CN106569172A - Two-dimensional doa estimation method - Google Patents
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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
- G01S3/14—Systems for determining direction or deviation from predetermined direction
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Abstract
The invention provides a two-dimensional DOA estimation method. Under the assumption that adjacent P array elements are in the coupling state, two DOA estimation algorithms, higher in degree of accuracy, are provided based on the reconstruction of an array direction vector matrix and the selection of auxiliary array elements. Meanwhile, a processing method in the signal coherent condition is provided. Based on two methods provided in the invention, the two-dimensional DOA of a uniform rectangular antenna array in the coupling state can be accurately estimated in both the signal coherent condition and the signal incoherent condition.
Description
Technical field
The present invention relates to communication technical field, more particularly, to DOA estimation method.
Background technology
At present, DOA (direction of arrival) estimates have all the time very in field of signal processing, such as radar, Sonar system
Important effect.
In the past few decades, Many researchers have been that the DOA algorithm for estimating of even linear array has made many contributions,
Such as multiple signals classification (MUSIC) algorithm, ESPRIT algorithms etc., wherein MUSIC algorithms be the algorithm that is most widely used it
One.But these algorithms are proposed under the hypothesis that there is no coupling between antennas, and this will cause final DOA to estimate
Produce serious error.When the distance between antenna is less, the coupling between antenna DOA is estimated the impact that brings compared with
For serious, this influences whether the performance of DOA algorithm for estimating.In order to make up the impact that antenna strap comes, researchers propose
Some new algorithms are adding the performance of strong algorithms.For example, the impact of antenna coupling is made up by the coupled impedance for receiving, this
Kind of method is easily achieved, but because the coupled relation between antenna is usually with time and environmental change, therefore in reality
Accomplish that it is extremely difficult to measure coupled impedance in real time using in.There is scholar to propose new algorithm again later, using antenna most
The a period of time in outside, as auxiliary a period of time, only receives signal using middle submatrix unit, accordingly even when in the situation of antenna coupling
Under, original MUSIC algorithms still can be used directly.With the help of auxiliary array element, we can estimate to DOA
Meter, it is correct under then calculating the coefficient of coup between antenna such that it is able to redefine coupling condition by the DOA to pre-estimation
Array direction vector matrix.Algorithm major part above is both for uniform linear array (ULA) proposition, in practical application
In, uniform linear array can only be realized to the one-dimensional estimated of DOA, and because uniform rectangular planar array (URA) can be entered to DOA
The estimation of row two dimension, and the accuracy estimated is higher than uniform linear array, therefore to URA in the case of antenna coupling
The research that DOA estimates is more with practical value.
The content of the invention
The present invention provides two kinds and overcomes the problems referred to above or at least in part solution to the problems described above.
Under the hypothesis that this patent has coupling between P adjacent array element, by the weight to array direction vector matrix
Build and aid in the selection of array element, it is proposed that two kinds of higher DOA algorithm for estimating of two kinds of accuracy, and propose in signal phase
Processing method in the case of dry.
According to an aspect of the present invention, there is provided a kind of arrival direction estimation method, including：
S1, based on the assumption that there is coupling between each antenna element and P adjacent a period of time in uniform rectangular planar antenna array
On the basis of conjunction relation, tectonic coupling matrix and receipt signal model；
S2, based on the receipt signal model, tries to achieve its correlation matrix, and carrying out Eigenvalues Decomposition, to obtain noise empty
Between；
S31, based on coupling matrix and noise subspace, using sense vector matrix restructing algorithm is based on, estimates two
Dimension DOA.
According to a further aspect of the present invention, there is provided another kind of arrival direction estimation method, including：
S1, based on the assumption that there is coupling between each antenna element and P adjacent a period of time in uniform rectangular planar antenna array
On the basis of conjunction relation, tectonic coupling matrix and receipt signal model；
S2, based on the receipt signal model, tries to achieve its correlation matrix, and carrying out Eigenvalues Decomposition, to obtain noise empty
Between；
S32, using companion matrix Meta algorithm, based on coupling matrix and noise subspace, using companion matrix Meta algorithm, estimates two
Dimension DOA.
The application proposes arrival direction estimation method, under the hypothesis that there is coupling between P adjacent array element, by right
The reconstruction of array direction vector matrix and the selection of auxiliary array element, it is proposed that two kinds of two kinds of higher DOA of accuracy estimate to calculate
Method, and propose the processing method in the case of signal coherence.Two methods proposed by the present invention can in signal coherence and
In the case of incoherent, two-dimentional DOA of the uniform rectangular antenna plane in the case where there is coupling condition is accurately estimated.
Description of the drawings
Fig. 1 is the structural representation of the uniform rectangular aerial array according to the embodiment of the present invention；
Fig. 2 is according to the coefficient of coup schematic diagram between each a period of time of the uniform rectangular aerial array of the embodiment of the present invention；
Fig. 3 is to be shown according to the auxiliary array element based on companion matrix Meta algorithm of the embodiment of the present invention and the structure of center subarray
It is intended to；
Fig. 4 is the array segmentation schematic diagram of the Search Space Smoothing according to the embodiment of the present invention.
Specific embodiment
With reference to the accompanying drawings and examples, the specific embodiment of the present invention is described in further detail.Hereinafter implement
Example is not limited to the scope of the present invention for illustrating the present invention.
First, the existing algorithm being based on to the present invention is illustrated.
1st, MUSIC algorithms
For uniform linear array, there is no coupling between antennas, and receive signal it is incoherent in the case of, construction
Receipt signal model X=AS+n；Then its covariance matrix R is sought receipt signal modelx=E [XXH]；To RxCarry out feature point
Solution can obtain noise subspace En；Construction space spectral function：
Wherein a (θ) is the direction vector of signal.When signal is injected, due to the direction vector and noise subspace of signal
Orthogonal, the denominator of the formula is approximately 0, so it is only necessary that θ changes, calculate spectral function, by the peak value for searching spectral function, its is right
The angle, θ answered is the direction of arrival (DOA) of signal.
2nd, the arrival direction estimation method in the case where intercoupling
For the uniform rectangular antenna plane of a M × N, it is assumed that in the case of signal is incoherent, each antenna element
Only there is the reception signal of coupled relation, tectonic coupling Matrix C and uniform rectangular antenna plane with 8 antenna element around it
Model X=CAS+n；Antenna element on the four edges of uniform rectangular aerial array border is considered as into auxiliary array element, therefore is actually connect
Effective a period of time of the collection of letters number is middle (M-2) × (N-2) individual a period of time, for effective a period of time, coupling matrix is write out again and is connect
Signal model is received, according to traditional MUSIC algorithms, covariance matrix R is calculatedxWith noise subspace En, in the case of tectonic coupling
Space spectral function
For space spectral function, because the coefficient of coup in coupling matrix is unknown, therefore traditional MUSIC can not be passed through calculates
Method obtains two-dimentional DOA, it is therefore desirable to the conversion on formula is carried out to Ca (θ), can be madeWhereinFor a scalar, sense vector and the orthogonality of noise subspace are not affected, can be ignored, therefore former spectral function
Can write：Now just can be by converting two dimension angularSearch the peak value of spectral function
So as to obtain two-dimentional DOA.
The concrete coupling matrix of uniform rectangular face battle array can be obtained by the two-dimentional DOA backsteppings for calculating.Due to signal vector
Have with the orthogonality of noise subspaceThrough calculating above, EnWith, it is known that therefore by one
Fixed fortran can obtain coupling matrix C.
3rd, a kind of new method that the DOA that there is unknown coupling in an aerial array estimates
For linear antenna array, signal it is irrelevant and exist in the case of coupling tectonic coupling Matrix C and
Receipt signal model X=CAS+n；Covariance matrix and noise subspace are calculated using traditional MUSIC algorithms；By to coupling
In the case of direction vector be reconstructed, i.e., certain fortran is carried out to Ca, can cause to use MUSIC algorithms finally
The impact that unknown coupling matrix brings can be ignored when seeking DOA, the DOA of signal is obtained.Specifically ask for an interview Part II background skill
Art.
In a specific embodiment of the invention, a kind of arrival direction estimation method is shown.On the whole, including：S1, base
Exist on the basis of coupled relation between each antenna element and P adjacent a period of time in hypothesis uniform rectangular planar antenna array,
Tectonic coupling matrix and receipt signal model；S2, based on the receipt signal model, tries to achieve its correlation matrix, and carries out feature
Value decomposition obtains noise subspace；S31, based on coupling matrix and noise subspace, using based on sense vector matrix weight
Structure algorithm, estimates two dimension DOA.
In another specific embodiment of the invention, step is utilized and is based on signal side based on coupling matrix and noise subspace
To vector matrix restructing algorithm, two dimension DOA is estimated：The direction vector matrix of signal is reconstructed；Calculated using traditional MUSIC
Method, based on the sense vector matrix of reconstruct DOA is estimated.
It is reconstructed firstly the need of the direction vector matrix to signal：
；
Wherein for CiaxCan write again：
Ciax=Tx(α,β)ci=[Tx1(α,β)+Tx2(α,β)]ci
Ci=[cI, 0 cI, 1 … CI, P-1]T,
Can obtain in the same manner：
Ty=Ty1(α, β)+Ty2(α, β),
Therefore have：
According to traditional MUSIC methods, in DOA estimates, when there is coupling between antenna, there is following formula to set up：
After to the direction vector matrix reconstruction of signal, the formula can be written as：
OrderThen have：
cHQ (α, β) c=0,
According to above formula it is estimated that the 2-d direction finding of signal is as follows：
In another specific embodiment of the invention, a kind of arrival direction estimation method.On the whole, including：S1, based on vacation
If existing on the basis of coupled relation between each antenna element and P adjacent a period of time in uniform rectangular planar antenna array, construction
Coupling matrix and receipt signal model；S2, based on the receipt signal model, tries to achieve its correlation matrix, and carries out eigenvalue point
Solution obtains noise subspace；S32, based on coupling matrix and noise subspace, using companion matrix Meta algorithm, estimates two dimension DOA.
In another specific embodiment of the present invention, in a kind of arrival direction estimation method, step is based on coupling matrix and makes an uproar
Phonon space, using companion matrix Meta algorithm, estimates two dimension DOA, also includes：In the battle array of squaerial face, outermost P-1 rows are made
It is companion matrix unit with the array element on P-1 row, only using the middle individual array elements of (M-P) × (N-P) as the effective array element for receiving signal,
As shown in Figure 3, then the signal model for receiving should be：
Wherein：
G=[P0 P1 P0],
P0It is the full null matrix of one (M-2P+2) (N-2P+2) × (P-1) N ranks, and P1It is a block diagonal matrix, can be with
Writing：
Wherein J=[0(N-2P+2)×(P-1)I(N-2P+2)0(N-2P+2)×(P-1)]。
Coupling matrix is reconstructed below, is madeSo coupling matrix is then reconstructed into：
WhereinAccording to the coupling matrix of reconstruct, receipt signal model can be written as：
The correlation matrix of so signal is：
The direction vector matrix of signal can be expressed as：
Wherein：
According to traditional MUSIC algorithms (it is to be understood that the invention is not restricted to be counted using traditional MUSIC algorithms
Calculate), there should be following formula to set up：
Certain conversion can be carried out to above formula：
Due toWithThere is similar structure, it is possible to obtain lower relation of plane,
Therefore have：
Because c (α, β) is a scalar, as c (α, β) ≠ 0,With UNBetween orthogonality will not be affected,
I.e.：
Therefore tradition MUSIC algorithms can be rewritten as：
Now antenna is coupled and there is no impact to the calculating that DOA estimates, can be by searching PMUSICSpectral peak find signal
Corresponding DOA.
As c (α, β)=0, now (α, β) is referred to as blind angle, and when signal is injected from the angle, the algorithm can not be estimated
Go out the DOA of signal, but the probability that such case occurs is less, only need to note adjusting in designing antenna array aerial array away from
From changing the coefficient of coup can avoid such case.
According to the DOA angles for estimating, the coefficient of coup of squaerial face battle array can be calculated.The two dimension that hypothesis is estimated
DOA angles areHad according to traditional MUSIC algorithmsCan be obtained by conversion by the formula
Define a new matrix Q：
Therefore former formula can be write：
Qc=0,
I.e.：
#
Wherein (.) represents pseudo inverse matrix, and according to above formula all coefficients of coup of squaerial face battle array can be obtained, according to asking
The coefficient of coup for obtaining can obtain coupling matrix, in the case of known coupling matrix, can be by being calculated accurate letter
Number DOA.
In actual applications, signal is often concerned with, and this can affect the calculating to signal noise subspace, space smoothing
Squaerial face battle array is divided into technology the submatrix of several overlaps, can obtain accurate noise by these submatrixs empty
Between, DOA is estimated to affecting so as to exclude signal coherence.
For the matrix of M × N rank, several M can be divided into1×N1The submatrix of rank, and to per individual sub- square
Battle array numbering is (i, j), i=1,2 ..., M-M1+ 1, j=1,2 ..., N-N1+ 1, as shown in figure 4, then (m, n) individual submatrix
Receiving signal is：
WhereinnmnT () is respectively the direction vector matrix and noise matrix of the reception signal of the submatrix,
Dx,DyCan be expressed as：
Dx=diag [u (α1, β1), u (α2, β2) ..., u (αK, βK)]
Dy=diag [v (α1, β1), v (α2, β2) ..., v (αK, βK)],
It is hereby achieved that the coherence matrix of (m, n) individual submatrix is：
As depicted in figs. 1 and 2, in another specific embodiment of the present invention, it is assumed that uniform rectangular planar antenna array
There is coupled relation between interior each antenna element and P adjacent a period of time.The step includes：The squaerial face of one M × N
Battle array, the row and column of face battle array is located at respectively on the straight line parallel with X-axis and Y-axis in rectangular coordinate system, each two phase on row and column
The distance between adjacent antenna element is d, as shown in Figure 1.If there is K signal to inject from unknown direction, with a (αi, βi) represent
The direction vector of i-th signal, wherein αiFor azimuth, βiFor the elevation angle, then planar array can be built and there is antenna coupling
In the case of receipt signal model be x (t)=CAs (t)+n (t), x (t) for rectangle battle array reception signal, C is coupling matrix, A
For the direction vector matrix of signal, A=[a (α can be expressed as1, β1), a (α2, β2) ..., a (αK, βK)], s (t) is source signal
Vector, n (t) is noise vector.
In another specific embodiment of the present invention, a kind of arrival direction estimation method, step tectonic coupling matrix is false
If certain a line antenna element in the battle array of face only has coupled relation and a period of time for being adjacent within P rows between, C is usediRepresenting should
The coefficient of coup matrix of row and the i-th row being adjacent, i=0,1 ..., P-1, as shown in Figure 2, then coupling matrix C can be with structure
Make as follows：
As can be seen that coupling matrix C is a symmetrical toeplitz matrix, each Elements C in matrixiWith knot
Structure is similar to, and is also a symmetrical toeplitz matrix, uses cj(cj≤ 1) represent some antenna element and the jth being adjacent
The coefficient of coup between individual a period of time, then CiCan be expressed as：
In another specific embodiment of the present invention, a kind of arrival direction estimation method, if having K signal from unknown parties
To squaerial face battle array is injected, signal wavelength is λ, then receiving signal can be expressed as：
X (t)=CAs (t)+n (t).
Wherein C is coupling matrix, and A is direction vector matrix, can be expressed as：
A=[a (α1, β1), a (α2, β2) ..., a (αK, βK)],
a(αi, βi) represent i-th signal direction vector, αiFor the azimuth of the signal, βiFor the elevation angle of the signal, and
And have：
Represent Kronecker product, ax(αi, βi) and ay(αi, βi) represent respectively direction vector prolong X-axis and Y-axis point
Amount, can be expressed as：
ax(αi, βi)=[1 u u2 … uM-1]T
ay(αi, βi)=[1 v v2 … vN-1]T,
Wherein：
S (t) and n (t) represent respectively K source signal vector matrix and noise matrix, are represented by：
S (t)=[s1(t), s2(t) ..., sK(t)]
N (t)=[n1(t), n2(t) ..., nK(t)],
According to the receipt signal model of antenna plane, the correlation matrix that can calculate it is as follows：
Rx=E [x (t) xH(t)]=CARsAHCH+σ2I,
Wherein (.)HRepresent the conjugation transformation of ownership, Rs=E [s (t) s (t)H].Obtain correlation matrix RxAfterwards, can be to RxCarry out feature
Value is decomposed：
Wherein ∑S∈RNIt is signal power diagonal matrix, ∑N∈RM-NIt is noise power diagonal matrix, US∈CM×NFor signal
Subspace, UN∈CMx(M-N)For noise subspace.
In another specific embodiment of the present invention, also include before step S1：Judgement injects whether face battle array signal is concerned with,
If so, then uniform rectangular antenna plane is divided into utilization space smoothing technique the submatrix of several overlaps.
In another specific embodiment of the present invention, also include before step S1：Judgement injects whether face battle array signal is concerned with,
If so, then uniform rectangular antenna plane is divided into utilization space smoothing technique the submatrix of several overlaps.
As shown in figure 4, in another specific embodiment of the present invention, also including before step S1：Face battle array letter is injected in judgement
Number whether it is concerned with, if so, then uniform rectangular antenna plane is divided into utilization space smoothing technique the submatrix of several overlaps：
In two-dimensional space smoothing technique, actual coherence matrix is RmnMeansigma methodss：
Wherein：
Now coherence matrix is full rank, and by Eigenvalues Decomposition correct noise subspace can be obtained, so as to avoid
The impact that signal coherence is brought in DOA estimations.
Finally, the present processes are only preferably embodiment, are not intended to limit protection scope of the present invention.It is all
Within the spirit and principles in the present invention, any modification, equivalent substitution and improvements made etc. should be included in the protection of the present invention
Within the scope of.
Claims (9)
1. a kind of arrival direction estimation method, it is characterised in that comprise the following steps：
S1, based on the assumption that there is coupling in uniform rectangular planar antenna array between each antenna element and P adjacent a period of time closing
On the basis of system, tectonic coupling matrix and receipt signal model；
S2, based on the receipt signal model, tries to achieve its correlation matrix, and carries out Eigenvalues Decomposition and obtain noise subspace；
S31, based on coupling matrix and noise subspace, using sense vector matrix restructing algorithm is based on, estimates two dimension
DOA。
2. the method for claim 1, it is characterised in that step S31 also includes：
Based on coupling matrix, the direction vector matrix of signal is reconstructed；
Based on noise subspace, DOA is estimated.
3. a kind of arrival direction estimation method, it is characterised in that comprise the following steps：
S1, based on the assumption that there is coupling in uniform rectangular planar antenna array between each antenna element and P adjacent a period of time closing
On the basis of system, tectonic coupling matrix and receipt signal model；
S2, based on the receipt signal model, tries to achieve its correlation matrix, and carries out Eigenvalues Decomposition and obtain noise subspace；
S32, based on coupling matrix and noise subspace, using companion matrix Meta algorithm, estimates two dimension DOA.
4. method as claimed in claim 3, it is characterised in that step S32 also includes：
In the battle array of squaerial face, outermost P-1 rows and the array element on P-1 row is made to be companion matrix unit, only by middle (M-P)
The individual array elements of × (N-P) are used as the effective array element for receiving signal；
Coupling matrix is reconstructed；
Using modified MUSIC, DOA is estimated based on the sense vector matrix of reconstruct.
5. the method as described in claim 1 or 3, it is characterised in that in step S1, it is assumed that uniform rectangular planar array antenna
There is coupled relation between each antenna element and P adjacent a period of time in row, including：The squaerial face battle array of one M × N, face
The row and column of battle array is located at respectively on the straight line parallel with X-axis and Y-axis in rectangular coordinate system, the adjacent day of each two on row and column
The distance between linear array is d, if there is K signal to inject from unknown direction, with a (αi,βi) represent i-th signal direction
Vector, wherein αiFor azimuth, βiFor the elevation angle, then reception letter of the planar array in the case where there is antenna coupling condition can be built
Number model x (t)=CAs (t)+n (t), x (t) for rectangle battle array reception signal, C is coupling matrix, A for signal direction vector
Matrix, can be expressed as A=[a (α1, β1), a (α2, β2) ..., a (αK, βK)], s (t) be source signal vector, n (t) be noise to
Amount.
6. the method as described in claim 1 or 3, it is characterised in that in step S1, tectonic coupling matrix also includes：Use Ci
The coefficient of coup matrix of the row and the i-th row being adjacent is represented, i=0,1 ..., P-1, coupling matrix C constructions are as follows,
7. the method as described in claim 1 or 3, it is characterised in that in step S2, also include：
According to the receipt signal model of antenna plane, the correlation matrix that can calculate it is as follows
Rx=E [x (t) xH(t)]=CARsAHCH+σ2I,
Wherein (.)HRepresent the conjugation transformation of ownership, Rs=E [s (t) s (t)H], obtain correlation matrix RxAfterwards, to RxCarry out Eigenvalues Decomposition：
Wherein ∑S∈RNIt is signal power diagonal matrix, ∑N∈RM-NIt is noise power diagonal matrix, US∈CM×NIt is empty for signal subspace
Between, UN∈CMx(M-N)For noise subspace..
8. the method as described in claim 1 or 3, it is characterised in that also include before step S1：Face battle array signal is injected in judgement
Whether it is concerned with, if so, then uniform rectangular antenna plane is divided into utilization space smoothing technique the submatrix of several overlaps.
9. method as claimed in claim 8, it is characterised in that step S1 also includes：Will be uniform using Eigenvalues Decomposition
Squaerial face battle array is divided into the submatrix of several overlaps.
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| CN109870668A (en) * | 2018-12-24 | 2019-06-11 | 哈尔滨工程大学 | A kind of planar array Adaptive beamformer coupling automatic correcting method based on auxiliary array element |
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| CN107907854B (en) * | 2017-10-31 | 2021-04-27 | 大连大学 | DOA estimation method under impulse noise environment |
| CN107907854A (en) * | 2017-10-31 | 2018-04-13 | 大连大学 | DOA estimation new methods under impulse noise environment |
| CN108519576A (en) * | 2018-03-21 | 2018-09-11 | 华南理工大学 | Underwater Wave arrival direction estimating method based on the adjustable Nonuniform Linear Array of angle and device |
| CN108519576B (en) * | 2018-03-21 | 2021-07-20 | 华南理工大学 | Underwater direction of arrival estimation method and device based on included angle adjustable non-uniform linear array |
| CN108414967A (en) * | 2018-04-11 | 2018-08-17 | 华南理工大学 | Based on L gusts of underwater two-dimension Wave arrival direction estimating method and device of angle adjustable double |
| CN109870668A (en) * | 2018-12-24 | 2019-06-11 | 哈尔滨工程大学 | A kind of planar array Adaptive beamformer coupling automatic correcting method based on auxiliary array element |
| CN110018438B (en) * | 2019-04-23 | 2020-09-25 | 北京邮电大学 | Direction-of-arrival estimation method and device |
| CN110018438A (en) * | 2019-04-23 | 2019-07-16 | 北京邮电大学 | A kind of Wave arrival direction estimating method and device |
| CN110542880A (en) * | 2019-08-13 | 2019-12-06 | 唐晓杰 | DOA estimation strategy under partial overlapping condition of frequency points |
| CN111413667A (en) * | 2020-03-25 | 2020-07-14 | 北京邮电大学 | Method and device for determining direction of arrival of signal and electronic equipment |
| CN112379327A (en) * | 2020-12-01 | 2021-02-19 | 北京工业大学 | Two-dimensional DOA estimation and cross coupling correction method based on rank loss estimation |
| CN113673317A (en) * | 2021-07-12 | 2021-11-19 | 电子科技大学 | Atomic norm minimization dimension reduction-based two-dimensional lattice DOA estimation method |
| CN113673317B (en) * | 2021-07-12 | 2023-04-07 | 电子科技大学 | Atomic norm minimization dimension reduction-based two-dimensional lattice DOA estimation method |
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