CN109613473A - The relatively prime linear array angle estimating method of expansion based on sparsity - Google Patents
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Abstract
The invention discloses the relatively prime linear array angle estimating methods of expansion based on sparsity, are related to Estimation of Spatial Spectrum field, can be applied in the fields such as wireless communication, sonar, positioning.The present invention includes: to carry out vectorization processing to the covariance matrix of array received signal, obtains the reception signal of virtual line arrays；It treats measuring angle space and carries out the excessively complete redundant dictionary that grid division obtains angle, convert rarefaction representation form for data model；The convex optimization problem of 1 norm is constructed on this basis, obtains Mutual coupling using orthogonal matching pursuit algorithm.Present invention utilizes relatively prime linear array is unfolded to obtain the advantage of high spatial freedom degree, while whole Virtual arrays that relatively prime linear array is unfolded and generates are made full use of using compressed sensing technology, the also angle estimation precision with higher while room for promotion freedom degree.
Description
Technical field
The present invention relates to Estimation of Spatial Spectrum fields, more particularly to the relatively prime linear array angle estimation side of expansion based on sparsity
Method.
Background technique
Currently, a kind of array antenna being referred to as relatively prime battle array, which is laid out, is paid close attention to, and relatively prime battle array breaches traditional antenna battle array
The limitation of array element spacing half-wavelength has many excellent characteristics.Wherein, the deployed configuration that relatively prime linear array is unfolded makes between array element
Away from further increasing, the mutual coupling effect between array element has obtained effective weakening；Meanwhile the angle of virtualization is used to relatively prime linear array is unfolded
Estimation method is spent, spatial degrees of freedom more higher than practical array number can be obtained, substantially increase detectable information source number.So
And the endless Total continuity of Virtual array due to being unfolded to generate after relatively prime linear array virtualization, and common Search Space Smoothing can only
The uniform array continuously distributed for array element, therefore can not use relatively prime linear array is unfolded.So common space smoothing at this time
Technical failure.
To sum up, lack a kind of relatively prime linear array angle estimating method of expansion in the prior art, whole Virtual arrays can be utilized
Method, high-precision angle estimation is realized in including discontinuous part.
Summary of the invention
The present invention provides the relatively prime linear array angle estimating methods of expansion based on sparsity, by compressed sensing technology and space
Power estimation problem combines, and has biggish spatial degrees of freedom and higher estimated accuracy.
In order to achieve the above objectives, the present invention adopts the following technical scheme:
Technical problem to be solved by the invention is to provide a kind of relatively prime linear array angle estimation sides of the expansion based on sparsity
Method, this method combine compressed sensing technology with Estimation of Spatial Spectrum problem, have biggish spatial degrees of freedom and higher estimate
Precision is counted, can be applied in the fields such as wireless communication, sonar, positioning.
The relatively prime linear array angle estimating method of expansion based on sparsity, comprising:
S1, it obtains receiving signal using according to the antenna acquisition signal that relatively prime linear array structure framework is unfolded, to reception signal
Covariance matrix carry out vectorization processing, obtained vector is sorted by phase and deletes redundant row, virtual array is obtained and connects
The collection of letters number.
S2, the angular region for receiving signal source is equidistantly divided, complete angle set is obtained.It will be according to mistake
The propagation direction matrix of complete angle set construction is used as observing matrix, using virtual array reception signal as observation signal, from
It and is compressed sensing model by array signal model conversation.
S3, by compressed sensing model conversation be a convex optimization problem of 1 norm, utilize orthogonal matching pursuit algorithm solve 1
The convex optimization problem of norm obtains the angle estimation value of information source by iteration.
Further, the S1 includes:
S11, using M+N-1 antennas, carry out framework according to relatively prime linear array structure is unfolded, M and N are mutual prime rwmber, institute
It states in antenna reception space from direction θ1,θ2,…,θKThe irrelevant far field narrow band signals of K.
S12, to L sampling snap of array received signal acquisition, obtain array received signal matrix
S13, the covariance matrix for calculating receipt signal matrix X
S14, to covariance matrixVectorization processing is carried out, the vector of acquisition is ranked up by phase and is deleted superfluous
Yu Hang, obtains the vector z that a length is 2MN-1, and vector z is that virtual array receives signal.
Further, S2 includes:
S21, the angular range of direction of arrival angle in the reception signal is equidistantly divided into D (D > > K) a grid
Point, the set of all mesh point compositionsFor the excessively complete angle set, the i.e. excessively complete redundancy word of angle
Allusion quotation.
S22, propagation direction matrix is constructed according to excessively complete redundant dictionary ΘI.e.
Wherein, dvIt is the column vector for showing Virtual array position, λ is carrier wavelength.
S23, by the array signal model conversation be the compressed sensing model, i.e.,
Wherein, vector z is observation signal, and z herein is exactly that the virtual array receives signal, is only converted into compression sense
Regarded as observation signal after perception model；For observing matrix,For sparse signal to be solved,For noise power,To be 1 except the MN element, remaining element is 0 column vector.
Further, S3 includes:
It is a convex optimization problem of 1 norm by the compressed sensing model conversation, i.e.,
S32, the convex optimization problem of 1 norm is solved using orthogonal matching pursuit algorithm, initialized first, define residual error r0=z,
Indexed setRebuild column setThe number of iterations t=1；
S33, calculatingγtFor matrixIn footnote with the most matched column of residual error, wherein
For matrixD (d=1,2 ..., D) column；
S34, indexed set Γ is updatedt=Γt-1∪{γt, it updates and rebuilds column set
S35, residual error is updatedAnd enable t=t+1；
S36, K are the numbers of far field narrow band signal, if t≤K, return to S33；If t > K, indexed set Γ at this timeKIn angle
Corresponding angle is the angle estimation value of the information source in set Θ.
Further, it is respectively that M is connected with the even linear array first place of N that relatively prime linear array structure, which is unfolded, by two array numbers, only
At the origin has an array element to be overlapped, and array element sum is M+N-1, and the even linear array array element spacing that array number is M is λ/2 M, array element
The even linear array array element spacing that number is N is N λ/2, and λ is carrier wavelength.
Further, S14 includes:
To covariance matrixVectorization processing is carried out, is obtained
Wherein,A long void can be regarded as
The direction matrix of matroid column, A=[a (θ1),a(θ2),…,a(θK)] andRelatively prime linear array is respectively unfolded
Direction matrix and kth (k=1,2 ..., K) a direction vector, d is the column vector for showing practical element position,For single snap signal vector,WithThe respectively signal power of noise power and k-th of signal,
Un=vec (I),For unit matrix.Matrix at this timeThere are redundancies, are ranked up and leave out by phase
After duplicate row vector, the signal received by virtual array can be obtained
Wherein,For the direction matrix of virtual array, (l, k) is a
Element isVectorOnly the MN element is 1, remaining element
It is zero.
The beneficial effects of the present invention are:
Angle estimation is carried out using relatively prime linear array is unfolded, higher spatial degrees of freedom and weaker mutual coupling effect can be obtained
It answers；
Compressed sensing technology is combined with angle estimation problem, whole array elements that array can be made full use of to generate are kept away
The loss for having exempted from spatial degrees of freedom makes full use of whole Virtual arrays of array, including discontinuous part；
The reduction of space smoothing bring spatial degrees of freedom is avoided, to realize high-precision angle estimation, is obtained fine
Angle estimation performance.
Detailed description of the invention
It to describe the technical solutions in the embodiments of the present invention more clearly, below will be to needed in the embodiment
Attached drawing is briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, for ability
For the those of ordinary skill of domain, without creative efforts, it can also be obtained according to these attached drawings other attached
Figure.
Fig. 1 is the relatively prime linear array structure schematic diagram of expansion used in the present invention；
Fig. 2 is M=3, virtual array schematic diagram when N=4；
Fig. 3 be when 11 signals be incident on relatively prime linear array is unfolded when, the angle estimation knot that is obtained using compressed sensing algorithm
Fruit；
Fig. 4 be under different number of snapshots algorithm performance with the comparison of signal-to-noise ratio variation tendency；
Fig. 5 be under different array numbers algorithm performance with the comparison of signal-to-noise ratio variation tendency；
Fig. 6 be under various information source number algorithm performance with the comparison of signal-to-noise ratio variation tendency.
Specific embodiment
Technical solution in order to enable those skilled in the art to better understand the present invention, With reference to embodiment to this
Invention is described in further detail.
The embodiment of the invention provides the relatively prime linear array angle estimating method of expansion based on sparsity, what the present embodiment used
Array antenna structure is made of the even linear array that two array numbers are respectively M and N, and array element spacing is respectively λ/2 N and λ/2 M,
Middle M and N is a pair of of mutual prime rwmber, and λ is carrier wavelength, and two submatrix first places are connected, and only at the origin has an array element to be overlapped.
One, data model
Being as shown in Figure 1 one can be used the relatively prime linear array example of expansion of the invention, wherein M=3, N=4.
Assuming that K come from θkThe uncorrelated narrow band signal of (k=1,2 ..., K) is incident on relatively prime linear array as shown in Figure 1
On, then array received signal may be expressed as:
X=AS+N
Wherein, S=[s1,s2,…,sK]TFor signal matrix, sk=[sk(1),sk(2),…,sk(L)], L is number of snapshots, sk
It (l) is the l times sampled result to k-th of signal, l=1,2 ..., L；N be array additive white Gaussian noise, mean value zero,
Variance isA=[a (θ1),a(θ2),…,a(θK)] be array direction matrix, a (θk) it is θkDirection vector on direction.
The direction vector of two submatrixs of relatively prime linear array can be expressed as
Wherein, λ/2 d=.When carrying out DOA estimation using entire array, direction vector is represented by
Wherein, a21(θk) it is a2(θk) remove the vector after the first row.
Two, angle estimating method
1, it virtualizes
Firstly, seeking the covariance matrix of relatively prime linear array reception signal X.In Practical Project, since signal sampling is all to have
Carried out under limit number of snapshots, receive the covariance matrix of signal byIt is calculated.It willIt carries out at vectorization
Reason obtains
Wherein,It can regard as one long
The direction matrix of virtual array,For single snap signal vector,WithRespectively noise power and
The signal power of k signal, Un=vec (I),For unit matrix.
Matrix at this timeThere are redundancies for represented Virtual array position, it can be proved that submatrix number is respectively the exhibition of M and N
Opening relatively prime linear array can produce 2MN-1 Virtual array.It is M=3 as shown in Figure 2, virtual array when N=4.Leave out duplicate
After row vector, the signal received by virtual array can be obtained
Wherein,For the direction matrix of virtual array, matrix B (l,
K) a element isVectorOnly MN element is 1, remaining member
Element is zero.Next we use compressed sensing algorithm to the reception signal z of virtual array.
2, rarefaction representation
The angular range of direction of arrival is equidistantly divided into D (D > > K) a mesh point, all mesh point compositions first
SetThe as excessively complete redundant dictionary of angle, it contains all possible angle estimation result.
According to the direction matrix of redundant dictionary Θ construction extensionI.e.
Wherein, dvIt is the column vector for showing Virtual array position.The data model that above-mentioned virtual array receives signal is turned
Compressed sensing model is turned to, i.e.,
Wherein,It is the sparse vector (vector for there was only K nonzero element) that a degree of rarefication is K: ifThere is information source distribution in direction, thenD-th of elementOtherwiseObviously, it finds outIn it is non-
The position of neutral element can be obtained the DOA estimation of information source.At this point, known vector z and matrixIt can regard as in compressed sensing model
Observation signal and observing matrix, vectorFor sparse signal to be solved.
3, optimization problem
Above-mentioned compressed sensing model is one and owes fixed equation, its solution can be solved by following formula
Since 0 norm minimum is a NP problem, not only numerically can not effectively realize, but also anti-noise ability is very
Difference does not meet the requirement of signal recovery, so being herein the convex optimization problem of 1 norm by model conversation, i.e.,
4, OMP (Orthogonal Matching Pursuit orthogonal matching pursuit) algorithm
The reconstruction that the present invention carries out sparse signal using OMP algorithm restores, and specific step is as follows for the algorithm:
(1) it initializes: defining residual error r0=z, indexed setRebuild column setThe number of iterations t=1；
(2) it calculatesγtFor matrixIn footnote with the most matched column of residual error, wherein
For matrixD (d=1,2 ..., D) column；
(3) indexed set Γ is updatedt=Γt-1∪{γt, it updates and rebuilds column set
(4) residual error is updatedAnd enable t=t+1；
(5) if t≤K, return step 5b)；If t > K, indexed set Γ at this timeKThe corresponding angle in angle set Θ
As information source azimuth estimated value.
Three, performance evaluation
1, spatial degrees of freedom (Degree of freedom, DOF)
As the above analysis, total array number is that the relatively prime linear array of expansion of M+N-1 can produce 2MN-1 Virtual array,
Whole array elements that algorithm proposed by the present invention can make full use of array to generate simultaneously, therefore spatial degrees of freedom DOF=2MN-1.Phase
Than under, common space smoothing class algorithm requires Virtual array continuous, while space smoothing process can be further decreased and can be visited
Survey information source number.It can be seen that the relatively prime linear array angle estimating method of the expansion proposed by the present invention based on sparsity can obtain compared with
High spatial degrees of freedom.
2, computation complexity
To multiply number again as complexity judgment criteria, then the computation complexity of compressed sensing algorithm specifically includes that calculating
It receives signal covariance matrix and needs O { (2M+N-1)2L }, K iterative process of OMP algorithm needs altogether O { KD (2MN-1)+K
(K+1) [K (K+1)/4+2 (K+2) (2MN-1)/3] }, total complexity is O { (2M+N)2L+KD(2MN-1)+K(K+1)[K(K+
1)/4+2(K+2)(2MN-1)/3]}。
Fig. 3 be when 11 signals be incident on relatively prime linear array is unfolded when, the estimated result that is obtained using compressed sensing algorithm.This
The array number of the relatively prime linear array of Shi Zhankai is M=5, N=6, number of snapshots L=500, Signal to Noise Ratio (SNR)=0dB.It can be seen from the figure that
Information source angle can be effectively estimated out in the algorithm, and estimable information source number is greater than practical array number.
Fig. 4 is that algorithm performance compares under different number of snapshots, and the array number that relatively prime linear array is unfolded at this time is M=5, N=6, letter
Number azimuth be (10 °, 20 °).
Fig. 5 is that the algorithm performance under different array numbers compares, and the azimuth of signal is (10 °, 20 °), L=500.
Fig. 6 is that algorithm performance compares under various information source number, and the array number that relatively prime linear array is unfolded at this time is M=5, N=6, L=
500.As information source number K=2, azimuth is (10 °, 20 °)；When K=3, azimuth is (10 °, 20 °, 30 °)；When K=4,
(10°,20°,30°,40°)。
The beneficial effects of the present invention are:
Angle estimation is carried out using relatively prime linear array is unfolded, higher spatial degrees of freedom and weaker mutual coupling effect can be obtained
It answers；
Compressed sensing technology is combined with angle estimation problem, whole array elements that array can be made full use of to generate are kept away
The loss for having exempted from spatial degrees of freedom makes full use of whole Virtual arrays of array, including discontinuous part；
Compressed sensing is a set of novel signal sampling theory for acquiring and restoring about sparse signal, it can make full use of
The sparsity of signal carries out stochastical sampling to signal with the sample frequency far below nyquist sampling rate, then by non-thread
Property algorithm for reconstructing reconstruction signal, significantly reduce data transmission, storage, processing burden.
The reduction of space smoothing bring spatial degrees of freedom is avoided, to realize high-precision angle estimation, is obtained fine
Angle estimation performance.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by those familiar with the art, all answers
It is included within the scope of the present invention.Therefore, protection scope of the present invention should be subject to the protection scope in claims.
Claims (6)
1. the relatively prime linear array angle estimating method of expansion based on sparsity characterized by comprising
S1, it obtains receiving signal using according to the antenna acquisition signal that relatively prime linear array structure framework is unfolded, to the association for receiving signal
Variance matrix carries out vectorization processing, and obtained vector is sorted by phase and deletes redundant row, obtains virtual array and receives letter
Number；
S2, the angular region for receiving signal source is equidistantly divided, complete angle set is obtained, it will be according to excessively complete
The propagation direction matrix of angle set construction receives signal as observation signal as observing matrix, using virtual array, thus will
Array signal model conversation is compressed sensing model；
S3, by compressed sensing model conversation be a convex optimization problem of 1 norm, utilize orthogonal matching pursuit algorithm solve 1 norm
Convex optimization problem obtains the angle estimation value of information source by iteration.
2. the method according to claim 1, wherein the S1 includes:
S11, using M+N-1 antennas, carry out framework according to relatively prime linear array structure is unfolded, M and N are mutual prime rwmber, the day
Direction θ is come from line reception space1,θ2,…,θKThe irrelevant far field narrow band signals of K；
S12, to L sampling snap of the reception signal acquisition, obtain array received signal matrix
S13, the covariance matrix for calculating receipt signal matrix X
S14, to covariance matrixVectorization processing is carried out, the vector of acquisition is ranked up by phase and is deleted redundant row,
The vector z that a length is 2MN-1 is obtained, vector z is that virtual array receives signal.
3. the method according to claim 1, wherein the S2 includes:
S21, the angular range of direction of arrival angle in the reception signal is equidistantly divided into D (D > > K) a mesh point, institute
The set being made of mesh pointFor the excessively complete angle set, the i.e. excessively complete redundant dictionary of angle；
S22, the propagation direction matrix is constructed according to excessively complete redundant dictionary ΘI.e.
Wherein, dvIt is the column vector for showing Virtual array position, λ is carrier wavelength；
S23, by the array signal model conversation be the compressed sensing model, i.e.,
Wherein, vector z is observation signal,For observing matrix,For sparse signal to be solved,For noise power,To be 1 except the MN element, remaining element is 0 column vector.
4. the method according to claim 1, wherein the S3 includes:
It is a convex optimization problem of 1 norm by the compressed sensing model conversation, i.e.,
S32, the convex optimization problem of 1 norm is solved using orthogonal matching pursuit algorithm, initialized first, define residual error r0=z, index
CollectionRebuild column setThe number of iterations t=1；
S33, calculatingγtFor matrixIn footnote with the most matched column of residual error, whereinFor square
Battle arrayD (d=1,2 ..., D) column；
S34, indexed set Γ is updatedt=Γt-1∪{γt, it updates and rebuilds column set
S35, residual error is updatedAnd enable t=t+1；
S36, K are the numbers of far field narrow band signal, if t≤K, return to S33；If t > K, indexed set Γ at this timeKIn angle set
Corresponding angle is the angle estimation value of the information source in Θ.
5. according to the method described in claim 2, it is characterized in that, described open relatively prime linear array structure by two array numbers and be respectively
M is connected with the even linear array first place of N, and only at the origin has an array element to be overlapped, and array element sum is M+N-1, and array number is the equal of M
Even linear array array element spacing is λ/2 M, the even linear array array element spacing that array number is N is N λ/2, and λ is carrier wavelength.
6. according to the method described in claim 2, it is characterized in that, the S14 includes:
To covariance matrixVectorization processing is carried out, is obtained
Wherein,A long virtual array can be regarded as
The direction matrix of column, A=[a (θ1),a(θ2),…,a(θK)] andThe side of relatively prime linear array is respectively unfolded
To matrix and kth (k=1,2 ..., K) a direction vector, d is the column vector for showing practical element position,For single snap signal vector,WithThe respectively signal power of noise power and k-th of signal,
Un=vec (I),For unit matrix, matrix at this timeThere are redundancies, are ranked up and leave out by phase
After duplicate row vector, the signal received by virtual array can be obtained
Wherein,For the direction matrix of virtual array, (l, k) a element
ForVectorOnly the MN element is 1, remaining element is
Zero.
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