CN107907855A - A kind of coprime array switching DOA estimation method and device for even linear array - Google Patents
A kind of coprime array switching DOA estimation method and device for even linear array Download PDFInfo
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- CN107907855A CN107907855A CN201711014157.XA CN201711014157A CN107907855A CN 107907855 A CN107907855 A CN 107907855A CN 201711014157 A CN201711014157 A CN 201711014157A CN 107907855 A CN107907855 A CN 107907855A
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Abstract
A kind of coprime array switching DOA estimation method and device for even linear array, method include：Element position is carried out by ascending order arrangement according to coprime Array Model, obtains the delay set that any two element position makes the difference, forms difference set table；The difference set table is traveled through, the coordinate of institute's some need delay is found in sparse covariance matrix, corresponding covariance function value is done into statistical average, calculates the auto-correlation function value for needing to postpone；Toepltz matrixes (being identical i.e. with the element value on the diagonal of main diagonal parallel) are constructed according to auto-correlation function value；Based on MUSIC algorithm construction spatial spectrum search functions, Toepltz matrixes are solved, when spatial spectrum search vector is consistent with signal guide vector, you can find correct DOA estimates.Device includes：External RAM, digital signal processor and output driving and display circuit.Multiplier is not required in the present invention, easy to operate, but can obtain the effect identical with space smoothing matrix, considerably reduces the free degree.
Description
Technical field
The present invention relates to digital processing field, more particularly to a kind of coprime array switching DOA for even linear array to estimate
Count method and device.
Background technology
Array signal process technique attention rate in past 20 years is higher and higher, and array antenna can extract other types
The information for the incident signal source that antenna cannot extract, therefore, the incoming signal direction of arrival in array signal process technique
The achievements such as the algorithm for estimating of (Direction of Arrival, DOA) have had been applied to the neck such as sonar, radar, communication, earthquake
Domain.
Array signal process technique is especially applied to mobile and satellite communication system in the communications field, complex condition
In system, it can effectively change the integrated communication environment of system.Such as：Array signal process technique is applied to mobile communication system
In, can be by accurately estimating signal radiation source, so as to effectively be positioned to the mobile terminal in region.In recent years
In evolution, the method for array signal processing has very much, and in terms of comprehensive, classical way has sub-space decomposition, compression sense
Tracking optimization method known etc..For model be also classified near field source model[1]And far field source[2]Model, model algorithms of different
It is different.Initial one-dimensional estimated method also develops into two dimension, even multidimensional[3]Situation.
In tradition, usually to meet the uniform linear array of Nyquist sampling thheorems[4](Uniform Linear
Array, ULA) receiving array is used as to realize that DOA estimates.Advantage is：Process is simple, centre also without too many signal at
Reason process, directly calculates covariance matrix and can carry out Subspace Decomposition scheduling algorithm and estimate DOA.Shortcoming is：The source of identification
Number is limited, and resolution ratio is not high.
Reason is as follows：The resolution ratio of angle recognition depends on array sizes, and size is bigger, i.e., array aperture is bigger, differentiates
Rate is better.And graing lobe effect is caused according to the too conference of nyquist sampling theorem array element interval, DOA estimations are obscured, are tied
Fruit is inaccurate, generally takes the half of wavelength.Therefore, the resolution ratio of algorithm is primarily limited to array element quantity, and array element quantity is too many, meeting
Pressure is caused to space, arrangement is required high.Although resolution ratio can be improved, substantial amounts of sample, middle sample can be brought
Analysis calculating process can also become complicated, it is necessary to which substantial amounts of multiplier adder supports, and the requirement to hardware device is more severe
Carve, destabilizing factor can also increase, and cost can also improve, and be unfavorable for actual real-time application, it is impossible to adapt to current people to logical
The strict demand of letter.
Therefore, how to realize high-resolution, accurate DOA estimations is that academia and engineering circles are needed extensively and furtherd investigate
Important topic.From algorithm angle, classic Power estimation method asks for local maximum by calculating spatial spectrum, so that
The direction of arrival of signal is estimated, Bartlett Beamforming Methods are classical Fourier analysis to the one of sensor array data
Kind natural extending.This method is to make the output power of Beam-former maximum relative to some input signal.Because by array institute
There is the available free degree to be all used to form a wave beam, when an only signal, this mode in required observed direction
It is feasible, but when there are during multiple sources, by the interference signal including desired signal, estimation performance can be drastically for the output of array
Decline.In addition, maximum entropy method (MEM) (MEM), Capon[5]The spatial domain non-linear processing methods such as least variance method and AR (autoregression) model
Etc linear prediction algorithm although improve resolution ratio, but need to do matrix a large amount of operations or object function carried out excellent
Change, poor robustness, computation complexity is high, is unfavorable for practical engineering application.
In terms of array structure, the estimable number of sources of traditional uniform linear array is limited, and resolution ratio is not met
Requirement of engineering, therefore this structure is rarely employed in practical application.Therefore non-uniform linear arrays just become the hot spot of research, most
Small redundant array[8,9], nested array[10], mutual pixel array[1,2]Although being all sparse nonuniform noise, it can increase aperture,
Improve the free degree.But minimum redundant array lacks clear and definite array position expression formula and free degree expression formula, it is difficult to clearly states
Its characteristic；Nested array structure is more complicated.
The content of the invention
The present invention provides a kind of coprime array switching DOA estimation method and device for even linear array, the present invention proposes
Toepltz matrixes relate only to simple element and retake, it is not necessary to multiplier, it is easy to operate, but can obtain and space
The identical effect of smoothing matrix, considerably reduces the free degree, described below：
A kind of coprime array switching DOA estimation method for even linear array, the DOA estimation method comprise the following steps：
1) element position is carried out by ascending order arrangement according to coprime Array Model, obtains any two element position and make the difference to obtain
Delay set, form difference set table；
2) the difference set table is traveled through, the coordinate of institute's some need delay is found in sparse covariance matrix, will be corresponding
Covariance function value does statistical average, calculates the auto-correlation function value for needing to postpone；
3) Toepltz matrixes are constructed according to auto-correlation function value obtained in the previous step, is operated for Subspace Decomposition；
4) MUSIC algorithm construction spatial spectrum search functions are based on, when spatial spectrum search vector is consistent with signal guide vector
When, you can find correct DOA estimates.
Before step 1), the DOA estimation method further includes：
The uncorrelated narrow band signal in far field is received, receiving array is to form translation mutually by two groups of uniform linear arrays
Pixel array, as coprime Array Model；
Estimation receives the sparse covariance matrix of signal.
The DOA estimation method further includes：The statistical average of multiple snaps is carried out to the sparse covariance matrix.
The coprime Array Model is specially：
Two arrays contain N number of array element and 2M array element respectively, and array element interval is Md and Nd respectively, is adopted according to Nyquist
Sample theorem, takes the half that d is wavelength, as unit gap.
The spatial spectrum search function is：
Wherein, PMUSIC(θ) is spatial spectrum search function, and a (θ) is steering vector, UNFor noise subspace, H is matrix
Conjugate transposition.
A kind of estimation device for the coprime array switching DOA estimation method for even linear array, the estimation device bag
Include：External RAM, digital signal processor and output driving and display circuit,
Signal, relatively prime integers will be received to M, N is stored in external RAM, then is input to the digital signal processor in real time
In；
By the internal core algorithm of the digital signal processor, covariance estimation is carried out to signal, utilizes independent square
Battle array extracts continuous auto-correlation, estimates DOA by improved MUSIC algorithms, finally shows and its show mould by output driving
Block display identification DOA situations.
The present invention proposes a kind of coprime array switching DOA estimation method and device for even linear array, if being used for space
Power estimation and Practical Project field, can produce following beneficial effect：
Firstth, cost and hardware requirement are reduced, lifts resolution ratio；
Relative to other DOA estimation methods, this method eliminates the step of sparse support area reconstructs, and reduces calculation amount.
For traditional DOA estimation arrays (even linear array, ULA), the aperture of array is small, and resolution ratio is low, believes for densely distributed source
Number, it is difficult to parse.The free degree is low, and optimization space is limited.For mutual pixel array, because the array element interval of two sub- linear arrays is coprime
, so mutual coupling is low, redundancy is few, on the basis of mutual pixel array, utilizes sample properties and the structure and traversal of difference set table
Search operation, the auto-correlation continuously postponed, realizes the DOA estimations of thinned array.
Secondth, the free degree improves；
Traditional ULA arrays need evenly distributed array element, it is desirable to which high, degree of rarefication is low, and resolution ratio is poor.Mutual pixel array N+
2M-1 array element, acquisition-MN arrive the continuous auto-correlation of MN, in the case where array element number is identical, improve the free degree, add
Identifiable target source quantity.
3rd, accuracy of estimation is improved；
Because N+2M-1 actual physical array element, is actually equivalent to MN Virtual array.So knowledge for source signal
Other precision is more accurate.
4th, computation complexity is greatly lowered.
Because traversal search method, the simple procedure such as relate only to travel through, judge, it is not necessary to the element such as multiplier, behind
Toepltz matrix constructions it is simpler, only element is retaken, and process is simple to operation, but effect is equivalent to space and puts down
It is sliding.Space smoothing process needs a large amount of matrix multiples and flat equalization operation, requires height to multiplier, adder, is unfavorable for reality
When engineer application, maintenance gets up, and difficulty is also high.
Brief description of the drawings
Fig. 1 is mutual pixel array DOA estimator design flow diagrams；
Fig. 2 is DOA estimator flow charts；
Fig. 3 is array element arrangement architecture schematic diagram；
Fig. 4 is M=2, delay (array element number N+2M-1=6) schematic diagram during N=3；
Fig. 5 is two array DOA estimated result schematic diagrames when array number is 10；
Fig. 6 is that two array DOA estimate schematic diagram when array number is 6；
Fig. 7 is direction of arrival root-mean-square error with signal-to-noise ratio situation of change schematic diagram；
The hardware that Fig. 8 is the present invention implements figure；
Fig. 9 is DSP internal processes flow graphs.
Embodiment
To make the object, technical solutions and advantages of the present invention clearer, embodiment of the present invention is made below further
It is described in detail on ground.
Multiple signal classification algorithm (MUSIC)[2,6,7]Proposition DOA algorithm for estimating is entered the new stage, this method is fitted
The situation of array number is less than for recognizable object source.Eigenvalues Decomposition is carried out according to the covariance matrix of array received sample,
Signal subspace and noise subspace can be obtained from feature vector, according to the characteristic that two sub-spaces are mutually orthogonal, construction
Space spectral function, by spectrum peak search, detects the DOA of signal.The algorithm is simply easily realized, to the algorithm based on subspace structure
Development has an important directive significance, and this method comparative maturity, can utilize space smoothing[2]Etc. technology, realize super
Resolution ratio DOA estimates.Therefore, the classical MUSIC algorithms of selection of the embodiment of the present invention carry out DOA estimations, and propose difference set table
The method of traversal search, handles receiving data, avoids the space smoothing process of complexity, it is not necessary to matrix operation, greatly
Complexity is reduced greatly, reduces the use of multiplier, reduces cost.
Mutual pixel array, it is simple in structure, it can accurately be described with mathematic(al) representation, there is good application in DOA estimations.
Coprime thought can also be with sampling[11-14], realize that spectrum estimation etc. is applied, advantage is reduction of sampling rate, alleviates
Hardware pressure, and calculate it is simple, it is functional.Mutual pixel array also has a wide range of applications in multidimensional DOA estimations[15]。
Analyzed based on more than, the embodiment of the present invention proposes that the method for difference set table traversal search will based on mutual pixel array
The array sample covariance matrix at Nyquist intervals is converted into the signal autocorrelation of virtual uniform linear array, and constructs one
A Toepltz matrixes, process substitution spatial smoothing operation, reduce complexity.Carry out a large amount of simulation analysis, it was demonstrated that sparse
Array sample can directly carry out MUSIC decomposition by the Toepltz matrixes of difference set table traversal search procedure construction, obtain DOA and estimate
Meter.The free degree of higher can be obtained, identifies more target sources.The embodiment of the present invention is being related to far field source signal DOA estimation
Occasion have wide application prospect.
Embodiment 1
A kind of coprime array switching DOA estimation method for even linear array, referring to Fig. 1 and Fig. 2, the DOA estimation method bag
Include following steps：
101：The uncorrelated narrow band signal in far field is received, receiving array is mutual pixel array, as mutual pixel array mould
Type；Estimation receives the sparse covariance matrix of signal；
Wherein, mutual pixel array is made of two groups of uniform linear arrays (respectively containing M and N number of array element).
102：Element position is carried out by ascending order arrangement according to coprime Array Model, any two element position is obtained and makes the difference
The delay set arrived, forms difference set table；
103：The difference set table is traveled through, the coordinate of institute's some need delay is found in sparse covariance matrix, by correspondence
Covariance function value do statistical average, calculating needs the auto-correlation function value that postpones；
104：According to the covariance function continuously postponed of equivalent virtual uniform array, make choice and retaken with element
Journey, constructs a Toepltz matrix；
105：Based on MUSIC algorithm construction spatial spectrum search functions, when spatial spectrum search vector and signal guide vector one
During cause, you can find correct DOA estimates.
Further, which further includes：The statistical average of multiple snaps is carried out to sparse covariance matrix.
In conclusion the embodiment of the present invention is realized identical with ULA array element numbers by above-mentioned steps 101- steps 105
In the case of, the free degree of higher can be obtained；Due to the sparse arrangement of the array element of mutual pixel array, integral array aperture is carried
Height, can realize that super-resolution source is estimated further combined with improved MUSIC algorithms；The precision of DOA estimations is improved, is reduced
Computation complexity, makes entire work flow simple, easy to operate.
Embodiment 2
The scheme in embodiment 1 is further introduced with reference to specific example, calculation formula, Fig. 1-Fig. 4,
It is described below：
Assuming that there is D narrow band signal s under far field conditiond(t), t=1,2 ..., T, d=1,2 ..., D, incide this hair
In the mutual pixel array of bright embodiment design, angle is respectively θ1,θ2,...,θD.Assuming that it is uncorrelated between signal source, independent same point
The white Gaussian noise of cloth is n (t), its average is 0, and variance isT is total snap quantity.Then signal model is represented by：
Wherein, s (t) is source signal, and x (t) is the signal model added after making an uproar, and parameter t represents t-th of snap, and A is array stream
Type matrix, si(t) it is i-th of source signal (i1 ..., D), a (θi) it is steering vector.
Then array manifold matrix is：
A=[a (θ1),...,a(θi),...,a(θD)] (2)
Wherein, θiFor the receiving angle of each reception array element.Steering vector a (θi) be：
Wherein, M, N are coprime positive integer (not having common factor i.e. in addition to 1), and P is the set of element position, and λ is signal wave
It is long.
201：Coprime Array Model；
Mutual pixel array[3]In order to obtain continuous auto-correlation function, it is necessary to there is enough initial data by making the difference.Therefore,
Two arrays contain N number of array element and 2M array element respectively, and array element interval is Md and Nd respectively, according to nyquist sampling theorem,
The half that d is wavelength is taken, as unit gap.
As shown in figure 3, the homogenous linear submatrix that two intervals are different, forms mutual pixel array, can according to Chinese remainder theorem
To know two uniform linear arrays in addition to first array element, then without the array element repeated.So contain N+2M-1 altogether
A array element (first array element is public), element position is：
P={ Mnd, 0≤n≤N-1 } ∪ { Nmd, 0≤m≤2M-1 } (4)
Made the difference according to formula (5), the autocorrelation lags such as Fig. 4 can be obtained：
C=z | z=u-v, u ∈ P, v ∈ P } (5)
Wherein, C is the delay set that any two element position makes the difference, and z is delay, and u, v are the position of two array element
Put.U is taken all over P, while v is taken all over P, you can obtain whole delay information composition C.
Fig. 4 is M=2, example during N=3.Visible delay section includes at least the successive range that-MN arrives MN.Therefore behind
Continuous auto-correlation function can be obtained according to difference set table, then construct mathematics mistake of the Toepltz matrixes by Eigenvalues Decomposition
Journey, obtains up to MN incoherent feature vectors, and the DOA that can realize at most MN source using MUSIC algorithms is identified.Examine
Consider L=MN, the available free degree is 2L+1.
202：Receive the sparse covariance matrix estimation of signal；
DOA estimations are exactly to obtain the direction of arrival θ of information source using array received data x (t)1,θ2,...,θD.Mould in formula (1)
The source signal that type represents is sparse, can utilize compressive sensing theory and MUSIC scheduling algorithm reconstruction signals, Support just corresponds to
The DOA estimated.And the performance reconstructed depends on the setting of array manifold matrix A, the mutual pixel array of design of the embodiment of the present invention
It can improve openness, farthest reduce redundancy, and utilize " difference set " to improve accuracy.
The essence of thinned array processing will exactly receive signal x (t) and be converted into second-order statistic (or higher order statistic).
The covariance matrix of x (t) is：
Wherein, E [x (t) xH(t)] it is mean value computation formula, for calculating covariance matrix, H (is conjugated for hermitian conversion
Transposition),For noise variance, IN+2M-1For the unit matrix of (N+2M-1) × (N+2M-1), σiFor the reception of i-th of source signal
When noise, i1 ..., D.
It is the covariance matrix of source signal,For mean value computation
Formula.
In fact, the embodiment of the present invention can utilize the statistical average of multiple snaps when calculating covariance matrix, to ensure standard
Exactness.T is snap quantity.Then covariance matrixFor：
Wherein,The incoming signal observed for each snap.
203：The construction of difference set table；
According to m-th of the array element and n-th of array element on P, relevant information can be obtained, corresponding delay is pm-pn, represent
For T (u, v).Therefore, can be significantly by building suitable array (formulating suitable sampling policy equivalent to discrete signal)
Increase calculates autocorrelative delayed scope.This is that the embodiment of the present invention carries out super-resolution spectrum estimation, completes narrow band signal ripple
Up to the key of angular estimation.The difference set that the mutual pixel array that the embodiment of the present invention proposes produces can complete super-resolution Power estimation, and
And the free degree is far longer than generic array, but need to select suitable integer.Mutual pixel array uses N+2M-1 using difference set
Actual array element generation-MN arrives the continuous integral number of MN, so as to fulfill the super-resolution spectrum estimation of O (MN) free degree.
To further illustrate the make of difference set table, with M=2, illustrated exemplified by N=3：
Formula (4) ascending order is arranged first, table 1 can be obtained according to formula (5), it is as follows：
The difference set table T that 1 mutual pixel array of table obtains
Wherein, T (u, v) is representedIn u rows, v row element representation delay.
204：Traversal search process；
, can be further in formula (7) according to difference set table obtained in the previous stepIn find the delay of institute some need
Coordinate, then does statistical average by corresponding covariance function value, you can calculates the auto-correlation function value for needing to postpone.
Such as：Wish to find delay for 1 auto-correlation, traveled through first in table 1, corresponding u when searching T (u, v)=1,
V, i.e. (u=3, v=2), (u=4, v=3).Then in matrixIn find corresponding elementWithTo institute
Some elements do statistical average, i.e.,This operation is repeated, all delays of MN are arrived until finding-MN
Auto-correlationArrive
205：The construction of Toepltz matrixes；
According to auto-correlation obtained in the previous stepArriveFollowing Toepltz matrixes can be constructed：
That is, it is identical with the element value on the diagonal of main diagonal parallel.The step is substantially grasped with space smoothing
Work acts on similar, matrixEigenvalues Decomposition is carried out with space smoothing matrix, obtained feature vector is the same, characteristic value
It is a square proportional relation, the MUSIC decomposition algorithms not influenced below carry out DOA estimations.But before the embodiment of the present invention eliminates
The process of smooth (being related to a large amount of matrix multiples, impartial process of then making even) afterwards, eliminates substantial amounts of multiplier and adder.
Only need byExtract, arrange reordering operations into row element, construct a Toepltz matrix, be exactly briefly regular
Ground is each element assignment of matrix.So easy to operate, be not related to plus, multiplication operation, therefore greatly reduce computation complexity,
Cost is reduced for engineer application, operation is also more convenient.
206：MUSIC algorithms；
MUSIC algorithms are to obtain feature vector using the Eigenvalues Decomposition of the i.e. covariance matrix of second-order statistic of signal,
Signal subspace and noise subspace are contained in feature vector, using the orthogonality of the two, space spectral function is constructed, by searching
Rope, identifies the DOA of multiple signals.
The space smoothing matrix obtained before is denoted as R, then the matrix is exactly the covariance matrix of ULA samples, can be with table
It is shown as：
Wherein, E (ssH) be source signal covariance matrix, E (nnH) be noise covariance matrix,Represent antenna
Noise power, RssIt is the covariance matrix of source signal, Eigenvalues Decomposition is carried out to R：
R=U Λ UH (10)
Wherein, U is characterized vector matrix, and Λ is characterized the diagonal matrix of value composition, can be expressed as form：
Wherein, eigenvalue λ1≥λ2≥...≥λk＞ λk+1=...=λL=σ2, i.e., characteristic value by the big characteristic value of preceding k and
Remaining L-k smaller eigenvalue clusters into.And corresponding feature vector is also classified into two parts, a part is that big characteristic value is corresponding
Feature vector forms signal subspace, and another part is the noise subspace of the corresponding feature vector composition of small characteristic value.Signal
Subspace USWith noise subspace UNMeetWithThe direction of arrival being likely to occur to
The vector vertical with noise subspace vector is found in amount, it is possible to determine DOA.
Wherein, MUSIC algorithms are exactly using the mutually orthogonal characteristic of the steering vector and noise subspace of signal, are searched out
The correct pseudo- spectrum in space.In practical engineering application, certain column vector in steering vector is consistent with sense vector, then
Their scalar product should be infinitely small, based on this, construct spatial spectrum search function：
Wherein, PMUSIC(θ) is spatial spectrum search function, and a (θ) is steering vector, UNFor noise subspace (feature vector square
Battle array).
When spatial spectrum search vector is consistent with signal guide vector, it may appear that peak value, you can find correct DOA estimations
Value.
In conclusion the embodiment of the present invention by above-mentioned steps in the case where ULA array element numbers are identical, can obtain more
The high free degree；Due to the sparse arrangement of the array element of mutual pixel array, integral array aperture is improved, further combined with improved
MUSIC algorithms can realize that super-resolution source is estimated；Improve the precision of DOA estimations.
Embodiment 3
A kind of coprime array switching DOA estimation devices for even linear array, the estimation device be with Examples 1 and 2
Method is corresponding, referring to Fig. 8 to and Fig. 9, it is described below：
In fig. 8, signal, relatively prime integers will be received first to M, N deposit external RAMs (Random Access Memory)
In, then they are input in DSP (Digital Signal Processor, digital signal processor) in real time, by DSP
Portion's core algorithm, covariance estimation is carried out to signal, is extracted continuous auto-correlation using independent matrix, is estimated by MUSIC algorithms
DOA, finally shows by output driving and its display module display identifies DOA situations.
Wherein, the DSP (Digital Signal Processor, digital signal processor) of Fig. 8 is core devices, in frequency
During spectrum perceives, following major function is completed：
1) internal core algorithm is called, actual signal is completed and receives and carry out covariance estimation, extracted using independent matrix
Continuous auto-correlation, estimates the processes such as DOA by MUSIC algorithms；
2) M, N and sample of signal are controlled, it is adjusted in real time, complies with actual needs；
3) by DOA estimated results output in real time to driving and display module.
It may be noted that as a result of digitized method of estimation, thus determine the complexities of Fig. 8 systems, correctness and steady
Qualitatively principal element is not the periphery connection of DSP devices in Fig. 8, but the core that DSP internal program memories are stored
Algorithm.
Fig. 9 flows are divided into the following steps：
1) array parameter (relatively prime integers M, N) is set according to actual needs first；
2) then, CPU main controllers read the parameter of setting from I/O ports, into internal RAM；
3) present invention is the most crucial part of DSP algorithm by the design that the processing procedure of Fig. 1 carries out DOA estimators, operation
After the algorithm, you can must observe the situation of identification DOA；
4) judge whether the DOA estimation devices meet actual demand, if not satisfied, program returns, set as requested again
Determine signal parameter；
5) until design result meets actual requirement, then exported by the output bus of DSP to outside and show that driving is set
It is standby, DOA estimated results are subjected to digital-scroll technique.
It may be noted that realized as a result of DSP so that whole DOA estimators design becomes more flexibly and fast, can basis
Actual needs in DOA estimator design processes, parameter needed for flexible transformation, is allowed to finally meet requirement of engineering.
In conclusion the embodiment of the present invention by above-mentioned steps in the case where ULA array element numbers are identical, can obtain more
The high free degree；Due to the sparse arrangement of the array element of mutual pixel array, integral array aperture is improved, further combined with improved
MUSIC algorithms can realize that super-resolution source is estimated；Improve the precision of DOA estimations.
Embodiment 4
Feasibility verification is carried out to the scheme in embodiment 1-3 with reference to specific experimental data, it is described below：
Experiment 1
The reception of signal is carried out with uniform linear array and mutual pixel array respectively, it is contemplated that even linear array is in array element quantity one
When determining, the free degree is limited, and the source signal that can be identified is less than array element quantity, thus only allow ULA identify before 9 target sources,
It is accurate to compare.Array element quantity is set to 10, number of source 15, angle is uniformly distributed in the range of [- 50 °, 62 °], and step-length is
8 degree, wavelength 1, minimum array element spacing takes half-wavelength 1/2.Relatively prime integers takes M=3, N=5, then array element number is N+2M-1=
10.In order to make experiment that there is comparability, snap quantity is set to sufficiently large, is 2000.Signal-to-noise ratio is set to 0.As a result it is as follows：
(a) in Fig. 5 utilizes mutual pixel array ULA arrays, and results contrast is accurate, can be from figure it can be clearly seen that 15 thin
Spectral peak, represents 15 target sources, and all angles are also essentially coincided with line of reference, and obtained DOA estimations are relatively more successful；In Fig. 5
(b) represent that ULA only identifies 5 sources and accuracy is not high, DOA estimation failures.It is not high mainly due to resolution ratio, it is impossible to differentiate
Go out so multi-source, if the degree of rarefication of source angular distribution, accuracy can be improved accordingly, but at this moment, the precision of mutual pixel array
By higher.
Can with it is concluded that, mutual pixel array of the invention using difference set table traversal search technology with uniform linear array
When array number is identical (10), more sources (MN=15) can be identified, and ULA can only at most identify 9 (noise
Space accounts for 1).In addition, the sparse covariance that coprime receiving array can be obtained using the method for difference set table traversal search
Matrix is converted into virtual ULA covariance functions, obtains the auto-correlation continuously postponed.This process can greatly improve DOA estimations
Resolution ratio, relaxes the requirement openness to target source.
Array element quantity is changed to 6 by experiment 2, and number of source is changed to 4, and angle is respectively -10 °, 20 °, 25 °, 60 °, by centre
Two angle initialization comparatively denses, are spaced 5 °, other conditions are identical with experiment 1.As a result such as Fig. 6：
The coprime array of the present invention, which combines difference set table, can clearly tell two sources of concentration, and result is accurate,
And the ULA recognition results shown in Fig. 6 (b) can only identify three sources, by two of concentration incident sources as an identification, differentiate
Power is not high.
Experiment 3
The uniform linear array of 6 array element and mutually pixel array (M=2, N=3) proposed in this paper, two methods are in different letters
Make an uproar than in the case of while do Estimation of Spatial Spectrum.Consider the situation in single incident source, incidence angle is set to 45 °, and signal-to-noise ratio takes -20dB
To 25dB, at intervals of 1dB.For each signal-to-noise ratio condition of test signal, 1000 Monte Carlos (Monte-Carlo) are done
Experiment, and count corresponding root-mean-square error (RMSE).
Fig. 7 represents that two methods carry out the root-mean-square error of DOA estimations with the situation of change of signal-to-noise ratio, it can be deduced that knot
By, it is proposed in this paper based on the coprime array approach of difference set thought at low signal-to-noise ratio (- 20dB arrives 0dB) and uniform linear array
Estimate that the performance of DOA is similar, in high s/n ratio, the root-mean-square error of identification is slightly less than traditional ULA arrays.Accuracy higher.
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To the model of each device in addition to specified otherwise is done, the model of other devices is not limited the embodiment of the present invention,
As long as the device of above-mentioned function can be completed.
It will be appreciated by those skilled in the art that attached drawing is the schematic diagram of a preferred embodiment, the embodiments of the present invention
Sequence number is for illustration only, does not represent the quality of embodiment.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all the present invention spirit and
Within principle, any modification, equivalent replacement, improvement and so on, should all be included in the protection scope of the present invention.
Claims (6)
1. a kind of coprime array switching DOA estimation method for even linear array, it is characterised in that the DOA estimation method includes
Following steps：
1) element position is carried out by ascending order arrangement according to coprime Array Model, what acquisition any two element position made the difference prolongs
Set late, forms difference set table；
2) the difference set table is traveled through, the coordinate of institute's some need delay is found in sparse covariance matrix, by corresponding association side
Difference function values do statistical average, calculate the auto-correlation function value for needing to postpone；
3) Toepltz matrixes are constructed according to auto-correlation function value, for follow-up Subspace Decomposition；
4) MUSIC algorithm construction spatial spectrum search functions are based on, when spatial spectrum search vector is consistent with signal guide vector, i.e.,
Correct DOA estimates can be found.
A kind of 2. coprime array switching DOA estimation method for even linear array according to claim 1, it is characterised in that
Before step 1), the DOA estimation method further includes：
The uncorrelated narrow band signal in far field is received, receiving array is to form the mutual primitive matrix of translation by two groups of uniform linear arrays
Row, as coprime Array Model；
Estimation receives the sparse covariance matrix of signal.
3. a kind of coprime array switching DOA estimation method for even linear array according to claim 1 or 2, its feature exist
In the DOA estimation method further includes：The statistical average of multiple snaps is carried out to the sparse covariance matrix.
A kind of 4. coprime array switching DOA estimation method for even linear array according to claim 1, it is characterised in that
The coprime Array Model is specially：
Two arrays contain N number of array element and 2M array element respectively, and array element interval is Md and Nd respectively, is determined according to nyquist sampling
Reason, takes the half that d is wavelength, as unit gap.
A kind of 5. coprime array switching DOA estimation method for even linear array according to claim 1, it is characterised in that
The spatial spectrum search function is：
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>M</mi>
<mi>U</mi>
<mi>S</mi>
<mi>I</mi>
<mi>C</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msup>
<mi>a</mi>
<mi>H</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>U</mi>
<mi>N</mi>
</msub>
<msubsup>
<mi>U</mi>
<mi>N</mi>
<mi>H</mi>
</msubsup>
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</mrow>
Wherein, PMUSIC(θ) is spatial spectrum search function, and a (θ) is steering vector, UNFor noise subspace, H is conjugate transposition.
6. a kind of estimation device of coprime array switching DOA estimation method for even linear array for described in claim 1, its
It is characterized in that, the estimation device includes：External RAM, digital signal processor and output driving and display circuit,
Signal, relatively prime integers will be received to M, N is stored in external RAM, then is input in real time in the digital signal processor；
By the internal core algorithm of the digital signal processor, covariance estimation is carried out to signal, is carried using independent matrix
Continuous auto-correlation is taken, DOA is estimated by improved MUSIC algorithms, is finally shown by output driving and its display module is shown
Show identification DOA situations.
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