 2 is a graph of the co-array redundancy rate as a function of the number of array elements for three array configurations of the present invention, a Nested Array (NA) and a differential sum co-prime array with multiple periodic sub-arrays (DsCAMpS). As can be seen from the figure, the co-array redundancy rate of the NA is increased along with the increase of the array element number, and the final value tends to 1; the co-array redundancy rate of the k-time expanded sparse array configuration and the DsCAMpS provided by the invention is reduced along with the increase of the array elements, and the final value tends to 0; the array configuration provided by the invention has lower array redundancy under the condition that the array elements are the same.
FIG. 3 is a graph of the continuous degrees of freedom of three array configurations of the present invention, a relatively prime array (CPA), a Nested Array (NA), and a differential sum relatively prime array with multi-periodic sub-arrays (DsCAMpS), as a function of the number of array elements. As can be seen from the figure, the degrees of freedom of all four array configurations are increased along with the increase of the array element number; the array configuration provided by the invention has more array freedom under the condition of the same array element number, and the advantages are more obvious along with the increase of the array element number.
In another embodiment, the invention further provides a k-time expansion sparse array configuration antenna designed by the k-time expansion sparse array configuration antenna design method provided by the first embodiment.
In summary, the sparse array configuration antenna with k times of expansion and the design method thereof introduce k times of expansion factors, reduce the number of overlapping array elements between a summation common array and a differential common array, and reduce the redundancy of the common array; the array configuration has a non-hole sum difference common array, and the array freedom degree is superior to most existing array configurations.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (10)

1. A k-time expansion sparse array configuration antenna is characterized in that the sparse array configuration comprises two levels of sparse sub-arrays which are respectively
Figure FDA0003897992810000011
And
Figure FDA0003897992810000012
according to the following
Figure FDA0003897992810000013
In a sequence of sub-arrays
Figure FDA0003897992810000014
In the array element number is N 1 And the array element interval is N 1 d, pair subarrays
Figure FDA0003897992810000015
Performing k times expansion to obtain
Figure FDA0003897992810000016
Sub-array
Figure FDA0003897992810000017
In the array element number is N 2 And the array element spacing is d, wherein 2 < N 1 ≤N 2 D = λ/2, λ is the incident signal wavelength, and the total array element number N = kN 1 +N 2 。
2. A k-fold spread sparse array configuration antenna as claimed in claim 1 wherein: array element position distribution in the sparse array configuration
Figure FDA0003897992810000018
Satisfy the requirement of
Figure FDA0003897992810000019
The following were used:
Figure FDA00038979928100000110
wherein, K level (. H) denotes a spreading factor of order k, k denotes a spreading factor and this value is related to N 1 And N 2 The value is irrelevant.
3. A k-fold spread sparse array configuration antenna as claimed in claim 2 wherein: the sum and difference common array of the sparse array configuration is symmetrical about an origin, and the sum and difference common array
Figure FDA00038979928100000111
Positive part thereof
Figure FDA00038979928100000112
Negative part
Figure FDA00038979928100000113
Expressed as:
Figure FDA00038979928100000114
Figure FDA00038979928100000115
wherein the content of the first and second substances,
Figure FDA00038979928100000116
a set of positive differential co-arrays is represented,
Figure FDA00038979928100000117
represents a positive sum co-array set, expressed as:
Figure FDA00038979928100000118
Figure FDA00038979928100000119
Figure FDA00038979928100000120
Figure FDA00038979928100000121
Figure FDA00038979928100000122
Figure FDA00038979928100000123
positive part of differential common matrix
Figure FDA00038979928100000124
The continuous interval of the differential common matrix is
Figure FDA00038979928100000125
Positive part of summation array
Figure FDA0003897992810000021
The summation co-array has a continuous interval of
Figure FDA0003897992810000022
The whole summation difference common array has a continuous interval of
Figure FDA0003897992810000023
4. A k-fold spread sparse array configuration antenna as claimed in claim 3 wherein: the degrees of freedom of the sparse array configuration are:
Figure FDA0003897992810000024
the common array redundancy of the sparse array configuration is as follows:
Figure FDA0003897992810000025
wherein D is diff Representing the maximum value of the differential common matrix, D sum Representing the minimum of the largest continuous interval of the summed co-matrix.
5. A k-time expansion sparse array configuration antenna design method is characterized by comprising the following steps:
step 1: determining the array element number and the array element spacing of each sparse subarray in the two levels of sparse subarrays;
step 2: designing a k-time expanded sparse array configuration and deducing array element position distribution according to the parameters set in the step 1;
and step 3: based on the sparse array configuration designed in the step 2, calculating continuous intervals of the sparse array configuration with k times of expansion in a differential common array domain, a summation common array domain and a summation differential common array domain;
and 4, step 4: calculating the degree of freedom of the sparse array configuration expanded by k times based on the sparse array configuration designed in the step 2 and by combining each continuous interval calculated in the step 3;
and 5: and (4) calculating the degree of freedom of the sparse array configuration with k times of expansion based on the sparse array configuration designed in the step (2) and in combination with the degree of freedom calculated in the step (4).
6. The method for designing a k-fold expanded sparse array configuration antenna as claimed in claim 5, wherein: in step 1, a sparse sub-array is defined
Figure FDA0003897992810000026
And
Figure FDA0003897992810000027
according to
Figure FDA0003897992810000028
In a sequential arrangement of sub-arrays
Figure FDA0003897992810000029
In the array element number is N 1 And the array element interval is N 1 d, pair subarrays
Figure FDA00038979928100000210
Performing k times expansion to obtain
Figure FDA00038979928100000211
Sub-array
Figure FDA00038979928100000212
In the array element number is N 2 And the array element spacing is d, wherein 2 < N 1 ≤N 2 D = λ/2, λ is the incident signal wavelength, and the total array element number N = kN 1 +N 2 。
7. The method for designing a k-fold expanded sparse array configuration antenna as claimed in claim 6, wherein: in the step 2, the array element positions in the sparse array configuration are distributed
Figure FDA00038979928100000213
Satisfy the requirement of
Figure FDA00038979928100000214
The following were used:
Figure FDA00038979928100000215
wherein, K level (. H) denotes a spreading factor of order k, k denotes a spreading factor and this value is related to N 1 And N 2 The value is irrelevant.
8. The method for designing a k-fold expanded sparse array configuration antenna as claimed in claim 7, wherein: in the step 3, the sum and difference common array of the sparse array configuration is symmetrical about the origin, and the sum and difference common array
Figure FDA0003897992810000031
Positive part thereof
Figure FDA0003897992810000032
Negative part
Figure FDA0003897992810000033
Expressed as:
Figure FDA0003897992810000034
Figure FDA0003897992810000035
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003897992810000036
a set of positive differential co-arrays is represented,
Figure FDA0003897992810000037
represents a positive sum co-array set, expressed as:
Figure FDA0003897992810000038
Figure FDA0003897992810000039
Figure FDA00038979928100000310
Figure FDA00038979928100000311
Figure FDA00038979928100000312
Figure FDA00038979928100000313
calculated from this, the positive part of the differential common matrix
Figure FDA00038979928100000314
The continuous interval of the differential common matrix is
Figure FDA00038979928100000315
Positive part of summation array
Figure FDA00038979928100000316
The successive intervals of the summation array are
Figure FDA00038979928100000317
The whole summation difference common array has a continuous interval of
Figure FDA00038979928100000318
9. The method for designing a k-fold extended sparse array configuration antenna as claimed in claim 8, wherein: in the step 4, the degree of freedom of the k times expansion sparse array configuration is
Figure FDA00038979928100000319
10. The method for designing a k-fold extended sparse array configuration antenna as claimed in claim 9, wherein: in the step 5, the common array redundancy of the k-fold expanded sparse array configuration is as follows:
Figure FDA00038979928100000320
wherein D is diff Representing the maximum value of the differential common matrix, D sum Representing the minimum of the largest continuous interval of the sum co-matrix.
CN202211283237.6A 2022-10-19 2022-10-19 K-time expansion sparse array configuration antenna and design method thereof Pending CN115693183A (en)

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