CN109521393A - A kind of DOA estimation algorithm based on signal subspace revolving property - Google Patents
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- 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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Abstract
The present invention relates to a kind of Wave arrival direction estimating method, especially a kind of DOA estimation algorithm based on signal subspace revolving property belongs to signal processing technology field.Present invention proposition combines signal subspace rotation transformation thought with invariable rotary Subspace algorithm, obtains a kind of new DOA estimation algorithm.Signal subspace by row piecemeal and is carried out rotation transformation and obtains the lower signal subspace of new dimension by the present invention using rank of matrix loss characteristic, solves direction of arrival angle then in conjunction with the invariable rotary characteristic between signal subspace.Compared with prior art, the present invention mainly solving the problems, such as that ESPRIT algorithm estimation stability under low signal-to-noise ratio and few number of snapshots is poor, while this method reduces the dimension of signal subspace using rotation transformation, to reduce the computation complexity of algorithm.
Description
Technical field
The present invention relates to a kind of Wave arrival direction estimating method, especially a kind of wave based on signal subspace revolving property reaches
Direction estimation algorithm, belongs to signal processing technology field.
Background technique
Mutual coupling is the Men Xueke to grow up on the basis of airspace filter, time domain Power estimation, in thunder
It reaches, before the military and civilians field such as passive sonar, biomedicine, radio astronomy and earthquake prospecting suffers from wide application
Scape is the research hotspot of field of signal processing.
The invariable rotary sub-space technique (ESPRIT algorithm) of signal subspace is special using signal subspace invariable rotary
Property, the azimuth information of signal is extracted to carry out a kind of algorithm of DOA estimation.The algorithm has good under high s/n ratio
Estimate performance and avoid spectrum peak search, but in low signal-to-noise ratio, few number of snapshots, estimation stability is poor.
Summary of the invention
The invention proposes a kind of DOA estimation algorithms based on signal subspace revolving property, mainly solve
ESPRIT algorithm poor problem of estimation stability under low signal-to-noise ratio and few number of snapshots.
Estimate down to stablize less in low signal-to-noise ratio and number of snapshots the technical scheme is that mainly solving ESPRIT algorithm
The poor problem of property, comprises the following specific steps that:
(1) antenna array, including submatrix X and submatrix Y are constructed
Antenna array is the even linear array that M array element occasionally forms, and each array element occasionally includes that two response characteristics are identical
Array element, and array element spacing is displacement vector Δ, the spacing between array element idol is d, and even linear array, which is divided into two translation vectors, is
The submatrix X and submatrix Y of Δ, submatrix X is by array element idol x1,x2,…xMComposition, submatrix Y is by array element idol y1,y2,…yMComposition, array element x1
And y1It is corresponding to constitute an array element idol, behind to be corresponding in turn to a total of M array element even, it is assumed that P is a from space far-field narrowband
Pinpoint target signal source is incident on the equidistant even linear array, and the incident direction of signal is θ1,θ2,…θP, wherein M >=P,λ is the wavelength of incoming signal.
(2) the reception signal of submatrix X and submatrix Y are respectively obtained to spacing wave sampling by the aerial receiver in antenna array
Vector i.e. its output signal vector X (t), Y (t), and merged to obtain the output signal vector Z (t) of entire array；
The output signal vector of submatrix X and submatrix Y are as follows:
X (t)=[x1(t),x2(t),…xM(t)]T=AS (t)+Nx(t)
Y (t)=[y1(t),y2(t),…yM(t)]T=A Φ S (t)+Ny(t)
In formula,Expression links together submatrix X and submatrix Y
Rotation operator, j is imaginary number, j2=-1, A (t)=[a (θ1),a(θ2),…,a(θP)] indicate steering vector, wherein a (θi)=
exp[j(m-1)2πdsinθi/ λ], i=1,2,3 ..., P, a (θi) indicate i-th of information source steering vector, NxAnd NyTable respectively
Show the noise vector that submatrix X and submatrix Y is generated.
The output signal vector of submatrix X and submatrix Y is merged, the total output signal vector Z (t) of array is obtained:
(3) the autocorrelation matrix R of signal phasor Z (t) is calculatedz, and Eigenvalues Decomposition is carried out to it and obtains signal subspace；
It exports to obtain its autocorrelation matrix according to array and carries out Eigenvalues Decomposition:
In formula, RSIndicate signal autocorrelation matrix, σ2Indicate noise variance, expectation is asked in E expression, and the conjugation of H representing matrix turns
It sets, USThe corresponding characteristic vector of the larger characteristic value of preceding P is at signal subspace, U after indicating feature decompositionNIndicate remaining 2M-
The corresponding characteristic vector of the smaller characteristic value of P is at noise subspace；Characteristic value after feature decomposition is arranged from big to small, before coming
P characteristic values are equal to the sum of signal and noise variance, and subsequent 2M-P characteristic value is equal to the variance of noise, ΛSAnd ΛNPoint
Not Biao Shi P larger characteristic value characteristic values and the formation of subsequent 2M-P characteristic value diagonal matrix.
(4) piecemeal processing is carried out by row to signal subspace, obtains the submatrix signal subspace U of low dimensionalnew；Due to letter
Work song space USMatrix is tieed up for 2M × P, matrix by rows is subjected to piecemeal:Wherein, submatrix US1For 2M-P
× P ties up matrix, US2Matrix is tieed up for P × P；
Due to US2For row non-singular matrix, then there is right inverse matrixSo thatI is unit battle array；
By original signal subspace USCarry out conversion process:
As can be seen that actually can be regarded as matrix U to the conversion process of original signal subspaceSThe weighted sum of column vector,
Namely by matrix USColumn space span (US) in 2M dimension space carry out angle rotation.And the matrix after rotating meets:UnewRank of matrix is less than matrix USWithThe minimum value of order,Signal subspace i.e. after rotation processing is the subset of original signal subspace.
(5) rotation relationship matrix is constructed using the invariable rotary characteristic between submatrix signal subspace, is reached to acquire wave
Deflection is then passed through since the space of the steering vector of the signal subspace and signal of characteristic vector is the same space
Meet after crossing conversion process: span { Unew}=span { a (θ1),a(θ2),…,a(θP),
So there are a unique nonsingular matrix T, so that:
Array output is merged to obtain by the output of submatrix X and submatrix Y
UnewY=UnewXT-1Φ T=UnewXΨ, and when A is non-singular matrix, Φ=T Ψ T-1；
Finally, matrix can be calculated using least square methodTo matrix Ψ into
Row feature decomposition, P characteristic value corresponds to the angle of arrival of P signal, to acquire the direction of arrival angle of signal.
The beneficial effects of the present invention are: the present invention is by signal subspace rotation transformation thought and invariable rotary Subspace algorithm
It combines, obtains a kind of new direction of arrival algorithm.Signal subspace is gone forward side by side by row piecemeal using rank of matrix loss characteristic
Row rotation transformation obtains the lower signal subspace of new dimension, then special using the invariable rotary between new signal subspace
Property solves the direction of arrival angle of signal.The present invention makes to contain more letters in new signal subspace by rotation transformation
Number parameter information estimates stability low signal-to-noise ratio and number of snapshots are lower less to improve ESPRIT algorithm, while this method drops
The low dimension of signal subspace, to reduce the computation complexity of algorithm.
Detailed description of the invention
Fig. 1 is general flow chart of the invention；
Fig. 2 be the present invention from ESPRIT algorithm under the conditions of different signal-to-noise ratio mean square error comparison diagram；
Fig. 3 be the present invention from ESPRIT algorithm under different hits mean square error comparison diagram.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings and specific examples.
Embodiment 1: as shown in Figure 1, a kind of DOA estimation algorithm based on signal subspace revolving property, specific to walk
It is rapid as follows:
Step 1: forming two submatrixs using aerial receiver
A pair of of aerial receiver is placed at interval of distance d, each pair of receiver includes two identical battle arrays of response characteristic
Member, and array element spacing is known displacement vector Δ, places M altogether, forms even linear array, divides the array into two translation vectors
For the submatrix X and submatrix Y of Δ, and submatrix X and submatrix Y are respectively by the x of array element idol1,x2,…xMAnd y1,y2,…yMIt constitutes.Assuming that
There is P far field narrow band signal to be incident on even linear array, and signal joined the white Gaussian noise of zero-mean in communication process,
Wherein, M >=P,λ is the wavelength of incoming signal.
Step 2: being sweared by the reception signal that array antenna receiver respectively obtains submatrix X and submatrix Y to spacing wave sampling
Amount is output signal vector X (t), Y (t), and output is merged and obtains the output signal vector Z (t) of entire array.
For convenience, we divide the array into the submatrix X and submatrix Y that two translation vectors are Δ, and submatrix X and son
Y is respectively by the x of array element idol for battle array1,x2,…xMAnd y1,y2,…yMIt constitutes.
2) then two submatrixs generate output vector are as follows:
X (t)=[x1(t),x2(t),…xM(t)]T=AS (t)+Nx(t)
Y (t)=[y1(t),y2(t),…yM(t)]T=A Φ S (t)+Ny(t)
In formula,Expression contacts submatrix 1 and submatrix 2
Rotation operator together, A (t)=[a (θ1),a(θ2),…,a(θP)] indicate steering vector, wherein a (θi)=exp [j (m-
1)2πdsinθi/ λ], i=1,2,3 ..., P, a (θi) indicate i-th of information source steering vector, NxAnd NyRespectively indicate 1 He of submatrix
The noise vector that submatrix 2 generates.
3) output of two submatrixs is merged, obtains the total output of array are as follows:
Step 3: calculating the autocorrelation matrix R of signal phasor Z (t)z, and carry out Eigenvalues Decomposition to it and obtain signal subspace sky
Between.
Its autocorrelation matrix is obtained according to the output of array and carries out Eigenvalues Decomposition:
In formula, RSIndicate signal autocorrelation matrix, σ2Indicate noise variance, expectation is asked in E expression, and the conjugation of H representing matrix turns
It sets, USThe corresponding characteristic vector of the biggish characteristic value of P is at signal subspace, U after indicating feature decompositionNIndicate remaining 2M-
The corresponding characteristic vector of the smaller characteristic value of P is at noise subspace；ΛSAnd ΛNRespectively indicate characteristic value formation to angular moment
Battle array.
Step 4: piecemeal processing being carried out by row to signal subspace, obtains the submatrix signal subspace U of low dimensionalnew。
1) due to signal subspace USMatrix is tieed up for 2M × P, matrix by rows can be subjected to piecemeal:
Wherein, submatrix US1Matrix, U are tieed up for (2M-P) × PS2Matrix is tieed up for P × P.
2) due to US2For row non-singular matrix, that is, there is right inverse matrixMeet formula
3) original signal subspace is subjected to conversion process:
4) as can be seen that actually can be regarded as matrix U to the conversion process of original signal subspaceSThe weighting of column vector
With, that is, by matrix USColumn space span (US) in 2M dimension space carry out angle rotation.And the matrix after rotating is full
Foot:
∴Signal subspace i.e. after rotation processing is the subset of original signal subspace.
5) since the space of the signal subspace of characteristic vector and the steering vector of signal is the same space, then
Meet after conversion process: span { Unew}=span { a (θ1),a(θ2),…,a(θP)}
So unique, the nonsingular matrix T there are one, so that:
6) there are two the outputs of submatrix to merge to obtain for the output of ∵ array
∴
∴UnewY=UnewXT-1Φ T=UnewXΨ, and when A is non-singular matrix, Φ=T Ψ T-1。
7) finally, matrix can be calculated using least square methodTo square
Battle array Ψ carries out feature decomposition, and P characteristic value corresponds to the angle of arrival of P signal, so that the wave for acquiring signal reaches
Deflection.
The present invention using rank of matrix loss characteristic by signal subspace by row piecemeal and carry out rotation transformation obtain it is new
Then signal subspace solves the direction of arrival angle of signal using the invariable rotary characteristic between new signal subspace.It should
Algorithm is by rotation transformation, so that containing more signal parameter information in new signal subspace, improves ESPRIT calculation
Method estimates down stability in low signal-to-noise ratio and number of snapshots less, while this method reduces the dimension of signal subspace using rotation transformation
Degree, to reduce the computation complexity of algorithm.
Embodiment 2: being calculated according to the method in embodiment 1, wherein considering the uniform line of 8 omnidirectional's array element composition
Battle array, submatrix array number are 7, the output of preceding 7 array element are expressed as submatrix 1, rear 7 array element, which exports, is expressed as submatrix 2, between array element
Away from being 0.5, airspace angle searching range is [- 90 ° 90 °].
Mean square error calculating formula are as follows:
In formula, I indicates Monte Carlo Experiment number,Indicate the direction of arrival angle of i-th test, θpIndicate that signal is true
Direction of arrival angle.
Emulation 1: assuming that three independent sources are incident on the equidistant even linear array with angle [- 60 ° 0 ° 30 °] respectively,
Sampling number is 100, so that signal-to-noise ratio is increased to 10dB by -10dB, 50 independent direction of arrival are carried out under each signal-to-noise ratio
Estimation test, is compared using inventive algorithm and ESPRIT algorithm, calculates separately under different signal-to-noise ratio the equal of two kinds of algorithms
Square error, test result are as shown in Figure 2, in which: abscissa indicates that signal-to-noise ratio, ordinate indicate mean square error in Fig. 2.
Emulation 2: under conditions of emulating 1, setting signal-to-noise ratio is -10dB, so that hits is increased to 200 by 100, each adopts
50 independent Mutual coupling tests are carried out under number of samples, inventive algorithm and ESPRIT algorithm are compared, respectively
The mean square error of two kinds of algorithms under different hits is calculated, test result is as shown in Figure 3, in which: abscissa indicates sampling in Fig. 3
Number, ordinate indicate mean square error.
As can be seen that the estimation of two kinds of algorithm direction of arrival angle of increase with signal-to-noise ratio and hits from Fig. 2, Fig. 3
Mean square error fluctuates, but in low signal-to-noise ratio, few number of snapshots, mean square error fluctuation of the invention is significantly less than
ESPRIT algorithm, and the square mean error amount of inventive algorithm is again smaller than ESPRIT algorithm, illustrate this method stability and
Effective sexual clorminance.
In conclusion inventive algorithm estimates function admirable under the low and few number of snapshots of signal-to-noise ratio, has and stablize well
Property and validity.
Above in conjunction with attached drawing, the embodiment of the present invention is explained in detail, but the present invention is not limited to above-mentioned
Embodiment within the knowledge of a person skilled in the art can also be before not departing from present inventive concept
Put that various changes can be made.
Claims (3)
1. a kind of DOA estimation algorithm based on signal subspace revolving property, it is characterised in that: specific step is as follows:
(1) antenna array, including submatrix X and submatrix Y are constructed
Antenna array is the even linear array that M array element occasionally forms, and each array element occasionally includes two identical array elements of response characteristic,
And array element spacing is displacement vector Δ, the spacing between array element idol is d, and even linear array is divided into the son that two translation vectors are Δ
Battle array X and submatrix Y, submatrix X is by array element idol x1,x2,…xMComposition, submatrix Y is by array element idol y1,y2,…yMComposition, it is assumed that P come from
The pinpoint target signal source of space far-field narrowband is incident on the equidistant even linear array, and the incident direction of signal is θ1,θ2,…
θP, wherein M >=P,λ is the wavelength of incoming signal；
(2) the reception signal phasor of submatrix X and submatrix Y are respectively obtained to spacing wave sampling by the aerial receiver in antenna array
That is its output signal vector X (t), Y (t), and merged to obtain the output signal vector Z (t) of entire array；
(3) the autocorrelation matrix R of signal phasor Z (t) is calculatedz, and Eigenvalues Decomposition is carried out to it and obtains signal subspace；
(4) piecemeal processing is carried out by row to signal subspace, obtains the submatrix signal subspace U of low dimensionalnew；
(5) rotation relationship matrix is constructed using the invariable rotary characteristic between submatrix signal subspace, to acquire direction of arrival
Angle.
2. the DOA estimation algorithm according to claim 1 based on signal subspace revolving property, it is characterised in that:
Detailed process is as follows for the step (2) and step (3):
The output signal vector of submatrix X and submatrix Y are as follows:
X (t)=[x1(t),x2(t),…xM(t)]T=AS (t)+Nx(t)
Y (t)=[y1(t),y2(t),…yM(t)]T=A Φ S (t)+Ny(t)
In formula,Indicate the rotation that submatrix X and submatrix Y link together
Turn operator, j is imaginary number, A (t)=[a (θ1),a(θ2),…,a(θP)] indicate steering vector, wherein a (θi)=exp [j (m-1) 2
πd sinθi/ λ], i=1,2,3 ..., P, a (θi) indicate i-th of information source steering vector, NxAnd NyRespectively indicate submatrix X and son
The noise vector that battle array Y is generated；
The output signal vector of submatrix X and submatrix Y is merged, the total output signal vector Z (t) of array is obtained:
It exports to obtain its autocorrelation matrix according to array and carries out Eigenvalues Decomposition:
In formula, RSIndicate signal autocorrelation matrix, σ2Indicating noise variance, expectation is asked in E expression, the conjugate transposition of H representing matrix,
USThe corresponding characteristic vector of the larger characteristic value of preceding P is at signal subspace, U after indicating feature decompositionNIndicate remaining 2M-P
The corresponding characteristic vector of smaller characteristic value is at noise subspace；ΛSAnd ΛNRespectively indicate the diagonal matrix of characteristic value formation.
3. the DOA estimation algorithm according to claim 1 based on signal subspace revolving property, wherein step (4)
Detailed process is as follows with step (5):
A) the piecemeal processing of signal subspace
Due to signal subspace USMatrix is tieed up for 2M × P, matrix by rows is subjected to piecemeal:Wherein, submatrix
US1Matrix, U are tieed up for (2M-P) × PS2Matrix is tieed up for P × P；
Due to US2For row non-singular matrix, then there is right inverse matrixSo thatI is unit battle array；
By original signal subspace USCarry out conversion process:
Treated, and matrix meets:UnewRank of matrix is less than matrix USWithThe minimum value of order,Signal subspace i.e. after rotation processing is the son of original signal subspace
Collection；
B) direction of arrival angle of signal is solved using the invariable rotary relationship of submatrix
Since the space of the steering vector of the signal subspace and signal of characteristic vector is the same space, then by becoming
Meet after changing processing: span { Unew}=span { a (θ1),a(θ2),…,a(θP),
So there are a unique nonsingular matrix T, so that:
Array output is merged to obtain by the output of submatrix X and submatrix Y
UnewY=UnewXT-1Φ T=UnewXΨ, and when A is non-singular matrix, Φ=T Ψ T-1；
Finally, matrix can be calculated using least square methodMatrix Ψ is carried out special
Sign is decomposed, and P characteristic value corresponds to the angle of arrival of P signal, to acquire the direction of arrival angle of signal.
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| CN110515033A (en) * | 2019-08-09 | 2019-11-29 | 南京航空航天大学 | A kind of deficient channel direction-finding system and method restored based on Toeplitz matrix |
| CN110515033B (en) * | 2019-08-09 | 2022-06-28 | 南京航空航天大学 | Toeplitz matrix recovery-based under-channel direction finding system and method |
| CN112363106A (en) * | 2020-10-28 | 2021-02-12 | 西安电子科技大学 | Signal subspace direction of arrival detection method and system based on quantum particle swarm |
| CN112363106B (en) * | 2020-10-28 | 2022-11-01 | 西安电子科技大学 | Signal subspace direction of arrival detection method and system based on quantum particle swarm |
| CN118033531A (en) * | 2024-02-06 | 2024-05-14 | 昆明理工大学 | Single-bit DOA estimation method and system based on discrete time Fourier transform |
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