CN114280531A - Distributed super nested antenna array and method for acquiring target position by using same - Google Patents

Distributed super nested antenna array and method for acquiring target position by using same Download PDF

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CN114280531A
CN114280531A CN202111645357.1A CN202111645357A CN114280531A CN 114280531 A CN114280531 A CN 114280531A CN 202111645357 A CN202111645357 A CN 202111645357A CN 114280531 A CN114280531 A CN 114280531A
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antenna
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吴小川
邓维波
王洪永
索莹
张俊
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Zhongyi Zhilian Wuxi Industrial Automation Technology Co ltd
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Abstract

A distributed super nested antenna array and a method for acquiring a target azimuth thereof belong to the technical field of array signal processing and antennas. The problem that mutual coupling between antenna units is very serious when the distance between the existing antenna units is far less than half wavelength is solved, and the array comprises two identical super nested sub-arrays: when the array element spacing is in the range from one sixth wavelength to one half wavelength, the dense sub-arrays of the distributed nested array are redistributed, the spacing between the array element antennas of the dense sub-arrays is enlarged, the mutual coupling between the antenna units is reduced, the good characteristic of the distributed nested array is achieved, and the DOA estimation precision is effectively improved. The invention is suitable for array signal processing.

Description

Distributed super nested antenna array and method for acquiring target position by using same
Technical Field
The invention belongs to the technical field of array signal processing and antennas.
Background
The mutual coupling between the aperture of the array and the antenna elements is two important factors that affect the accuracy of the DOA (direction-of-arrival) estimation. In array signal processing, electromagnetic characteristics cause mutual coupling between antennas, so that antenna responses interfere with each other, and DOA estimation accuracy is reduced. Therefore, it is desirable to increase the array aperture and reduce the mutual coupling between antenna elements to improve the accuracy of DOA estimation. The distributed antenna array is usually composed of a plurality of sub-arrays with larger base line length, which can effectively increase the aperture of the array and obviously improve the parameter estimation precision, but cannot increase the number of detectable source signals.
Sparse arrays, such as minimally redundant arrays, co-prime arrays, nested arrays, and the like, can significantly increase the number of degrees of freedom to increase the number of distinguishable source signals. Therefore, much research has been conducted on distributed sparse arrays to improve DOA estimation accuracy and increase the number of detectable source signals, combining the advantages of distributed arrays and sparse arrays. The distributed sparse array which is currently studied more is a distributed nested array, but the array comprises a dense uniform linear array, and when the influence of mutual coupling between antennas is not negligible, the parameter estimation is adversely affected. In order to achieve high range resolution, radars generally operate over a wide frequency band, and to satisfy the spatial sampling theorem, the spacing between antenna elements is typically less than or equal to one-half wavelength. Thus, the spacing between the antenna elements is typically equal to one-half the wavelength of the highest operating frequency. However, when the radar operates at a low frequency point, the distance between the antenna elements is much less than a half wavelength, and thus mutual coupling between the antenna elements becomes very serious.
Disclosure of Invention
The invention aims to solve the problem that when the distance between the existing antenna units is far less than half wavelength, the mutual coupling between the antenna units is very serious, and provides a distributed super nested antenna array and a method for acquiring a target direction by the same.
The invention discloses a distributed super nested antenna array, which comprises two identical super nested sub-arrays: each super nested subarray comprises two levels of nested units; the distribution of two levels of nested units meets the following conditions:
Figure BDA0003443803860000021
Figure BDA0003443803860000022
Figure BDA0003443803860000023
Figure BDA0003443803860000024
Figure BDA0003443803860000025
Figure BDA0003443803860000026
Figure BDA0003443803860000027
wherein, S'(2)Representing a set of antenna positions for the super-nested sub-arrays,
Figure BDA0003443803860000028
a set of left-hand antenna positions of a stage is shown,
Figure BDA0003443803860000029
a set of antenna positions on the right side of the primary is shown,
Figure BDA00034438038600000210
represents twoThe set of antenna positions on the left side of the stage,
Figure BDA00034438038600000211
a set of secondary right-hand antenna positions is represented,
Figure BDA00034438038600000212
a set of long-spaced antenna positions is represented,
Figure BDA00034438038600000213
representing a set of complementary antenna positions, l being an integer, N1Array element number, N, representing a first level nested array2Representing the array element number of the second-level nested array; parameter a1，b1，a2And b2Expressed as:
Figure BDA00034438038600000214
wherein r is a positive integer.
Further, in the present invention, N is1＝N2＝5。
The method for acquiring the target position based on the distributed super nested antenna array comprises the following steps:
the method comprises the following steps: receiving a radar echo signal by adopting a distributed super nested antenna array, sampling a received signal, and obtaining a sampling signal X (t) of the received signal;
step two: obtaining a covariance matrix R by using a sampling signal X (t);
step three: vectorizing, removing redundancy and rearranging the covariance matrix R to obtain an equivalent received signal z of the collaborative array1；
Step four: equivalent received signal z using a cooperative array1Constructing a spatially smooth matrix
Figure BDA00034438038600000215
Step five: to the space smoothing matrix
Figure BDA00034438038600000216
And (4) decomposing the characteristic value, and estimating the azimuth angle of the target source by adopting a multi-scale rotation invariant subspace algorithm.
Further, in the present invention, in the first step, the obtained sampling signal x (t) of the received signal is:
Figure BDA0003443803860000031
wherein the content of the first and second substances,
Figure BDA0003443803860000032
representing an array manifold matrix, S (t) representing a signal vector, N (t) being a zero-mean additive white Gaussian noise vector, C representing a cross-coupling matrix, and A being a guide vector matrix;
the cross-coupling matrix is calculated using a simplified model, the formula:
Figure BDA0003443803860000033
where N is the total number of antennas, N1And n2Denotes the n-th1And n2An antenna, n1And n2Is any positive integer between 1 and N,
Figure BDA0003443803860000034
denotes the n-th1The distance of the individual antennas from the reference antenna,
Figure BDA0003443803860000035
denotes the n-th2Distance of individual antenna to reference antenna, c0Representing the mutual coupling coefficient of the antenna elements themselves, c1Representing the mutual coupling coefficient when the spacing between two antenna elements is d, c2Representing the mutual coupling coefficient when the spacing between two antenna elements is 2d, cB-1Representing the mutual coupling coefficient when the two antenna elements are spaced at (B-1) d, ckRepresenting the mutual coupling coefficient when the spacing between two antenna elements is kd, clTo representThe mutual coupling coefficient when the distance between two antenna elements is ld, l and k represent any positive integer between 1 and B-1, and B represents the maximum position of the antenna.
Further, in the present invention, in the second step, the covariance matrix R is:
Figure BDA0003443803860000036
wherein E {. is } represents the mathematical expectation, the superscript H represents the conjugate transpose,
Figure BDA0003443803860000037
a manifold matrix of the array is represented,
Figure BDA0003443803860000038
representing the noise power, RsI represents an identity matrix, which is a covariance matrix of a source signal.
Further, in the present invention, in step three, the equivalent received signal z1：
Figure BDA0003443803860000039
Wherein the content of the first and second substances,
Figure BDA00034438038600000310
is a column vector with the middle element being 1 and the other elements being 0, A1＝[a1(θ1),a1(θ2),…,a1(θK)]，
Figure BDA00034438038600000311
Figure BDA00034438038600000312
M denotes the number of array elements of each sub-array of the cooperative array,
Figure BDA00034438038600000313
Figure BDA00034438038600000314
and the number of array elements of the super nested sub-array is shown. ThetakDenotes the K-th target source signal azimuth, K1, 2, K, λ denotes the carrier frequency wavelength, Φ phase difference component matrix, Φ*Representing the conjugate of the phase difference partial matrix, p represents the power of the source signal,
Figure BDA0003443803860000041
representing the noise power.
According to the antenna array, when the array element spacing is in the range from one sixth wavelength to one half wavelength, the dense sub-arrays of the distributed nested array are redistributed, the spacing between the array element antennas of the dense sub-arrays is enlarged, the mutual coupling between the antenna units is reduced, and the antenna array has the good characteristic of the distributed nested array. The accuracy of DOA estimation is improved, the number of distinguishable source signals is obviously increased, and the array structure is easy to realize.
Drawings
FIG. 1 is a schematic diagram of an arrangement structure of a distributed two-level super nested array;
FIG. 2 is a two-dimensional representation of a super nested sub-array;
fig. 3 is a comparison graph of simulation results of the antenna array according to the present invention and the conventional antenna array, without considering the mutual coupling between the array elements, d is λ/6, and the length of the base line is 63 wavelengths;
fig. 4 is a comparison graph of simulation results of the antenna array according to the present invention and the conventional antenna array in consideration of mutual coupling between array elements, where d is λ/6, and the length of the base line is 63 wavelengths;
fig. 5 is a comparison graph of simulation results of the antenna array according to the present invention and the conventional antenna array, without considering the mutual coupling between the array elements, d is 7 λ/24, and the length of the base line is 260 times of the wavelength;
fig. 6 is a comparison graph of simulation results of the antenna array according to the present invention and the conventional antenna array in consideration of mutual coupling between the array elements, d is 7 λ/24, and the length of the base line is 260 times the wavelength;
fig. 7 is a comparison graph of simulation results of the antenna array according to the present invention and the conventional antenna array, without considering the mutual coupling between the array elements, d ═ λ/2, and the length of the base line is 1500 times the wavelength;
fig. 8 is a comparison graph of simulation results of the antenna array according to the present invention and the conventional antenna array in consideration of mutual coupling between the array elements, where d is λ/2, and the length of the baseline is 1500 times the wavelength;
FIG. 9 is a graph of simulation results of RMSE as a function of the number of source signals;
FIG. 10 is a schematic diagram of a cooperative array of a distributed super nested array, in which the ULA1 Uniform subarrays 1, ULA representing synergistic arrays2 Uniform subarrays 2, ULA representing synergistic arrays3A uniform sub-array 3 representing a cooperative array.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The first embodiment is as follows: the following describes the present embodiment with reference to fig. 1 and 2, and the array described in the present embodiment includes two identical super nested sub-arrays: each super nested subarray comprises two levels of nested units; the distribution of two levels of nested units meets the following conditions:
Figure BDA0003443803860000051
Figure BDA0003443803860000052
Figure BDA0003443803860000053
Figure BDA0003443803860000054
Figure BDA0003443803860000055
Figure BDA0003443803860000056
Figure BDA0003443803860000057
wherein, S'(2)Representing a set of antenna positions for the super-nested sub-arrays,
Figure BDA0003443803860000058
a set of left-hand antenna positions of a stage is shown,
Figure BDA0003443803860000059
a set of antenna positions on the right side of the primary is shown,
Figure BDA00034438038600000510
a set of secondary left-hand antenna positions is represented,
Figure BDA00034438038600000511
a set of secondary right-hand antenna positions is represented,
Figure BDA00034438038600000512
a set of long-spaced antenna positions is represented,
Figure BDA00034438038600000513
representing a set of complementary antenna positions, l being an integer, N1Array element number, N, representing a first level nested array2Representing the array element number of the second-level nested array;parameter a1，b1，a2And b2Expressed as:
Figure BDA00034438038600000514
wherein r is a positive integer.
Further, preferably, N1＝N2＝5。
In this embodiment, when N is1＝N2When 5, the distributed two-level super nested array is as shown in fig. 1. The solid point represents an antenna unit, the cross sign represents the position of a virtual antenna unit, d is the spacing of a basic array element, d is less than or equal to lambda/2, and lambda represents the wavelength of the carrier frequency. The sequence of positions of the antenna elements is equal to a multiple of the basic spacing D, D being the base length. The position sets of the antenna units of the two super nested sub-arrays respectively use S1And S2The position set of the antenna unit of the distributed super nested array is S ═ S1∪S2The number of array elements of each subarray is
Figure BDA00034438038600000515
The total number of array elements is
Figure BDA00034438038600000516
The method for acquiring the target position based on the distributed super nested antenna array comprises the following steps:
the method comprises the following steps: receiving a radar echo signal by adopting a distributed super nested antenna array, sampling a received signal, and obtaining a sampling signal X (t) of the received signal;
there are K uncorrelated far-field narrow-band source signals incident on the array shown in FIG. 1, using θkDenotes the direction of the kth source signal, K1, 2. The received signal of the array at time t, considering the mutual coupling between the antenna elements, is denoted x (t):
Figure BDA0003443803860000061
wherein the content of the first and second substances,
Figure BDA0003443803860000062
representing an array manifold matrix, S (t) representing a signal vector, N (t) being a zero-mean additive white Gaussian noise vector, C representing a cross-coupling matrix, and A being a guide vector matrix;
the cross-coupling matrix is calculated using a simplified model, the formula:
Figure BDA0003443803860000063
where N is the total number of antennas, N1And n2Denotes the n-th1And n2An antenna, n1And n2Is any positive integer between 1 and N,
Figure BDA0003443803860000064
denotes the n-th1The distance of the individual antennas from the reference antenna,
Figure BDA0003443803860000065
denotes the n-th2Distance of individual antenna to reference antenna, c0Representing the mutual coupling coefficient of the antenna elements themselves, c1Representing the mutual coupling coefficient when the spacing between two antenna elements is d, c2Representing the mutual coupling coefficient when the spacing between two antenna elements is 2d, cB-1Representing the mutual coupling coefficient when the two antenna elements are spaced at (B-1) d, ckRepresenting the mutual coupling coefficient when the spacing between two antenna elements is kd, clThe mutual coupling coefficient when the distance between two antenna elements is ld is shown, l and k represent any positive integer between 1 and B-1, and B represents the maximum position of the antenna.
To evaluate the mutual coupling strengths of the mutual coupling matrices of different arrays, the mutual coupling leakage is defined as:
Figure BDA0003443803860000066
the larger L indicates the greater the effect of the mutual coupling effect on the array, and F represents the norm.
Step two: obtaining a covariance matrix R by using a sampling signal X (t);
the covariance matrix R is:
Figure BDA0003443803860000067
wherein E {. is } represents the mathematical expectation, the superscript H represents the conjugate transpose,
Figure BDA0003443803860000068
a manifold matrix of the array is represented,
Figure BDA0003443803860000069
representing the noise power, RsI represents an identity matrix, which is a covariance matrix of a source signal.
Step three: vectorizing, removing redundancy and rearranging the covariance matrix R to obtain an equivalent received signal z of the collaborative array1；
Figure BDA0003443803860000071
Wherein the content of the first and second substances,
Figure BDA0003443803860000072
is a column vector with the middle element being 1 and the other elements being 0, A1＝[a1(θ1),a1(θ2),…,a1(θK)]，
Figure BDA0003443803860000073
Figure BDA0003443803860000074
M denotes the number of array elements of each sub-array of the cooperative array,
Figure BDA0003443803860000075
Figure BDA0003443803860000076
representing the number of array elements of the super nested sub-array; thetakDenotes the K-th target source signal azimuth, K1, 2, K λ denotes the carrier frequency wavelength, Φ phase difference component matrix, Φ*Representing the conjugate of the phase difference partial matrix, p represents the power of the source signal,
Figure BDA0003443803860000077
representing the noise power. z is a radical of1The received signal can be equivalent to a distributed array shown in fig. 10, the array is called a cooperative array of a distributed thin super nested array, solid dots represent antenna units, crosses represent virtual antenna unit positions, and d is a basic array element spacing.
Step four: equivalent received signal z using a cooperative array1Constructing a spatially smooth matrix
Figure BDA0003443803860000078
Step five: to the space smoothing matrix
Figure BDA0003443803860000079
And (4) decomposing the characteristic value, and estimating the azimuth angle of the target source by adopting a multi-scale rotation invariant subspace algorithm.
z1The received signal can be equivalent to the distributed array shown in fig. 10, which is called a cooperative array of the distributed thin super nested array.
Simulation experiments were used to verify the DOA estimation properties of the proposed distributed super nested array. In order to show that the distributed super nested array provided by the invention can effectively reduce mutual coupling between array element antennas, the basic array element spacing d is set to be lambda/6, 7 lambda/24 and lambda/2 respectively to carry out simulation experiments.
Experiment 1 simulates DOA estimation characteristics of a distributed super nested array (SDNA), a distributed standard nested array (DNA), a distributed uniform array (DSA), and a uniform array with equal array element number (ULA). The simulation conditions were as follows: of the source signalThe angle is 30 degrees, the number of the array elements is 28, the snapshot number is 500, and when the distance d between the basic array elements is lambda/2, c is ordered0＝1,
Figure BDA00034438038600000710
Since the mutual coupling coefficient is approximately inversely proportional to the array element spacing, the smaller the basic array element spacing is, the more serious the mutual coupling between the array elements is. And calculating according to the proportional relation to obtain: when the basic array element spacing d is lambda/6, c0′＝1,
Figure BDA00034438038600000711
When the basic array element spacing d is 7 lambda/24, c0″＝1,c1″＝0.17ejθ(ii) a Wherein
Figure BDA00034438038600000712
And θ is a random value on [ - π, π). Each array element spacing value was subjected to 2000 monte carlo trials.
Fig. 3 and 4 are graphs comparing simulation results of root mean square error varying with signal-to-noise ratio obtained by using the antenna array of the present invention and the existing antenna array both using the multi-scale rotation invariant subspace algorithm when the carrier frequency wavelength is d ═ λ/6 and the base length is 63 times;
fig. 5 and fig. 6 are graphs comparing simulation results of root mean square error with signal-to-noise ratio variation obtained by using the antenna array of the present invention and the existing antenna array both using the multi-scale rotation invariant subspace algorithm when d is 7 λ/24 and the base length is 260 times of the carrier frequency wavelength;
fig. 7 and 8 are graphs comparing simulation results of root mean square error varying with signal-to-noise ratio obtained by using the multi-scale rotation invariant subspace algorithm for both the antenna array of the present invention and the existing antenna array when d is λ/2 and the base length is equal to 1500 times of the carrier frequency wavelength;
according to simulation results, when mutual coupling among array elements is not considered, the Root Mean Square Error (RMSE) of the distributed nested array and the distributed super nested array is consistent, and the estimation accuracy is far better than that of the distributed uniform array and the uniform array of the equal array elements when the signal to noise ratio is low. When mutual coupling among antenna units is considered, the estimation accuracy of the distributed super-nested array is better than that of the distributed super-nested array, and the performance advantage is more obvious under the condition that the smaller the distance d is and the more serious the mutual coupling is. The estimation performance of the distributed uniform array and the equal array element uniform array is rapidly deteriorated due to the influence of mutual coupling between the array elements and tends to a fixed value. In addition, the DOA estimation accuracy is also closely related to the base length, and the estimation accuracy is rapidly deteriorated if the fuzzy threshold of the base length is exceeded, so that an appropriate base length is also selected to obtain accurate DOA estimation.
The distributed super nested array can improve the DOA estimation precision and can also obviously increase the estimation number of source signals. Experiment 2 simulates DOA estimation characteristics of RMSE of a distributed super nested array, a distributed standard nested array, a distributed uniform array and a uniform array of equal array elements, which are changed along with the quantity of source signals when mutual coupling among the array elements is considered. FIG. 9 shows simulation results of RMSE as a function of the number of source signals for four array models.
From the simulation result of fig. 9, it can be seen that the maximum number of the estimable source signals of the distributed uniform array is 13, which is determined by the number of the array elements of the sub-array, when the number of the source signals is small, the estimation accuracy is better than that of the uniform array of the equal array elements, and as the number of the source signals is increased, the estimation accuracy is worse than that of the uniform array of the equal array elements, because the DOA estimation performance of the distributed uniform array is not only related to the mutual coupling between the array elements, but also closely related to the base length between the sub-arrays, and as the number of the source signals to be estimated is increased, the base length threshold becomes smaller, which results in the deterioration of the estimation accuracy. The maximum number of estimated source signals of the equal-array-element uniform array is 27, and when the number of source signals is greater than 22, the estimation error thereof is rapidly deteriorated. When the number of source signals of the distributed super nested array and the distributed standard nested array is less than 41, the RMSE of the distributed super nested array and the distributed standard nested array is less than that of the uniform array elements. Meanwhile, it can be seen that when the number of source signals is less than 36, the estimation error of the distributed super nested array is obviously better than that of the distributed standard nested array.
Through the simulation, the distributed super nested array provided by the invention is verified to be capable of obviously increasing the estimation quantity of source signals and improving the DOA estimation precision, and meanwhile, the DOA estimation performance of the distributed super nested array is superior to that of a distributed standard nested array. The method embodies the great advantage of the novel distributed super nested array and can be better applied to actual engineering.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.

Claims (6)

1. A distributed super nested antenna array, the array comprising two identical super nested sub-arrays: each super nested subarray comprises two levels of nested units; the distribution of two levels of nested units meets the following conditions:
Figure FDA0003443803850000011
Figure FDA0003443803850000012
Figure FDA0003443803850000013
Figure FDA0003443803850000014
Figure FDA0003443803850000015
Figure FDA0003443803850000016
Figure FDA0003443803850000017
wherein, S'(2)Representing a set of antenna positions for the super-nested sub-arrays,
Figure FDA0003443803850000018
a set of left-hand antenna positions of a stage is shown,
Figure FDA0003443803850000019
a set of antenna positions on the right side of the primary is shown,
Figure FDA00034438038500000110
a set of secondary left-hand antenna positions is represented,
Figure FDA00034438038500000111
a set of secondary right-hand antenna positions is represented,
Figure FDA00034438038500000112
a set of long-spaced antenna positions is represented,
Figure FDA00034438038500000113
representing a set of complementary antenna positions, l being an integer, N1Array element number, N, representing a first level nested array2Representing the array element number of the second-level nested array; parameter a1，b1，a2And b2Expressed as:
Figure FDA00034438038500000114
wherein r is a positive integer.
2. The distributed super nested antenna array of claim 1, in which N is N1＝N2＝5。
3. A method for obtaining a target position based on a distributed super nested antenna array, the method being implemented based on the distributed super nested antenna array of claim 1, the method comprising:
the method comprises the following steps: receiving a radar echo signal by adopting a distributed super nested antenna array, sampling a received signal, and obtaining a sampling signal X (t) of the received signal;
step two: obtaining a covariance matrix R by using a sampling signal X (t);
step three: vectorizing, removing redundancy and rearranging the covariance matrix R to obtain an equivalent received signal z of the collaborative array1；
Step four: equivalent received signal z using a cooperative array1Constructing a spatially smooth matrix
Figure FDA00034438038500000115
Step five: to the space smoothing matrix
Figure FDA00034438038500000116
And (4) decomposing the characteristic value, and estimating the azimuth angle of the target source by adopting a multi-scale rotation invariant subspace algorithm.
4. The method for obtaining the target position based on the distributed super-nested antenna array of claim 3, wherein in the step one, the obtained sampling signal X (t) of the received signal is:
Figure FDA0003443803850000021
wherein the content of the first and second substances,
Figure FDA0003443803850000022
representing an array manifold matrix, S (t) representing a signal vector, N (t) being a zero-mean additive white Gaussian noise vector, C representing a cross-coupling matrix, and A being a guide vector matrix;
the cross-coupling matrix is calculated using a simplified model, the formula:
Figure FDA0003443803850000023
where N is the total number of antennas, N1And n2Denotes the n-th1And n2An antenna, n1And n2Is any positive integer between 1 and N,
Figure FDA0003443803850000024
denotes the n-th1The distance of the individual antennas from the reference antenna,
Figure FDA0003443803850000025
denotes the n-th2Distance of individual antenna to reference antenna, c0Representing the mutual coupling coefficient of the antenna elements themselves, c1Representing the mutual coupling coefficient when the spacing between two antenna elements is d, c2Representing the mutual coupling coefficient when the spacing between two antenna elements is 2d, cB-1Representing the mutual coupling coefficient when the two antenna elements are spaced at (B-1) d, ckRepresenting the mutual coupling coefficient when the spacing between two antenna elements is kd, clThe mutual coupling coefficient when the distance between two antenna elements is ld is shown, l and k represent any positive integer between 1 and B-1, and B represents the maximum position of the antenna.
5. The method for obtaining the target azimuth based on the distributed super-nested antenna array of claim 4, wherein in the second step, the covariance matrix R is:
Figure FDA0003443803850000026
wherein E {. is } represents the mathematical expectation, the superscript H represents the conjugate transpose,
Figure FDA0003443803850000027
a manifold matrix of the array is represented,
Figure FDA0003443803850000028
representing the noise power, RsI represents an identity matrix, which is a covariance matrix of a source signal.
6. The method for obtaining the target azimuth based on the distributed super-nested antenna array of claim 5, wherein in step three, the equivalent received signal z1：
Figure FDA0003443803850000029
Wherein the content of the first and second substances,
Figure FDA00034438038500000210
is a column vector with the middle element being 1 and the other elements being 0, A1＝[a1(θ1),a1(θ2),…,a1(θK)]，
Figure FDA0003443803850000031
M denotes the number of array elements of each sub-array of the cooperative array,
Figure FDA0003443803850000032
Figure FDA0003443803850000033
representing the number of array elements of the super nested sub-array; thetakDenotes the K-th target source signal azimuth angle, K is 1,2,.. K, λ denotes the carrier frequency wavelength, and Φ is the phase difference component matrix，Φ*Representing the conjugate of the phase difference partial matrix, p represents the power of the source signal,
Figure FDA0003443803850000034
representing the noise power.
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CN114552237A (en) * 2022-04-25 2022-05-27 杭州洛微科技有限公司 Two-dimensional phased array antenna design method and device and two-dimensional phased array antenna

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114552237A (en) * 2022-04-25 2022-05-27 杭州洛微科技有限公司 Two-dimensional phased array antenna design method and device and two-dimensional phased array antenna
CN114552237B (en) * 2022-04-25 2023-04-07 杭州洛微科技有限公司 Two-dimensional phased array antenna design method and device and two-dimensional phased array antenna

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