CN111983552B - Nested array rapid DOA estimation method and device based on differential co-array - Google Patents
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Abstract
The application provides a method and a device for quickly estimating DOA of a nested array based on a differential co-array, wherein the method comprises the following steps: 1) Setting an antenna array, and sampling a received signal through a nested array; 2) Calculating covariance matrix of the received signal, and carrying out vectorization operation; 3) Sequencing the one-dimensional vectors according to the sequence of the differential co-array elements to obtain a differential co-array receiving signal; 4) Constructing DFT spectrum from the differential co-array received signal, searching spectrum peaks and calculating to obtain coarse DOA estimation; 5) The accurate DOA estimate is solved according to the Taylor expansion. According to the application, the array aperture of the nested array is fully utilized, the original physical array is expanded through the differential co-array, the DFT rough estimation result is substituted into the Taylor expansion formula to directly solve the high-precision DOA estimation, the equipment cost and the calculation cost are reduced, the complex phase searching process in the traditional DFT method precise estimation process is effectively avoided, and therefore, the high-precision rapid DOA estimation is realized under the condition of smaller physical array element size.
Description
Technical Field
The application relates to an array signal processing method, in particular to a nested array rapid DOA estimation method and device based on differential co-array.
Background
The array signal processing has been rapidly developed in more than twenty years due to the advantages of strong anti-interference capability, high signal gain, strong direction resolution capability and the like, and has been widely applied in a plurality of fields such as radar, communication, satellite navigation, sonar and the like. Array signal processing mainly studies adaptive beamforming and high resolution direction of arrival estimation (Direction of Arrival, DOA). Conventional DOA estimation methods, such as multiple signal classification (Multiple Signal Classification, MUSIC) methods, rotation-invariant signal parameter estimation algorithms (Estimation Of Signal Parameters Via Rotational Invariance Techniques, ESPRIT) and the like, have higher algorithm complexity when the array scale is relatively large, but if the DOA estimation method is directly applied to a sparse array, the DOA estimation method is ineffective due to the fact that the array element distance is larger than half wavelength of an incident signal.
Disclosure of Invention
The application aims to: aiming at the defects of the prior art, the application provides a nested array rapid DOA estimation method based on a differential co-array, which solves the problems of higher complexity and lower precision of the traditional large-scale array estimation process.
Another object of the application is to provide a nested array fast DOA estimation device based on differential co-array.
The technical scheme is as follows: in a first aspect, a method for quickly estimating DOA of a nested array based on a differential co-array includes the steps of:
(1) Setting an antenna array, and sampling a received signal through a nested array;
(2) Calculating covariance matrix of the received signal, carrying out vectorization operation on the covariance matrix, and reconstructing the covariance matrix into a one-dimensional vector;
(3) Sequencing the one-dimensional vectors according to the array element sequence of the differential co-array to obtain a receiving signal of the differential co-array;
(4) Constructing DFT spectrum from the differential co-array received signal, searching spectrum peaks and calculating to obtain coarse DOA estimation;
(5) Substituting the DTF rough estimate result into the taylor expansion and solving for the accurate DOA estimate.
Further, the array element sequence of the differential co-array is obtained by the corresponding relation between the difference set elements of the position set of the array elements of the nested array and the vectorized one-dimensional vector elements.
Further, the DFT spectrum is obtained by DFT conversion of the differential co-array received signal.
In a second aspect, a nested array fast DOA estimation device based on differential co-array includes:
the signal sampling module is used for setting an antenna array and sampling a received signal through the 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 sequencing module is used for sequencing the one-dimensional vectors according to the array element sequence of the differential co-array to obtain a receiving signal of the differential co-array;
the coarse estimation module is used for constructing a DFT spectrum from the differential co-array received signals, searching spectrum peaks and calculating to obtain a coarse 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, there is provided 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 as described in the first aspect of the present application.
The beneficial effects are that: compared with the prior art, the application has the following beneficial effects:
1. the array size 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 signal is reconstructed into a uniform array receiving signal with the expanded array element number, the required physical array element number is reduced, and the equipment cost is reduced.
2. The DFT (Discrete Fourier Transform) coarse estimation result of the differential co-array received signal is substituted into the Taylor expansion formula to directly solve the DOA estimation with high precision, so that a complex searching process in the conventional DFT method fine estimation process is avoided, the algorithm complexity is reduced, the calculation cost is reduced, and the DOA estimation with higher precision and rapider can be realized. When the array size is large, 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.
Drawings
FIG. 1 is a flow chart of a method for estimating a fast DOA of a nested array based on a differential co-array;
FIG. 2 is a schematic diagram of a nested array according to an embodiment of the present application;
FIG. 3 is a graph showing the performance of the method of the present application compared to a conventional DOA method at different snapshot numbers;
FIG. 4 is a graph showing the performance of the method of the present application 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 application and the conventional DOA method.
Detailed Description
The technical scheme of the application is further described below with reference to the accompanying drawings.
Referring to fig. 1, the method for estimating the rapid DOA of the nested array based on the differential co-array provided by the application comprises the following steps:
step 1, setting an antenna array, and sampling a received signal through a nested array;
in the embodiment, an antenna array is set as shown in fig. 2, and the nested array is formed by two-stage uniform linear arrays, wherein the first subarray is provided with N array elements, the array element spacing is half-wave d=lambda/2 of an incident signal, the second subarray is provided with M array elements, the array element spacing is (n+1) d, and the set of the array element positions is L ecp ＝{nd 1 |n＝1,2,…,N∪md 2 M=1, 2, …, M, where d } 1 Array element spacing d, d for the first subarray 2 And the array element distance (n+1) d of the second subarray.
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:
wherein a (θ) k ) Is incident angle theta k The direction vector of the signal of (2) can be described as T represents the matrix transpose, sk (T) is the envelope of the signal of the kth signal incident on the array at time T, n z (t) is independent zero-mean additive Gaussian white noise, and the signal and the noise are uncorrelated.
For the entire array, there are:
X(t)＝A(θ)S(t)+N(t) (2)
where a (θ) is the direction vector matrix of the signal, S (t) is the signal envelope matrix, and N (t) is the noise matrix.
The covariance matrix of the received signal is calculated according to the following formula:
R＝XX H /J (3)
where J is the snapshot number.
Vectorizing the covariance matrix of the received signal to obtain a column vector x:
x＝vec(R) (4)
step 3, sequencing the column vectors to obtain a differential co-array receiving signal;
difference set L of the set of array element positions diff ＝{l i -l u |i,u∈L ecp The order of the elements in the column vector x, the individual elements of the column vector x.
After reordering x, a differential co-array receiving signal x with a length extended is obtained, and a 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 coarse estimation of DOA estimation by a DFT spectrum searching method from the differential co-array received signals; constructing a normalized DFT matrix:
wherein the method comprises the steps ofWherein M is 0 Is the array element number of the differential co-array.
Calculating to obtain a DFT spatial spectrum:
wherein the q-th element is expressed as:
searching the top k maximum peaks of PA rough estimate of the initial angle can be obtained:
k represents the total number of sources.
And 5, performing accurate DOA estimation by a Taylor expansion method.
C (θ) can be regarded as C (θ) = [ C s (θ 1 ),...,c s (θ K )]Wherein the first-order taylor expansion of each term is expressed as:
the taylor expansion of C (θ) can be calculated as:
the signal model can be represented by taylor expansion as:
wherein w is θ ＝Λ θ p, p refers to the rearranged signal envelope matrix, Λ θ ＝diag(ζ θ1 ,…,ζ θK )，
Therefore, the method can be calculated by solving the least square method:
I K is a kxK identity matrix.
Thereby, the calculation results are:
Λ θ ＝w θ ./p (14)
the precise angle estimate is calculated by:
in order to verify the performance of the DOA estimation method, the simulation experiment is compared with the result of the traditional DOA estimation method. FIG. 3 is a graph showing DOA estimation performance of the method of the present application compared with that of the conventional DOA method. The simulation parameters are set as follows: the source locations are (10, 20,30, 40), the signal-to-noise ratio is 0, the number of simulations is 500, the snapshot count set is as shown in fig. 3, and the nested array set is as shown in fig. 2 (where n=7, m=8, d is half the wavelength of the incoming signal). As can be seen from fig. 3, as the snapshot count increases, the DOA estimation error of the present application decreases and is always smaller than that of the other conventional DOA methods for comparison, and has better DOA estimation performance.
Fig. 4 is a graph showing the DOA estimation performance of the method of the present application compared with other conventional DOA methods. The simulation parameters are set as follows: the source locations were (10, 20,30, 40), the snapshot count was 100, the number of simulations was 500, the signal to noise ratio set up was as shown in fig. 4, and the nested array set up was as shown in fig. 2 (where n=7, m=8, d is half the wavelength of the incoming signal). As can be seen from fig. 4, the DOA estimation error of the present application decreases with increasing signal-to-noise ratio and is always smaller than that of the other conventional DOA methods for comparison, and has better DOA estimation performance.
FIG. 5 shows the method and other aspects of the applicationThe algorithm of the unified DOA method is time-consuming to compare. 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) 2 L+Mlog (M ')+GKM ' +M '), SS-ESPRIT algorithm complexity is O (M) 2 L+0.25(M'+1) 3 +2(M'+1)K 2 +11K 3 ) The SS-PM algorithm complexity is O (M 2 L+0.125(M'+1) 3 +0.25(M'+1) 2 K+2(M'+1)K 2 +3K 3 ) Whereas the overall complexity of the method of the application is O (M 2 L+M'log(M')+(8K 2 +2k) M '), where G is the number of DFT refined searches (G is the value of len in the graph in the conventional DFT method mentioned in the present specification), K is the number of sources (k=4 in the graph), M is the number of physical array elements, M' is the number of differential co-array elements, and L is the snapshot number (l=100 in the graph). It can be seen from the figure that the complexity of the method provided by the application is obviously lower than that of other traditional DOA estimation methods under the condition that the number of array elements is the same.
Based on the concept of the above method embodiment, according to another embodiment of the present application, there is provided a nested array fast DOA estimation device based on differential co-array, including:
the signal sampling module is used for setting an antenna array and sampling a received signal through the 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 sequencing module is used for sequencing the one-dimensional vectors according to the array element sequence of the differential co-array to obtain a receiving signal of the differential co-array;
the coarse estimation module is used for constructing a DFT spectrum from the differential co-array received signals, searching spectrum peaks and calculating to obtain a coarse 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 a received signal through a nested array, the nested array is composed of two-stage uniform linear arrays, the first subarray is provided with N array elements, the distance between the array elements is half-wave d=lambda/2 of an incident signal, and the second subarray is provided with a plurality of linear arraysEach subarray is provided with M array elements, the spacing of the array elements is (N+1) d, and the set of the array element positions is L ecp ＝{nd 1 |n＝1,2,…,N∪md 2 M=1, 2, …, M, where d } 1 Array element spacing d, d for the first subarray 2 And the array element distance (n+1) d of the second subarray.
Further, the reconstruction module includes:
the signal model building unit, for the z-th array element, receives the signal model as follows:
wherein a (θ) k ) Is incident angle theta k Direction vector of the signal of (2), S k (t) is the envelope of the signal of the kth signal incident on the array, n z (t) is independent zero-mean additive white gaussian noise;
for the entire array, there are:
X(t)＝A(θ)S(t)+N(t) (17)
where a (θ) is the direction vector matrix of the signal, S (t) is the signal envelope matrix, and N (t) is the noise matrix.
The covariance matrix calculation unit is used for calculating a covariance matrix of the received signal according to the following formula:
R＝XX H /J (18)
wherein J is the snapshot number;
the vectorization operation unit is used for vectorizing the covariance matrix to obtain a column vector x:
x＝vec(R) (19)
the array element sequence of the differential co-array is obtained by the corresponding relation between the difference set elements of the position set of the array elements of the nested array and the vectorized one-dimensional vector elements. Specifically, the sorting module sorts the difference set L of the set according to the array element positions diff ＝{l i -l u |i,u∈L ecp The order of the elements in the column vector x, the individual elements of the column vector x.
After reordering x, a differential co-array receiving signal x with a length extended is obtained, and a 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, DFT spectrum is obtained by DFT conversion of differential co-array received signals. Specifically, the rough estimation module includes:
a DFT matrix construction unit for constructing a normalized DFT matrix:
wherein the method comprises the steps ofWherein M is 0 The array element number is the differential co-array;
the DFT spatial spectrum calculation unit is used for calculating and obtaining a DFT spatial spectrum according to the following formula:
wherein the q-th element is expressed as:
wherein θ is k Representing the angle of incidence of the kth signal;
a rough estimation calculation unit for searching the top k maximum peaks of PA rough estimate of the initial angle is obtained according to the following equation:
where K represents the total number of sources.
Further, the fine estimation module includes:
a taylor expansion unit for expressing the signal model as:
wherein w is θ ＝Λ θ p, p represents the rearranged signal envelope matrix, Λ θ ＝diag(ζ θ1 ,…,ζ θK )， For a rough estimate of the initial angle, n represents noise;
the solving unit is used for solving through a least square method, and calculating to obtain:
thereby, the calculation results are:
Λ θ ＝w θ a fine estimate calculation unit of/p (27) for calculating a fine angle estimate from:
it should be understood that the differential co-array based nested array fast DOA estimation device in the embodiment of the present application may implement all the technical solutions in the above method embodiments, and the functions of each functional module may be specifically implemented according to the methods in the above method embodiments, and the specific implementation process may refer to the relevant descriptions in the above embodiments, which are not repeated herein.
According to still another embodiment of the present application, 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, the programs when executed by the processors implement the steps in the method embodiments.
It will be appreciated by those skilled in the art that 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 flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations 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 aspects of the present application and not for limiting the same, and although the present application has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the application without departing from the spirit and scope of the application, which is intended to be covered by the claims.
Claims (7)
1. The nested array rapid DOA estimation method based on the differential co-array is characterized by comprising the following steps of:
(1) An antenna array is arranged, and a receiving signal is sampled through a nested array, wherein the nested array is formed by two-stage uniform linear arrays, the first subarray is provided with N array elements, the array element interval is half-wave d=lambda/2 of an incident signal, the second subarray is provided with M array elements, the array element interval is (n+1) d, and the set of the array element positions is L ecp ＝{nd 1 |n＝1,2,…,N∪md 2 M=1, 2, …, M, where d } 1 Array element spacing d, d for the first subarray 2 An array element spacing (n+1) d for the second subarray;
(2) Calculating covariance matrix of the received signal, carrying out vectorization operation on the covariance matrix, and reconstructing the covariance matrix into a one-dimensional vector, wherein the method comprises the following steps: for the z-th array element, the received signal model is:wherein a (θ) k ) Is incident angle theta k Direction vector of the signal of (a) at time t, S k (t) is the envelope of the signal of the kth signal incident on the array, n z (t) are each otherIndependent zero-mean additive white gaussian noise; for the entire array, there are: x (t) =a (θ) S (t) +n (t), where a (θ) 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 according to the following formula: r=xx H J, wherein J is the snapshot number; vectorizing the covariance matrix to obtain a column vector x: x=vec (R);
(3) Sequencing the one-dimensional vectors according to the array element sequence of the differential co-array to obtain a receiving signal of the differential co-array, wherein the method comprises the following steps:
difference set L of the set of array element positions diff ＝{l i -l u |i,u∈L ecp The order of the elements in the column vector x is ordered;
after reordering x, a differential co-array receiving signal x with a length extended is obtained, and a signal model is as follows:
x(t)＝C(θ)p(t)+n(t)
wherein x (t) is a rearranged received signal, C (θ) is a rearranged signal direction vector matrix, p (t) is a rearranged signal envelope matrix, and n (t) is a rearranged noise matrix;
(4) Constructing DFT spectrum from the differential co-array received signal, searching spectrum peaks and calculating to obtain coarse DOA estimation;
(5) Substituting the DTF rough estimate result into the taylor expansion and solving for the accurate DOA estimate.
2. The differential co-array based nested array fast DOA estimation method of claim 1, wherein the DFT spectrum is obtained by DFT conversion of a differential co-array received signal.
3. The differential co-array based nested array fast DOA estimation method of claim 1, wherein step (4) comprises:
constructing a normalized DFT matrix:
wherein the method comprises the steps ofWherein M is 0 The array element number is the differential co-array;
calculating to obtain a DFT spatial spectrum:
wherein the q-th element is expressed as:
wherein θ is k Representing the angle of incidence of the kth signal;
searching the top k maximum peaks of PObtaining rough estimation of the initial angle:
where K represents the total number of sources.
4. The differential co-array based nested array fast DOA estimation method of claim 1, wherein step (5) comprises:
the signal model is represented by taylor expansion as:
wherein w is θ ＝Λ θ p and p are reordered signal envelope matrix, Λ θ ＝diag(ζ θ1 ,…,ζ θK )，For coarse estimation of the initial angle, n represents noise, and C represents a reordered signal direction vector matrix;
solving by a least square method, and calculating to obtain:
thereby, the calculation results are: Λ type θ ＝w θ ./p；
The precise angle estimate is calculated by:
5. a nested array fast DOA estimation device based on differential co-array, comprising:
the signal sampling module is used for setting an antenna array and sampling a received signal through a nested array, wherein the nested array is formed by two-stage uniform linear arrays, the first subarray is provided with N array elements, the array element distance is half-wave d=lambda/2 of an incident signal, the second subarray is provided with M array elements, the array element distance is (n+1) d, and the set of the array element positions is L ecp ＝{nd 1 |n＝1，2，…，N∪md 2 M=1, 2, …, M, where d } 1 Array element spacing d, d for the first subarray 2 An array element spacing (n+1) d for the second subarray;
the reconstruction module is used for calculating a covariance matrix of the received signal, carrying out vectorization operation on the covariance matrix, reconstructing the covariance matrix into a one-dimensional vector, and comprises the following steps: for the z-th array element, the received signal model is:wherein a (θ) k ) Is incident angle theta k Direction vector of the signal of (a) at time t, S K (t) is the envelope of the signal of the kth signal incident on the array, n z (t) is independent zero-mean additive white gaussian noise; for the entire array, there are: x (t) =a (θ) S (t) +n (t), where a (θ) 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 according to the following formula: r=xx H J, wherein J is the snapshot number; vectorizing the covariance matrix to obtain a column vector x: x=vec (R);
the sorting module is used for sorting the one-dimensional vectors according to the array element sequence of the differential co-array to obtain a receiving signal of the differential co-array, and comprises the following steps: difference set L of the set of array element positions diff ＝{l i -l u |i，u∈L ecp The order of the elements in the column vector x is ordered; after reordering x, a differential co-array receiving signal x with a length extended is obtained, and a signal model is as follows: x (t) =c (θ) p (t) +n (t), 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;
the coarse estimation module is used for constructing a DFT spectrum from the differential co-array received signals, searching spectrum peaks and calculating to obtain a coarse 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.
6. The differential co-array based nested array fast DOA estimation device of claim 5, wherein the DFT spectrum is obtained by DFT transforming a differential co-array received signal.
7. 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 1-4.
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