CN111983552A - Nested array rapid DOA estimation method and device based on differential common array - Google Patents

Nested array rapid DOA estimation method and device based on differential common array Download PDF

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CN111983552A
CN111983552A CN202010734907.6A CN202010734907A CN111983552A CN 111983552 A CN111983552 A CN 111983552A CN 202010734907 A CN202010734907 A CN 202010734907A CN 111983552 A CN111983552 A CN 111983552A
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CN111983552B (en
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赖欣
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
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Abstract

The invention provides a differential common array based nested array rapid DOA estimation method and a device, wherein the method comprises the following steps: 1) setting an antenna array, and sampling a received signal through a nested array; 2) calculating a covariance matrix of the received signals, and performing vectorization operation; 3) sorting the one-dimensional vectors according to the sequence of the differential common array elements to obtain differential common array receiving signals; 4) constructing a DFT spectrum by the differential common-array receiving signals, searching a spectrum peak and calculating to obtain a rough estimation of DOA estimation; 5) the exact DOA estimate is solved according to taylor expansion. The method fully utilizes the array aperture of the nested array, expands the original physical array through the differential common array, directly solves the high-precision DOA estimation by substituting the DFT rough estimation result into the Taylor expansion, reduces the equipment cost and the calculation cost, effectively avoids the complex phase search process in the fine estimation process of the traditional DFT method, and realizes the high-precision rapid DOA estimation under the smaller physical array element size.

Description

Nested array rapid DOA estimation method and device based on differential common array
Technical Field
The invention relates to an array signal processing method, in particular to a nested array rapid DOA estimation method and a nested array rapid DOA estimation device based on a differential common array.
Background
The array signal processing has the advantages of strong anti-interference capability, high signal gain, strong direction resolution and the like, is rapidly developed in nearly twenty years, and is widely applied to the fields of radars, communication, satellite navigation, sonars and the like. Array signal processing is mainly studied for adaptive beamforming and high resolution Direction of Arrival (DOA). Conventional DOA Estimation methods such as a Multiple Signal Classification (MUSIC) method, an Estimation Of Signal parameter with rotation Invariance (ESPRIT) method, etc. have a relatively high complexity when the array size is relatively large, and if the DOA Estimation method is directly applied to a sparse array, the DOA Estimation method is more ineffective because the array element spacing is larger than the half wavelength Of the incident Signal.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects of the prior art, the invention provides a nested array rapid DOA estimation method based on a differential common array, which solves the problems of high complexity and low precision of the traditional large-scale array estimation process.
The invention also aims to provide a nested array rapid DOA estimation device based on the differential common array.
The technical scheme is as follows: in a first aspect, a nested array fast DOA estimation method based on a differential common array comprises the following steps:
(1) setting an antenna array, and sampling a received signal through a nested array;
(2) calculating a covariance matrix of a received signal, carrying out vectorization operation on the covariance matrix, and reconstructing the covariance matrix into a one-dimensional vector;
(3) sorting the one-dimensional vectors according to the array element sequence of the differential common array to obtain a receiving signal of the differential common array;
(4) constructing a DFT spectrum by the differential common-array receiving signals, searching a spectrum peak and calculating to obtain a rough estimation of DOA estimation;
(5) and substituting the DTF rough estimation result into a Taylor expansion equation and solving an accurate DOA estimation.
Further, the array element sequence of the differential common array is obtained from the corresponding relationship between the difference set element of the position set where the array elements of the nested array are located and the vectorized one-dimensional vector element.
Furthermore, the DFT spectrum is obtained by DFT conversion of the differential common-matrix receiving signal.
In a second aspect, a differential common array based nested array fast DOA estimation apparatus includes:
the signal sampling module is used for setting an antenna array and sampling a received signal through a nested array;
the reconstruction module is used for calculating a covariance matrix of the received signal, carrying out vectorization operation on the covariance matrix and reconstructing the covariance matrix into a one-dimensional vector;
the sorting module is used for sorting the one-dimensional vectors according to the array element sequence of the differential common array to obtain a receiving signal of the differential common array;
the rough estimation module is used for constructing a DFT spectrum from the differential common-matrix receiving signals, searching a spectrum peak and calculating to obtain rough estimation of DOA estimation;
and the fine estimation module is used for substituting the DTF coarse estimation result into the Taylor expansion and solving the accurate DOA estimation.
In a third aspect, a computer device is provided, the device comprising:
one or more processors;
a memory; and
one or more programs, wherein the one or more programs are stored in the memory and configured for execution by the one or more processors, which when executed by the processors perform the steps of the first aspect of the invention.
Has the advantages that: compared with the prior art, the invention has the following beneficial effects:
1. the size of the array is expanded by utilizing the differential common array of the nested array, the array aperture of the nested array is fully utilized, the nested array is a sparse array, the sparse array receiving signals are reconstructed into uniform array receiving signals with an array element number expanded, the required physical array element number is reduced, and the equipment cost is reduced.
2. The high-precision DOA estimation is directly solved by substituting the DFT (discrete Fourier transform) rough estimation result of the differential common-array receiving signal into the Taylor expansion, so that the complex search process in the fine estimation process of the traditional DFT method is avoided, the algorithm complexity is reduced, the calculation cost is reduced, and the DOA estimation with higher precision and higher speed can be realized. When the array size is larger, the method has higher information source resolution, and is more suitable for a large-scale MIMO system in 5G communication and has important practical value.
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FIG. 1 is a flowchart of a differential common array-based nested array fast DOA estimation method provided by the present invention;
FIG. 2 is a schematic diagram of a nested array configuration provided in an embodiment of the present invention;
FIG. 3 is a comparison of the performance of the method of the present invention compared to a conventional DOA method at different snapshot counts;
FIG. 4 is a comparison of the performance of the method of the present invention compared to a conventional DOA method at different signal-to-noise ratios;
fig. 5 is a comparison of the algorithm complexity of the method of the present invention and a conventional DOA method.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
Referring to fig. 1, the method for rapidly estimating the DOA of the nested array based on the differential common array provided by the invention comprises the following steps:
step 1, an antenna array is arranged, and received signals are sampled through a nested array;
in the embodiment, as shown in fig. 2, the antenna array is provided, and the nested array is formed by two stages of uniform linear arrays, where the first sub-array has N array elements, the array element spacing is half-wave d ═ λ/2 of the incident signal, the second sub-array has M array elements, the array element spacing is (N +1) d, and the set of the array element positions is Lecp＝{nd1|n＝1,2,…,N∪ md 21,2, …, M, where d1Is the array element spacing d, d of the first sub-array2The array element spacing (N +1) d of the second sub-array.
Step 2, calculating a covariance matrix of the received signal, and carrying out vectorization operation on the covariance matrix;
for the z-th array element, the received signal model is as follows:
Figure BDA0002604596920000031
wherein, a (theta)k) Is incident angle of thetakCan be described as the direction vector of
Figure BDA0002604596920000032
Figure BDA0002604596920000033
T denotes the matrix transposition, at time T, Sk (T) is the envelope of the signal incident on the array for the k-th signal, nzAnd (t) is mutually independent zero-mean additive white Gaussian noise, and signals and noise are not related to each other.
For the entire array, there are:
X(t)＝A(θ)S(t)+N(t) (2)
where A (theta) is a direction vector matrix of the signal, S (t) is a signal envelope matrix, and N (t) is a noise matrix.
The covariance matrix of the received signal is calculated as follows:
R＝XXH/J (3)
where J is the number of fast beats.
Carrying out vectorization operation on the covariance matrix of the received signals to obtain a column vector x:
x＝vec(R) (4)
step 3, sequencing the column vectors to obtain differential common array receiving signals;
difference set L of the set of array element positionsdiff＝{li-lu|i,u∈LecpThe order of the elements in the column vector x, the elements of the column vector x are ordered.
And after reordering the x, obtaining a length-extended differential common array receiving signal x, wherein the signal model is as follows:
x(t)＝C(θ)p(t)+n(t) (5)
where x (t) is the rearranged received signal, C (θ) is the rearranged signal direction vector matrix, p (t) is the rearranged signal envelope matrix, and n (t) is the rearranged noise matrix.
Step 4, calculating the rough estimation of DOA estimation by the DFT spectrum search method according to the differential common array receiving signals; constructing a normalized DFT matrix:
Figure BDA0002604596920000041
wherein
Figure BDA0002604596920000042
Wherein M is0The array element number of the differential common array is shown.
Calculating to obtain a DFT space spectrum:
Figure BDA0002604596920000043
wherein the qth element is represented as:
Figure BDA0002604596920000044
searching for the first k maximum peaks of P
Figure BDA0002604596920000045
A rough estimate of the initial angle can be obtained:
Figure BDA0002604596920000046
k denotes the total number of sources.
And 5, carrying out accurate DOA estimation by a Taylor expansion method.
C (θ) can be regarded as C (θ) ═ Cs(θ1),...,cs(θK)]Wherein the first order Taylor expansion of each term is represented as:
Figure BDA0002604596920000047
then the taylor expansion of C (θ) can be calculated as:
Figure BDA0002604596920000048
the signal model can be represented by taylor expansion as:
Figure BDA0002604596920000049
wherein wθ＝Λθp, p refers to the rearranged signal envelope matrix, Λθ＝diag(ζθ1,…,ζθK)，
Figure BDA00026045969200000410
Therefore, the following can be calculated by solving with the least square method:
Figure BDA0002604596920000051
IKis an identity matrix of K × K.
Thus, it is calculated that:
Λθ＝wθ./p (14)
the precise angle estimate is calculated from:
Figure BDA0002604596920000052
in order to verify the performance of the DOA estimation method provided by the invention, the results are compared with the results of the traditional DOA estimation method through simulation experiments. FIG. 3 is a graph illustrating DOA estimation performance of the method of the present invention compared to a conventional DOA method. The simulation parameters are set as follows: the source is located at (10,20,30,40), the snr is 0, the number of simulations is 500, the snapshot number is set as shown in fig. 3, and the nested array is set as shown in fig. 2 (where N is 7, M is 8, and d is half the wavelength of the incident signal). As can be seen from fig. 3, with increasing number of fast beats, the DOA estimation error of the present invention decreases and is always smaller than the other conventional DOA methods for comparison, with better DOA estimation performance.
Figure 4 is a comparison of DOA estimation performance of the method of the present invention with other conventional DOA methods. The simulation parameters are set as follows: the source position is (10,20,30,40), the snapshot number is 100, the simulation times are 500, the signal-to-noise ratio is set as shown in fig. 4, and the nested array is set as shown in fig. 2 (where N is 7, M is 8, and d is half the wavelength of the incident signal). As can be seen from fig. 4, as the signal-to-noise ratio increases, the DOA estimation error of the present invention decreases and is always smaller than the other conventional DOA methods for comparison, with better DOA estimation performance.
Fig. 5 is a time consuming comparison of the algorithm of the method of the present invention with other conventional DOA methods. The algorithm complexity of the traditional DFT method in the rough estimation and the fine estimation is O (M 'log (M') + GKM '+ M'), and the total algorithm complexity is O (M '+ M')2L + Mlog (M ') + GKM ' + M '), SS-ESPRIT algorithm complexity is O (M `2L+0.25(M'+1)3+2(M'+1)K2+11K3) The SS-PM algorithm has the complexity of O (M)2L+0.125(M'+1)3+0.25(M'+1)2K+2(M'+1)K2+3K3) The total complexity of the method of the present invention is O (M)2L+M'log(M')+(8K2+2K) M '), where G is a DFT fine estimation search frequency (in the conventional DFT method mentioned in this specification, G is a value size of len in the drawing), K is an information source number (K is 4 in the drawing), M is a physical array element number, M' is a differential common array element number, and L is a snapshot number (L is 100 in the drawing). It can be seen from the figure that, under the condition of the same number of array elements, the complexity of the method provided by the invention is obviously lower than that of other traditional DOA estimation methods.
Based on the concept of the above method embodiment, according to another embodiment of the present invention, there is provided a nested array fast DOA estimation apparatus based on a differential common array, including:
the signal sampling module is used for setting an antenna array and sampling a received signal through a nested array;
the reconstruction module is used for calculating a covariance matrix of the received signal, carrying out vectorization operation on the covariance matrix and reconstructing the covariance matrix into a one-dimensional vector;
the sorting module is used for sorting the one-dimensional vectors according to the array element sequence of the differential common array to obtain a receiving signal of the differential common array;
the rough estimation module is used for constructing a DFT spectrum from the differential common-matrix receiving signals, searching a spectrum peak and calculating to obtain rough estimation of DOA estimation;
and the fine estimation module is used for substituting the DTF coarse estimation result into the Taylor expansion and solving the accurate DOA estimation.
The signal sampling module samples received signals through a nested array, the nested array is composed of two-stage uniform linear arrays, the first sub-array is provided with N array elements, the array element interval is half-wave d ═ lambda/2 of incident signals, the second sub-array is provided with M array elements, the array element interval is (N +1) d, and the position set of the array elements is Lecp＝{nd1|n＝1,2,…, N∪md 21,2, …, M, where d1Is the array element spacing d, d of the first sub-array2The array element spacing (N +1) d of the second sub-array.
Further, the reconstruction module includes:
and the signal model construction unit is used for constructing a receiving signal model of the z-th array element as follows:
Figure BDA0002604596920000061
wherein, a (theta)k) Is incident angle of thetakOf the signal of (2), Sk(t) envelope of the signal incident on the array for the k-th signal, nz(t) is zero-mean additive white gaussian noise independent of each other;
for the entire array, there are:
X(t)＝A(θ)S(t)+N(t) (17)
where A (theta) is a direction vector matrix of the signal, S (t) is a signal envelope matrix, and N (t) is a noise matrix.
A covariance matrix calculation unit, configured to calculate a received signal covariance matrix according to the following formula:
R＝XXH/J (18)
wherein J is the number of fast beats;
a vectorization operation unit, configured to perform vectorization operation on the covariance matrix to obtain a column vector x:
x＝vec(R) (19)
the array element sequence of the differential common array is obtained by the corresponding relation between the difference set elements of the position set where the array elements of the nested array are located and the vectorized one-dimensional vector elements. Specifically, the sorting module sorts the difference set L of the set where the array element positions are locateddiff＝{li-lu|i,u∈LecpThe order of the elements in the column vector x, the elements of the column vector x are ordered.
And after reordering the x, obtaining a length-extended differential common array receiving signal x, wherein the signal model is as follows:
x(t)＝C(θ)p(t)+n(t) (20)
where x (t) is the rearranged received signal, C (θ) is the rearranged signal direction vector matrix, p (t) is the rearranged signal envelope matrix, and n (t) is the rearranged noise matrix.
In the rough estimation module, a DFT spectrum is obtained by DFT conversion of a differential common array receiving signal. Specifically, the rough estimation module includes:
a DFT matrix construction unit, configured to construct a normalized DFT matrix:
Figure BDA0002604596920000071
wherein
Figure BDA0002604596920000072
Wherein M is0The array element number of the differential common array is;
a DFT spatial spectrum calculating unit, configured to calculate a DFT spatial spectrum according to the following formula:
Figure BDA0002604596920000073
wherein the qth element is represented as:
Figure BDA0002604596920000074
wherein theta iskRepresents the k < th >The angle of incidence of the signal;
a coarse estimation calculation unit for searching the first k maximum peaks of P
Figure BDA0002604596920000075
A rough estimate of the initial angle is obtained according to:
Figure BDA0002604596920000076
where K represents the total number of sources.
Further, the fine estimation module comprises:
a Taylor expansion unit for expressing the signal model as:
Figure BDA0002604596920000081
wherein wθ＝Λθp, p denotes the rearranged signal envelope matrix, Λθ＝diag(ζθ1,…,ζθK)，
Figure BDA0002604596920000082
Figure BDA0002604596920000083
For a coarse estimate of the initial angle, n represents noise;
and the solving unit is used for solving by a least square method, and calculating to obtain:
Figure BDA0002604596920000084
thus, it is calculated that:
Λθ＝wθa/p (27) fine estimate calculation unit for calculating a fine angle estimate by:
Figure BDA0002604596920000085
it should be understood that, in the embodiment of the present invention, the differential common array-based nested array fast DOA estimation apparatus may implement all technical solutions in the above method embodiments, functions of each functional module may be implemented specifically according to the method in the above method embodiments, and a specific implementation process thereof may refer to relevant descriptions in the above embodiments, which is not described herein again.
According to still another embodiment of the present invention, there is provided a computer apparatus including: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, which when executed by the processors implement the steps in the method embodiments.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (10)

1. A nested array rapid DOA estimation method based on a differential common array is characterized by comprising the following steps:
(1) setting an antenna array, and sampling a received signal through a nested array;
(2) calculating a covariance matrix of a received signal, carrying out vectorization operation on the covariance matrix, and reconstructing the covariance matrix into a one-dimensional vector;
(3) sorting the one-dimensional vectors according to the array element sequence of the differential common array to obtain a receiving signal of the differential common array;
(4) constructing a DFT spectrum by the differential common-array receiving signals, searching a spectrum peak and calculating to obtain a rough estimation of DOA estimation;
(5) and substituting the DTF rough estimation result into a Taylor expansion equation and solving an accurate DOA estimation.
2. The Taylor expansion-based nested array fast DOA estimation method in accordance with claim 1, wherein the step (2) comprises:
for the z-th array element, the received signal model is as follows:
Figure FDA0002604596910000011
wherein, a (theta)k) Is incident angle of thetakOf the signal of (a), at times t, Sk(t) envelope of the signal incident on the array for the k-th signal, nz(t) is zero-mean additive white gaussian noise independent of each other;
for the entire array, there are:
X(t)＝A(θ)S(t)+N(t)
wherein, A (theta) is a direction vector matrix of the signal, S (t) is a signal envelope matrix, and N (t) is a noise matrix;
and calculating a received signal covariance matrix according to the following formula:
R＝XXH/J
wherein J is the number of fast beats;
carrying out vectorization operation on the covariance matrix to obtain a column vector x:
x＝vec(R)。
3. the Taylor expansion-based nested array rapid DOA estimation method according to claim 1, wherein the array element sequence of the difference common array is obtained from a corresponding relation between a difference set element of a position set where the array elements of the nested array are located and a vectorized one-dimensional vector element.
4. The Taylor expansion-based nested array rapid DOA estimation method in accordance with claim 1, wherein the DFT spectrum is obtained by DFT transforming the received signal of the differential co-array.
5. The Taylor expansion-based nested array fast DOA estimation method in accordance with claim 1, wherein the step (4) comprises:
constructing a normalized DFT matrix:
Figure FDA0002604596910000021
wherein
Figure FDA0002604596910000022
Wherein M is0The array element number of the differential common array is;
calculating to obtain a DFT space spectrum:
Figure FDA0002604596910000023
wherein the qth element is represented as:
Figure FDA0002604596910000024
wherein theta iskRepresents the angle of incidence of the kth signal;
searching for the first k maximum peaks of P
Figure FDA0002604596910000025
Get a rough estimate of the initial angle:
Figure FDA0002604596910000026
where K represents the total number of sources.
6. The Taylor expansion-based nested array fast DOA estimation method in accordance with claim 1, wherein the step (5) comprises:
the signal model is represented by taylor expansion as:
Figure FDA0002604596910000027
wherein wθ＝Λθp, p being the reordered signal envelope matrix, Λθ＝diag(ζθ1，...，ζθK)，
Figure FDA0002604596910000028
Figure FDA0002604596910000029
The rough estimation of the initial angle is carried out, n represents noise, and C represents a reordered signal direction vector matrix;
solving by a least square method, and calculating to obtain:
Figure FDA00026045969100000210
thus, it is calculated that: lambdaθ＝wθ./p；
The precise angle estimate is calculated from:
Figure FDA00026045969100000211
7. a nested array rapid DOA estimation device based on a differential common array is characterized by comprising:
the signal sampling module is used for setting an antenna array and sampling a received signal through a nested array;
the reconstruction module is used for calculating a covariance matrix of the received signal, carrying out vectorization operation on the covariance matrix and reconstructing the covariance matrix into a one-dimensional vector;
the sorting module is used for sorting the one-dimensional vectors according to the array element sequence of the differential common array to obtain a receiving signal of the differential common array;
the rough estimation module is used for constructing a DFT spectrum from the differential common-matrix receiving signals, searching a spectrum peak and calculating to obtain rough estimation of DOA estimation;
and the fine estimation module is used for substituting the DTF coarse estimation result into the Taylor expansion and solving the accurate DOA estimation.
8. The taylor expansion-based nested array rapid DOA estimation apparatus according to claim 7, wherein the array element sequence of the difference co-array is obtained from a correspondence between a difference set element of a position set where the array elements of the nested array are located and a vectorized one-dimensional vector element.
9. The taylor expansion-based nested array fast DOA estimation device in accordance with claim 7, wherein the DFT spectrum is obtained by DFT-transforming the differential co-arrayed received signal.
10. A computer device, the device comprising:
one or more processors;
a memory; and
one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, which when executed by the processors implement the steps of the method of any of claims 1-6.
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