CN104698433B - DOA Estimation in Coherent Signal method based on single snapshot data - Google Patents
DOA Estimation in Coherent Signal method based on single snapshot data Download PDFInfo
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- CN104698433B CN104698433B CN201510114319.1A CN201510114319A CN104698433B CN 104698433 B CN104698433 B CN 104698433B CN 201510114319 A CN201510114319 A CN 201510114319A CN 104698433 B CN104698433 B CN 104698433B
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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
- G01S3/00—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
- 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
- G01S3/74—Multi-channel systems specially adapted for direction-finding, i.e. having a single antenna system capable of giving simultaneous indications of the directions of different signals
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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
- G01S3/00—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
- 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
- G01S3/04—Details
- G01S3/06—Means for increasing effective directivity, e.g. by combining signals having differently oriented directivity characteristics or by sharpening the envelope waveform of the signal derived from a rotating or oscillating beam antenna
Abstract
The invention discloses a kind of DOA Estimation in Coherent Signal method based on single snapshot data, being related to can be while indicates array antenna system or the method and technology field in unlike signal direction.Methods described receives data by the single snap to array and enters rearrangement, obtains two pseudocovariance matrixes, the pseudocovariance matrix of reconstruct Subspace algorithm is then extended using the two pseudocovariance matrixes.Singular value decomposition is carried out to new pseudocovariance matrix and obtains signal subspace and noise subspace, recycles MUSIC Power estimations method to carry out DOA estimations to relevant incoming wave signal.This method can release coherence between source signal under the conditions of single snap, while further increase DOA estimated accuracy, the quick estimation for the arrival bearing being mainly used under the conditions of single snap to coherent signal.
Description
Technical field
The present invention relates to the array antenna system that can indicate unlike signal direction simultaneously or method and technology field, more particularly to
A kind of DOA Estimation in Coherent Signal method based on single snapshot data.
Background technology
With multiple signal classification algorithm (MUSIC, multiple signal classification) and based on rotation not
Signal parameter estimation algorithm (ESPRIT, estimation of signal parameter the via rotational of change technology
Inviance techniques) etc. classic algorithm for super-resolution direction of arrival (DOA) technology of representative be modern space Power estimation
An important research point.Its accuracy to signal space angle-of- arrival estimation, real-time and its be widely applied prospect and draw
Play the very big concern of people.In classical DOA algorithm for estimating, the realization of MUSIC algorithms and ESPRIT algorithms, which is all relied on, to be connect
The covariance matrix of data is received, receiving data covariance matrix can only calculate approximately to obtain by limited number of time snapshot data, and
It is required that the order of the covariance matrix is equal to the number of signal source.In actual applications, in processing short-term burst data or reception letter
When only single snapshot data is available number after coherent accumulation, the order of the covariance matrix is reduced to 1, then classical MUSIC algorithms
With the failure of ESPRIT algorithms.DOA estimations under the conditions of single snap are a practical problems of Estimation of Spatial Spectrum urgent need to resolve.
At present, the method for the DOA estimations under the conditions of single snap includes：Direct data domain class method, weighted sum side
Method and the related algorithm etc. pre-processed based on data cross-correlation.In immediate data class algorithm, most of such algorithms all only make
With the reception data configuration pseudocovariance matrix of odd number array element, if element number of array is even number, it can cause to receive data message
Waste；Also some such algorithms increased constraint to signal source form when constructing pseudocovariance matrix, works as signal
When source form is unsatisfactory for constraints, algorithm failure.Weighted sum method receives the data configuration after data summation using part
Pseudocovariance matrix, this method obtains the lifting of signal to noise ratio by increasing the signal number of summation, while reducing pseudo- association side
The free degree of poor matrix.The algorithm pre-processed based on data cross-correlation can obtain preferable DOA estimations performance, but locate in advance in data
Extra amount of calculation is added in terms of reason, and DOA estimation performances are received data by reference point and influenceed.At present under the conditions of list snap
DOA algorithm for estimating in the pseudocovariance matrix that constructs all be square formation mostly, the pseudocovariance matrix of other forms is not yet obtained
Fully application.
The content of the invention
The technical problems to be solved by the invention are to provide a kind of DOA Estimation in Coherent Signal side based on single snapshot data
Method, methods described make use of single all reception data taken soon, improve the accuracy of DOA estimations.
In order to solve the above technical problems, the technical solution used in the present invention is:It is a kind of relevant based on single snapshot data
Signal DOA estimation method, it is characterised in that the described method comprises the following steps：
Step one：The array number of the uniform linear array of antenna is M, and there is the unknown far field arrowband letter of N number of correlation in space
Number incide on the uniform linear array, M>2N-1, then each array element of t output data matrix X (t)=A (θ) S (t)+N
(t) it is the complex matrix of M × 1, wherein A (θ)=[a (θ1),a(θ2)...a(θN)], the array steering vector matrix for being M × N, a
(θi) it is corresponding direction vector, wherein 1≤i≤N, S (t) represent source signal vector matrix；N (t) represents making an uproar for array output
Sound average is that zero, variance is σ2Additive white Gaussian noise, it is and uncorrelated to source signal；
Step 2：Output data matrix X (t)=[x of each array element of t1(t),x2(t),…,xM(t)]T, wherein xk(t)
For the output signal of k-th of array element, 1≤k≤M constructs pseudocovariance matrix R using the output data of each array element1And R2,
Wherein R1And R2It is defined as follows：
When the array number M of uniform linear array is odd number, R1It is expressed as
R2It is expressed as
In formula, Jm1 square formation is all for element on counter-diagonal, dimension is [(M+1)/2] × [(M+1)/2]；
When the array number M of uniform linear array is even number, R1It is expressed as
R2It is expressed as
Step 3：For the odd even situation of used antenna array elements, the pseudo- association that step 2 is constructed is calculated
Variance matrix R1Transposition, i.e. R1 T；
Step 4：Construct the pseudocovariance matrix R=[R of new extension1 T R2]；
Step 5：Singular value decomposition is carried out to R, (M+1)/2 feature under conditions of odd number bay, is decomposited
It is worth for λ1≥λ2≥…≥λN≥λN+1=...=λ(M+1)/2=σ2；Under conditions of even number of antenna array element, (M+2)/2 are decomposited
Individual characteristic value is λ1≥λ2≥…≥λN≥λN+1=...=λ(M+2)/2=σ2, σ is more than by judging characteristic value2Characteristic value
Number respectively obtains signal subspace Us and noise subspace matrix to estimate signal source number according to corresponding characteristic vector
UN；
Step 6：Space spectral function is built using MUSIC algorithmsθ is source signal
Space angle of arrival, when M be odd number when,A (θ) the rear row of (M+1)/2 is represented, when M is even number,Represent a's (θ)
The row of (M+2)/2 afterwards, a (θ) is corresponding direction vector, space angle of arrival θ is changed in the range of (- 90 °, 90 °), finds out
Spatial spectrum PMUSICAngle corresponding to (θ) maximum point is the DOA of source signal.
It is using the beneficial effect produced by above-mentioned technical proposal：Methods described passes through to antenna array under the conditions of single snap
The reception data of row enter rearrangement and obtain different pseudocovariance matrixes, and the pseudocovariance square newly extended on this basis
Battle array, the construction of the pseudocovariance matrix make use of all data of antenna array receiver, and its form is not limited to square formation, energy
The coherence between source signal is enough released, its order is equal to the number of antenna source signal.Singular value point is carried out to new correlation matrix
Solution obtains signal subspace and noise subspace, recycles MUSIC Power estimations algorithm to carry out DOA estimations to signal, in single snap
Under the conditions of release antenna source signal coherence while further increase DOA estimation accuracy.
Brief description of the drawings
Fig. 1 is the structural representation of the uniform linear array of M array element；
Embodiment
With reference to the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Ground is described, it is clear that described embodiment is only a part of embodiment of the present invention, rather than whole embodiments.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
Many details are elaborated in the following description to facilitate a thorough understanding of the present invention, still the present invention can be with
It is different from other manner described here using other to implement, those skilled in the art can be without prejudice to intension of the present invention
In the case of do similar popularization, therefore the present invention is not limited by following public specific embodiment.
The invention discloses a kind of DOA Estimation in Coherent Signal method based on single snapshot data, methods described can be divided into
Three parts.
Part I is array received data modeling：
If the uniform straight line array that M omnidirectional's array element is constituted is incided in space by a unknown far field narrow band signal of N correlations
On row, if array pitch is d, Array Model is as shown in Figure 1.If fast umber of beats is K, then receipt signal model can be expressed as
X (t)=A (θ) S (t)+N (t) (1)
X (t) is the reception data matrix that M × K is tieed up, A (θ)=[a (θ in formula1),a(θ2)...a(θN)], it is M × N-dimensional
Array prevalence matrix, S (t) is N × K incoming signal matrix, and N (t) is the noise signal matrix that M × K is tieed up.Under normal circumstances
Seek K ＞ ＞ M ＞ N.The covariance matrix of array received data can be expressed as
Wherein, RS=E [S (t) SH(t)], it is the covariance matrix of incoming signal, RN=E [N (t) NH(t)]=σ2I is to make an uproar
Sound covariance matrix, σ2For noise power, I is M × M unit matrix.Ideally, incoming signal is orthogonal, signal
It is independent between noise and separate between noise, now RSIt is also Hermitian for the diagonal matrix of full rank
Toeplitz matrixes, its diagonal element is the power of corresponding signal.In the specific implementation, the correlation matrix of signal data is to pass through
Sampling seeks correlation matrix after obtaining K snapshot dataCome what is replaced：
Wherein, XkIt is the data vector of kth time sampling snap output, is needed to obtain accurate signal correlation matrix
Enough fast umber of beats of sampling are wanted to estimate.The subspace class algorithm of DOA estimations is all based on the correlation matrix of above formula and deployed,
Thus, when only single snapshot data is available, i.e. K=1, the order of sample covariance matrix will be reduced to 1, and son based on this is empty
Between class algorithm (such as：MUISC, ESPRIT etc.) will failure.
Part II is the construction based on the pseudocovariance matrix for receiving data, comprising two parts content, first against connecing
The odd even situation for receiving array elements constructs the pseudocovariance matrix of two different structures, next to that utilizing obtained pseudocovariance
Matrix construction goes out new pseudocovariance matrix, and new pseudocovariance matrix reaches solution phase on the basis of using all reception data
Dry purpose.
Under the conditions of single snap, an order can be constructed for signal by entering rearrangement by single snapshot data to array received
The matrix of source number, this matrix is called pseudocovariance matrix.Structural matrixWherein,For by A (θ)
In a submatrix constituting of some continuous rows, if line number is J, thenFor J × N matrix；D is the full rank square of N × N-dimensional
Battle array.To ensure that pseudocovariance rank of matrix is equal to number of source, it is desirable to J ＞ N, while assuming that D is that a diagonal entry is source
The diagonal matrix of signal.As long as D diagonal element is not 0, the pseudocovariance rank of matrix of construction is just number of sources N, so that
Ensure the correct estimation of coherent signal DOA information.
The phase of M array received signal is positionIn the range of arithmetic progression, denotable phase
Scope isWherein,Value it is relevant with the selection of reference point,This
Exactly construct available information during pseudocovariance matrix.Pseudocovariance matrix is J × J dimensions, pseudocovariance matrix R element
It is represented by
Wherein, dnmFor the element of matrix D.When matrix D is diagonal matrix, formula (4) is represented by
M-n value is the integer of [1-J, J-1] in formula (5), therefore the phase of pseudocovariance is to be located atIn the range of arithmetic progression, phase range isOrder
Then there is J=(M+1)/2.It follows that when the whole array received signals utilized, pseudocovariance matrix R dimension is Jmax
=(M+1)/2.When array element quantity M is even number, Jmax=M/2, now, will inevitably waste available single snapshot data.
Assuming that dnn=sn, the even linear array using M omnidirectional's array element composition is receiving array, and it is reference to set first array element
Array element, ignore the influence of noise, R=A (θ) DAH(θ) is represented by
When M is odd number, formula (6) can be expressed as：
Pseudocovariance matrix can be constructed as follows
Clearly for R1Have：R1=R1 T, contrast (7) are it can be found that by R1The pseudocovariance matrix of expression can be by formula (7)
In submatrix exchange row sequence obtain.Another pseudocovariance matrix R is constructed on this basis2, R2It is expressed as follows
The easily discovery, R of contrast (8) formula (9)2=R1 T×Jm.Wherein, Jm1 square formation is all for element on counter-diagonal,
Dimension is [(M+1)/2] × [(M+1)/2].Observation type (7) is it can be found that R1It is later A (θ) DA to exchange row sequenceHOne of (θ)
Submatrix, and R2Inherently A (θ) DAHOne submatrix of (θ).Structural matrix Dimension be [(M+1)/2]
× (M+1), referred to herein asFor the pseudocovariance matrix of extension reconstruct.ByConstruction understand, the extension pseudocovariance matrix repeat
It make use of signal message, R2The construction of itself is metForm, wherein,
The popular matrix of even linear array array is met for [(M+1)/2] × N.For [(M+1)/2+1]
× N's meets the popular matrix of even linear array array.R1Can be by R2Obtained by row-column transform, they are all the matrixes that order is M,
Ability with decorrelation LMS, therefore, by R1And R2The new extended matrix constitutedOrder also be M, also possess the ability of decorrelation LMS.
When M is even number, equally ignore the influence of noise, R=A (θ) DAH(θ) is represented by
Pseudocovariance matrix can be constructed as follows
Now R1For (M/2) × (M/2+1), then R1 TFor (M/2+1) × (M/2) matrix.Construct another pseudocovariance
Matrix R2, R2It is expressed as follows
Observation type (10) it can be found that, R1The matrix and R exchanged after row sequence2All it is A (θ) DAHThe submatrix of (θ), structural matrix Dimension be (M/2+1) × M.It can be obtained by derivingWherein,
The popular matrix of even linear array array is met for (M/2+1) × N,For (M/2) × N's
Meet the popular matrix of even linear array array.As long as diagonal element is not zero, then the matrix constructed is the matrix that order is more than N,
The decorrelation LMS of array can be achieved.FromConstruction process understand, whole process does not enter row constraint to incoming signal, in reality
The waste for receiving data is not resulted in while existing decorrelation LMS.
On the basis of extension reconstruct correlation matrix, DOA estimations mainly are carried out using Subspace algorithm for Part III
Processing.According to the theory analysis of Part II it is recognised that for the source signal that is concerned with, the new related rank of matrix of reconstruct increases,
Information source coherence can be released, on this basis, step 5 carries out singular value decomposition to R, under conditions of odd number bay,
(M+1)/2 characteristic value is decomposited for λ1≥λ2≥…≥λN≥λN+1=...=λ(M+1)/2=σ2, in the bar of even number of antenna array element
Under part, (M+2)/2 characteristic value is decomposited for λ1≥λ2≥…≥λN≥λN+1=...=λ(M+2)/2=σ2, by judging big feature
The number of value respectively obtains signal subspace Us and noise sky to estimate signal source number according to corresponding characteristic vector
Between matrix UN.If the corresponding characteristic vector of big characteristic value is e1,e2,…,eN, then Us=[e are defined1,e2,…,eP,eP+1,…eN],
The corresponding characteristic vector of small characteristic value is UN=[eN+1,…,e(M+1)/2] (odd number array element) or UN=[eN+1,…,eM/2+1] (even
Several array elements).Step 6 builds space spectral function using MUSIC algorithms, as shown in formula (12)
Wherein, θ is the space angle of arrival of source signal, when M is odd number,A (θ) the rear row of (M+1)/2 is represented, works as M
During for even number,A (θ) the rear row of (M+2)/2 is represented, a (θ) is corresponding direction vector.Make space angle of arrival θ (-
90 °, 90 °) in the range of change, find out spatial spectrum PMUSICAngle corresponding to (θ) maximum point is the DOA of source signal.
Methods described enters rearrangement by the reception data to aerial array under the conditions of single snap and obtains different pseudo- association sides
Poor matrix, and the pseudocovariance matrix newly extended on this basis, the construction of the pseudocovariance matrix make use of antenna array
All data received are arranged, and its form is not limited to square formation, can release the coherence between source signal, its order is equal to antenna
The number of source signal.Singular value decomposition is carried out to new correlation matrix and obtains signal subspace and noise subspace, is recycled
MUSIC Power estimations algorithm carries out DOA estimations to signal, further while the coherence of source signal is released under the conditions of single snap
Improve the accuracy of DOA estimation.
Claims (1)
1. a kind of DOA Estimation in Coherent Signal method based on single snapshot data, it is characterised in that the described method comprises the following steps：
Step one：The array number of the uniform linear array of antenna is M, and the far field narrow band signal that space has N number of correlation unknown enters
It is mapped on the uniform linear array, M>2N-1, then each array element of t output data matrix X (t)=A (θ) S (t)+N (t)
For the complex matrix of M × 1, wherein A (θ)=[a (θ1),a(θ2)...a(θN)], the array steering vector matrix for being M × N, a (θi)
For corresponding direction vector, wherein 1≤i≤N, S (t) represent source signal vector matrix；N (t) represents that the noise of array output is equal
Value is that zero, variance is σ2Additive white Gaussian noise, it is and uncorrelated to source signal；
Step 2：Output data matrix X (t)=[x of each array element of t1(t),x2(t),…,xM(t)]T, wherein xk(t) it is the
The output signal of k array element, 1≤k≤M constructs pseudocovariance matrix R using the output data of each array element1And R2, wherein
R1And R2It is defined as follows：
When the array number M of uniform linear array is odd number, R1It is expressed as
R2It is expressed as
In formula, Jm1 square formation is all for element on counter-diagonal, dimension is [(M+1)/2] × [(M+1)/2]；
When the array number M of uniform linear array is even number, R1It is expressed as
R2It is expressed as
Step 3：For the odd even situation of used antenna array elements, the pseudocovariance that step 2 is constructed is calculated
Matrix R1Transposition, i.e. R1 T；
Step 4：Construct the pseudocovariance matrix R=[R of new extension1 T R2]；
Step 5：Singular value decomposition is carried out to R, under conditions of odd number bay, decompositing (M+1)/2 characteristic value is
λ1≥λ2≥…≥λN≥λN+1=...=λ(M+1)/2=σ2；Under conditions of even number of antenna array element, (M+2)/2 spy is decomposited
Value indicative is λ1≥λ2≥…≥λN≥λN+1=...=λ(M+2)/2=σ2, σ is more than by judging characteristic value2Characteristic value number come
Estimate signal source number, and signal subspace U is respectively obtained according to corresponding characteristic vectorsWith noise subspace matrix UN；
Step 6：Space spectral function is built using MUSIC algorithmsθ is the space of source signal
Angle of arrival, when M is odd number,A (θ) the rear row of (M+1)/2 is represented, when M is even number,Represent a (θ) rear (M+
2)/2 row, a (θ) is corresponding direction vector, space angle of arrival θ is changed in the range of (- 90 °, 90 °), finds out space
Compose PMUSICAngle corresponding to (θ) maximum point is the DOA of source signal.
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