CN115275600A - Relatively prime array antenna structure with multilayer sub-arrays - Google Patents

Relatively prime array antenna structure with multilayer sub-arrays Download PDF

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CN115275600A
CN115275600A CN202210849533.1A CN202210849533A CN115275600A CN 115275600 A CN115275600 A CN 115275600A CN 202210849533 A CN202210849533 A CN 202210849533A CN 115275600 A CN115275600 A CN 115275600A
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array
array element
antenna structure
sparse
prime
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赖欣
张小飞
李建峰
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/52—Means for reducing coupling between antennas; Means for reducing coupling between an antenna and another structure
    • H01Q1/521—Means for reducing coupling between antennas; Means for reducing coupling between an antenna and another structure reducing the coupling between adjacent antennas
    • H01Q1/523—Means for reducing coupling between antennas; Means for reducing coupling between an antenna and another structure reducing the coupling between adjacent antennas between antennas of an array
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q21/00—Antenna arrays or systems

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Abstract

The invention discloses a co-prime array antenna structure with a plurality of layers of sub-arrays, which consists of four sparse sub-arrays, wherein the total number of array elements is T, and the number of antennas is N, k (M-1),
Figure DDA0003752863730000011
And M, where the integer k>0, M and N are relatively prime integers of 2<M<And N is added. The array element position in the CAMLS antenna structure is
Figure DDA0003752863730000012
Wherein
Figure DDA0003752863730000013
Figure DDA0003752863730000014
And is
Figure DDA0003752863730000015
Figure DDA0003752863730000016
The antenna structure of the invention expands the aperture of the antenna, increases the degree of freedom, weakens the mutual coupling effect, has simple antenna array layout and can obtain the degree of freedom higher than that of the existing sparse array. The virtual array generated by CAMLS is a uniform array with unit array element spacing, a classical DOA estimation algorithm can be directly applied by combining a space smoothing method, and the problem of angle ambiguity cannot be caused.

Description

Mutual-prime array antenna structure with multilayer sub-arrays
Technical Field
The invention belongs to the field of array antenna layout, and particularly relates to a co-prime array antenna structure with a multilayer sub-array.
Background
The traditional antenna layout is limited by half wavelength, namely, the spacing between array elements is smaller than the half wavelength, so that the aperture of the antenna is limited under the condition of a certain number of antennas. Meanwhile, the small array elements also cause stronger mutual coupling effect among the antenna units. In addition, the number of targets recognizable by the conventional direction-of-arrival estimation algorithm is limited by the number of antenna elements in the physical array, i.e., the degree of freedom. Many algorithms fail when the number of targets exceeds the number of antenna elements.
Currently, an antenna structure layout called a co-prime array receives wide attention, and the array element spacing breaks through the half-wavelength limitation, so that the antenna aperture is greatly expanded, the mutual coupling effect is weakened, the angle estimation performance can be well improved, and the number of identifiable targets is increased. However, the Difference co-array (virtual array) generated by the co-prime array exists, and the holes in the array cause a great loss of the obtainable degrees of freedom.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects in the prior art, a Coprime array antenna (Coprime array with multi-layer subarrays) structure with a plurality of layers of sub-arrays is provided, the antenna structure is composed of four sparse sub-arrays, and under the condition that the total number of antennas is the same, more degrees of freedom can be obtained compared with the existing sparse arrays, the mutual coupling effect can be more effectively weakened, and better angle estimation performance and spatial resolution can be obtained. The CAMLS antenna structure has the advantages of simple layout mode, higher degree of freedom and better angle estimation performance, and can be applied to the fields of wireless communication, sonar, positioning and the like.
In order to achieve the purpose, the invention adopts the following technical scheme:
relatively prime array antenna with multilayer sub-arraysLine structure, its characterized in that: the antenna structure consists of four sparse subarrays, the total number of array elements is T, the number of antennas is N, k (M-1),
Figure BDA0003752863710000011
And M, where the integer k>0, M and N are relatively prime integers of 2<M<N。
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, the position of the array element in the antenna structure is
Figure BDA0003752863710000012
Wherein
Figure BDA0003752863710000013
The position of the array element is shown,
Figure BDA0003752863710000014
represents the set of all array element positions in the antenna structure, d < lambda/2 is unit array element spacing, lambda is incident signal wavelength,
Figure BDA0003752863710000015
Figure BDA0003752863710000021
Figure BDA0003752863710000022
respectively representing array elements of N, k (M-1),
Figure BDA0003752863710000023
And the array element position set of the M sparse subarrays.
Furthermore, the array element spacing of the sparse subarray with the array element number of N is M lambda/2, and the array element position set is
Figure BDA0003752863710000024
Wherein<a,b>And represents an integer value of a to b.
Further, the sparse subarray with the array element number k (M-1)Comprises k co-prime sub-array layers, each co-prime sub-array layer comprises (M-1) array elements with position set
Figure BDA0003752863710000025
The position set of the entire sparse sub-array is,
Figure BDA0003752863710000026
wherein<a,b>Denotes an integer value of a to b.
Further, the number of array elements is
Figure BDA00037528637100000210
The sparse subarray has an array element spacing of Nlambda/2 and an array element position set of
Figure BDA0003752863710000027
Wherein<a,b>Denotes an integer value of a to b.
Further, the number of array elements is
Figure BDA0003752863710000028
The sparse subarray has an array element spacing of (N-M) lambda/2 and an array element position set of
Figure BDA0003752863710000029
Wherein<a,b>And represents an integer value of a to b.
The invention has the beneficial effects that:
1. a co-prime array antenna structure with a plurality of layers of sub-arrays is constructed, and a co-prime array difference co-array has few holes, so that higher degree of freedom is obtained;
2. the number of antenna units with small array element spacing is reduced, so that the mutual coupling effect in the antenna array is weakened;
3. only four sub-arrays need to be designed and constructed, and the antenna has the characteristics of flexible and simple antenna layout;
4. the antenna layout can obtain better angle estimation performance and spatial resolution.
Drawings
Fig. 1 is a diagram of a co-prime array antenna structure with a multi-layer sub-array according to the present invention;
FIG. 2 is a comparison of the performance of the antenna structure of the present invention compared to a conventional antenna structure at different mutual coupling strengths;
FIG. 3 is a comparison of the performance of the antenna structure of the present invention compared to a conventional antenna structure at different signal-to-noise ratios;
fig. 4 is a comparison of the performance of the antenna structure of the present invention compared to a conventional antenna structure at different snapshot counts.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings and the specific embodiments as follows:
the invention discloses a co-prime array antenna structure with a plurality of layers of sub-arrays, which consists of four sparse sub-arrays, wherein the total number of array elements is T, and the number of antennas is N, k (M-1) respectively,
Figure BDA0003752863710000031
And M, wherein, the integer k>0, M and N are relatively prime integers, 2<M<And N is added. The array element position in the CAMLS antenna structure is
Figure BDA0003752863710000032
Figure BDA0003752863710000033
Figure BDA0003752863710000034
d < lambda/2 is unit array element distance, and lambda is incident signal wavelength.
Table 1 shows parameters of a related sparse array structure required by this patent, including array layout, DOF, uDOF, hole-aperture ratio, weight functions w (1), w (2), w (3), and mutual leakage rate, where ePCA represents extended padded co-prime array (extended padded co-prime array), TCA represents de-redundant co-prime array (connected co-prime array), ACA represents enhanced co-prime array (augmented co-prime array), CCA represents completed co-prime array (augmented co-prime array), MISC represents maximum distance-limited array (maximum distance-constrained array), ANA-2 represents number 2 enhanced nested array (2 augmented co-prime array), SNA represents super nested array (super-nested array), NA represents secondary nested array (secondary array), table 1:
Figure BDA0003752863710000035
an example of a 20-element CAMLS antenna structure is shown in fig. 1, where M =3, n =8 and k =4. Suppose K angles are thetak(k∈<1,K>) Is incident on a relatively homogeneous array, wherein the array element positions of the linear array are set as
Figure BDA0003752863710000036
dtThe direct distance from the t-th antenna to the selected reference point is shown, with unit length d = λ/2, where λ is the signal wavelength. Receive a signal of
x(l)＝As(l)+n(l)
Wherein
Figure BDA0003752863710000041
Is a signal vector,
Figure BDA0003752863710000042
Is a direction matrix, e<1,L>Is a snapshot variable, L is a snapshot number n (L) is a mean value of 0, and a covariance matrix is
Figure BDA0003752863710000043
Additive white Gaussian noise, wherein
Figure BDA0003752863710000044
Is the noise power. Direction matrix
Figure BDA0003752863710000045
Wherein a (v)k) As a guide vector
Figure BDA0003752863710000046
Wherein k belongs to <1,K >.
The signal covariance matrix is
Figure BDA0003752863710000047
Wherein the source signal matrix
Figure BDA0003752863710000048
Is the power of the kth source.
In sparse array signal processing, the physical domain is converted into the virtual domain by a differential-common array.
For a set of array element positions of
Figure BDA0003752863710000049
Physical array, differential co-array
Figure BDA00037528637100000410
The definition of (A) is:
Figure BDA00037528637100000411
for a physical array, the degree of freedom (DOF) is defined as
Figure BDA00037528637100000412
Is defined as the number of radicals, the continuous degree of freedom (uniform DOF)
Figure BDA00037528637100000413
The number of bases in the continuous portion.
To R isxPerforming vectoring operation to construct equivalent received signal of virtual domain
Figure BDA00037528637100000414
Wherein B = [ B (v)1),b(ν2),…,b(νK)]，
Figure BDA00037528637100000415
And
Figure BDA00037528637100000416
by extracting successive portions of the virtual domain equivalent received signal, the DOA may be estimated by a spatial smoothing ESPRIT (SS-ESPRIT) algorithm. In real scene, RxObtained by L snapshot approximation calculations, i.e.
Figure BDA0003752863710000051
The continuous degree of freedom of the CAMLS antenna structure is 2M (N-1) +4kM +2k (M-1) N +2N +2M-1, and the degree of freedom is 2M (N-1) +4kM +2k (M-1) N +2N +2M + (N-M-1) (M-1) -1.
The cross-coupling matrix of a linear array is approximate to a B-band Toeplitz matrix
Figure BDA0003752863710000052
Wherein [ C]m,nM-th row and n-th column elements, d, representing a cross-coupling matrix Cm,dnIs the normalized antenna element position, c0＝1＞|c1|＞|c2|＞…＞|cBAnd | is greater than 0. In particular, the mutual coupling coefficient may be by cs＝c1e-j(s-1)/8Calculated as/s. When the mutual coupling effect is considered, the received signal can be reconstructed as
Figure BDA0003752863710000053
Mutual coupling leakage is related to the distance between the antenna units, and a weighting function is introduced to more intuitively show the mutual coupling in the physical array. Firstly, a set formed by all array element pairs with array element spacing of s is introduced
Figure BDA0003752863710000054
Figure BDA0003752863710000055
For a set of array element positions of
Figure BDA0003752863710000056
The weight function is defined as
Figure BDA0003752863710000057
Where w(s) represents the number of pairs of elements with an element spacing s.
In the CAMLS antenna structure given in this patent,
w(1)＝1,w(2)＝3,w(3)＝N-1
mutual coupling leakage of a physical array is defined as
Figure BDA0003752863710000058
Here, the DOA estimate performance and c for the array structure given in Table 1 under the mutual coupling effect are given1Is the relationship between the amplitudes of (c)1＝|c1|ejπ/3Wherein the number of array elements is 20. Compared with nested arrays, i.e., NA, SNA, ANA-2, and other relatively prime arrays, i.e., ePCA, TCA, ACA, CCA, CAMLS proposed by this patent have more degrees of freedom and continuity. The MISC and MRA arrays have sub-arrays with smaller array element spacing, and the differential co-array has the characteristic of no holes, so that the MISC and MRA arrays have more degrees of freedom, but simultaneously cause larger mutual coupling leakage. The CAMLS proposed in this patent can obtain a difference array smaller than the MISC and MRA arrays, but can be at | c1With | > 0.05, much more accurate estimates of DOA are obtained than with MRA and MISC arrays, which benefits from the reduced effectiveness of the reduced array element spacings λ/2, 2 λ/2 and 3 λ/2 in reducing the effects of mutual coupling.
In addition, different sparse arrays are given at c1＝0.3ejπ/3The Root Mean Square Error (RMSE) results obtained. Fig. 2 shows the relationship between RMSE and SNR, where L =1000, 22 sources are uniformly distributed at-65 ° to 65 °, and the simulation order is 2000. From the second graph, CAMLS can obtain better DOA estimation performance than other sparse arrays, which also proves the effectiveness of the patent on the improvement of the sparse arrays in terms of the difference co-array and the weight function. Fig. 3 gives the relationship between RMSE and snapshot number, where SNR =5dB, simulation results also show that CAMLS can obtain better DOA estimates than other sparse arrays due to improvements in continuous degrees of freedom and mutual coupling effects.
The above are only preferred embodiments of the present invention, and the scope of the present invention is not limited to the above examples, and all technical solutions that fall under the spirit of the present invention belong to the scope of the present invention. It should be noted that modifications and adaptations to those skilled in the art without departing from the principles of the present invention may be apparent to those skilled in the relevant art and are intended to be within the scope of the present invention.

Claims (2)

1. A co-prime array antenna structure having a multi-layer sub-array, characterized by: the antenna structure consists of four sparse sub-arrays, the total array element number is T, and the array element numbers of the sparse sub-arrays are N, k (M-1) respectively,
Figure FDA0003752863700000011
And M; the position of the antenna structure array element
Figure FDA0003752863700000012
Figure FDA0003752863700000013
Expressing the set of all array element positions in the antenna structure, d < lambda/2 is unit array element distance, lambda is incident signal wavelength, k is the number of the cross-prime subarray layers, k is>0, M and N are relatively prime integers, and 2<M<N；
Figure FDA0003752863700000014
Figure FDA0003752863700000015
Figure FDA0003752863700000016
Respectively representing array elements of N, k (M-1),
Figure FDA0003752863700000017
And a set of array element positions of the sparse subarray of M, wherein<a,b>Represents an integer value of a to b;
the sparse subarray with the array element number of N has the array element spacing of M lambda/2 and the array element position set of
Figure FDA0003752863700000018
The sparse subarray with the array element number of k (M-1) comprises k co-prime subarray layers, each co-prime subarray layer comprises (M-1) array elements, and the position set of the ith co-prime subarray layer is
Figure FDA0003752863700000019
The position set of the whole sparse subarray is as follows:
Figure FDA00037528637000000110
the number of array elements is
Figure FDA00037528637000000111
The sparse subarray has an array element spacing of Nlambda/2 and an array element position set of
Figure FDA00037528637000000112
Number of array elementsThe array element spacing of the M sparse subarrays is (N-M) lambda/2, and the array element position set is
Figure FDA00037528637000000113
2. A relatively prime array antenna structure having a multilayer sub-array as claimed in claim 1, wherein: the antenna structure has the following continuous degrees of freedom:
2M(N-1)+4kM+2k(M-1)N+2N+2M-1,
the degree of freedom is as follows:
2M(N-1)+4kM+2k(M-1)N+2N+2M+(N-M-1)(M-1)-1。
CN202210849533.1A 2022-07-19 2022-07-19 Relatively prime array antenna structure with multilayer sub-arrays Pending CN115275600A (en)

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Cited By (1)

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