CN104931937B - Based on the normalized Subarray rectangular projection Beamforming Method of covariance matrix - Google Patents
Based on the normalized Subarray rectangular projection Beamforming Method of covariance matrix Download PDFInfo
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- CN104931937B CN104931937B CN201510209368.3A CN201510209368A CN104931937B CN 104931937 B CN104931937 B CN 104931937B CN 201510209368 A CN201510209368 A CN 201510209368A CN 104931937 B CN104931937 B CN 104931937B
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Abstract
The normalized Subarray rectangular projection Beamforming Method of covariance matrix is based on the invention discloses one kind.It can effectively suppress interference using the present invention, and the main lobe of adaptive direction figure can be made conformal and secondary lobe reduction, and higher output SINR and faster convergence rate can be obtained.The present invention receives signal to Subarray first and is normalized, and calculates corresponding normalization sample covariance matrix；Then interference signal source number is estimated using MDL criterions, and then obtains interference space；Static weight vector is finally projected into the orthogonal complement space of interference space and adaptive weight vector is obtained.
Description
Technical field
The present invention relates to array signal process technique field, and in particular to one kind is based on the normalized submatrix of covariance matrix
Level rectangular projection Beamforming Method.
Background technology
Array signal processing is an important branch of field of signal processing, and it is in radar, sonar, communication, navigation, earthquake
Monitoring, Speech processing and biomedical engineering etc. are widely used.Adaptive beamformer is array signal
An important research content in processing, it is substantially exactly, by adaptive weighted to each array element, airspace filter to be carried out, so as to reach
To enhancing desired signal, suppression interference signal and the purpose for weakening noise signal.Minimum variance is undistorted, and response (MVDR) is one
The more commonly used algorithm is planted, it is 1 by constraining array gain in desired signal direction, and makes array output power minimum, from
And reach the purpose for suppressing interference.Covariance matrix (SMI) algorithm of inverting is a kind of conventional method for realizing MVDR algorithms, but
In relatively low snap, the output SINR (Signal to Interference plus Noise Ratio) of this algorithm and the convergence rate of adaptive direction figure are slower.
In actual applications, consider hardware condition and environmental factor, calculate the sampling snap that adaptive weight is used
Number is less.In order in the case of low snap, solve the problem of SMI algorithms are brought, rectangular projection (OP) algorithm has been obtained widely
Using, its essence is in the orthogonal complement space (i.e. noise subspace) that static weight vector is projected to interference space, and then
To adaptive weight vector.In this algorithm, the corresponding characteristic vector of small characteristic value does not participate in the calculating of adaptive weight vector, institute
So that under the conditions of low snap, this algorithm can make output SINR and adaptive direction figure rapidly converge to optimal value.But when OP is calculated
When method is applied to Subarray, the uneven division of submatrix can cause each submatrix noise output power unequal, and then can influence MDL
The accuracy of criterion estimation, so as to cause the interference space of estimation inaccurate, causes adaptive direction figure main lobe to deform and other
Valve is raised, and exports SINR degradations.
The content of the invention
In view of this, it is based on the normalized Subarray rectangular projection Wave beam forming of covariance matrix the invention provides one kind
Method, can effectively suppress interference, and the main lobe of adaptive direction figure can be made conformal and secondary lobe reduction, and can obtain higher
Export SINR and faster convergence rate.
The present invention's is walked based on the normalized Subarray rectangular projection Beamforming Method of covariance matrix, including as follows
Suddenly：
Step 1, receive signal to Subarray to be normalized, calculate the interference-plus-noise covariance square after normalization
Battle array Rsub_norm：Wherein, Rin_subFor the covariance matrix of Subarray；TLFor normalized moments
Battle array：Wherein, L is submatrix number,wi
For the weight coefficient of i-th of array element, U=N0+N1+…+Nl-1-J0-J1-…-Jl-1+ 1, Q=N0+N1+…+Nl-J0-J1-…-
Jl-1, NiThe array number included for i-th (0≤i≤L-1) individual submatrix, JiFor i-th (0≤i≤L-2) individual submatrix and i+1 height
The overlapping array number of battle array；(·)HRepresent complex conjugate transposition；
Step 2, interference space is estimated using MDL criterions：
Step 2.1, to the interference plus noise covariance matrix R after normalizationsub_normEigenvalues Decomposition is carried out, feature is obtained
Value and its corresponding characteristic vector, and characteristic value is carried out to descending arrangement；
Step 2.2, using MDL criterions estimate interference signal source number be P, then in step 2.1 characteristic vector preceding P
Individual Column vector groups are into interference space；
Step 3, the interference space estimated using step 2, using rectangular projection Adaptive beamformer method, is solved
Go out adaptive weight vector；
Step 4, the adaptive weight vector obtained using step 3, is weighted processing to the echo data of reception, is derived from
Adapt to wave beam.
Beneficial effect：
The present invention solve Subarray partition it is uneven and it is relatively low sampling snap in the case of, traditional Subarray is just traded
The interference space of shadow algorithm estimation is inaccurate, and interfering to be effectively suppressed, and the main lobe of adaptive direction figure becomes
The problem of shape, secondary lobe are raised, can effectively complete Subarray Adaptive beamformer, in the formation zero of interference radiating way adaptively
Fall into, and cause the main lobe of adaptive direction figure conformal and secondary lobe reduction while effective suppression interference, the present invention is adaptive
There is higher output Signal to Interference plus Noise Ratio after Wave beam forming processing, and output Signal to Interference plus Noise Ratio has faster convergence rate.
Brief description of the drawings
Fig. 1 is flow chart of the present invention.
Fig. 2 is the inventive method and improves front method adaptive direction figure comparison diagram (when fast umber of beats is 2 times of submatrix numbers).
Fig. 3 is that (fast umber of beats is 10 times of submatrix numbers to the inventive method with front method adaptive direction figure comparison diagram is improved
When).
Fig. 4 is that the inventive method exports SINR with fast umber of beats change curve comparison diagram with improving front method.
Fig. 5 is that the inventive method exports SINR with beam position change curve comparison diagram with improving front method.
Embodiment
The present invention will now be described in detail with reference to the accompanying drawings and examples.
The normalized Subarray rectangular projection Beamforming Method of covariance matrix is based on the invention provides one kind, first
Signal is received to Subarray to be normalized, and calculates corresponding normalization sample covariance matrix；Then MDL is utilized
Criterion estimates interference signal source number, and then obtains interference space；Static weight vector is finally projected into interference space
The orthogonal complement space and obtain adaptive weight vector.Subarray partition it is uneven and it is relatively low sampling snap in the case of, the present invention
Interference can effectively be suppressed, and the main lobe of adaptive direction figure can be made conformal and secondary lobe reduction, and higher output can be obtained
SINR and faster convergence rate.The flow of the present invention is as shown in figure 1, comprise the following steps that：
Step 1: constructing normalized Subarray covariance matrix
1. the foundation of signal model
Assuming that an arrowband linear array, common N number of array element, array element is isotropism, and P interference signal, interference signal is remote
Field narrow band signal, it is assumed that each array element noise is space-time white noise separate, that power is equal and interference signal and noise are mutual
It is uncorrelated.Then array received to signal model be represented by
Xin(t)=AS (t)+N (t) (1)
In formula, A=[a (θ1),a(θ2),…a(θP)] it is array manifold matrix, a (θi) (i=1,2 ... P) believe for interference
Number steering vector, if the spacing of n-th of array element and reference point be dn(n=0,1,2 ..., N-1), generally using the 0th array element as
Reference point, now d0=0, λ are wavelength, thenθi(i=1,2 ... P) be
The incident angle of interference signal, []TFor matrix transposition, S (t)=[S1(t),S2(t),…Sp(t)]T, Si(t) (i=1,2 ...
P it is) complex envelope of i-th of interference signal, N (t)=[n1(t),n2(t),…,nN(t)] it is background white noise.
It is so as to obtain array covariance matrix
Rin=E { Xin(t)Xin H(t)} (2)
In formula, E { } represents mathematic expectaion, ()HRepresent complex conjugate transposition.
In practical application, according to maximal possibility estimation criterion, by limited snapshot data Xin(ti) estimate array covariance
Matrix, is obtained
In formula, Xin(ti) be i (i=1,2 ..., K) moment array sampled value, K is the fast umber of beats of sampling.
When Subarray is handled, array is divided into L submatrix, and (L >=P+1), can be non-overlapped submatrix or overlapping
Submatrix, submatrix transition matrix is represented by
T=φ0WT0 (4)
WhereinThe effect of phase shifter is represented, if beam position
It is identical with desired signal direction；W=diag (wn)N=0,1 ..., N-1, wherein wnFor the weight coefficient of n-th of array element, for the side of suppression
To the sidelobe level of figure；T0Matrix is formed for N × L submatrix, in all elements that its l (l=0,1 ..., L-1) is arranged, only
It is 1 to have the element value corresponding with the array element sequence number of l-th of submatrix, remaining be 0 (in the case of non-overlapped submatrix, T0's
Column vector is mutually orthogonal).
The sampling snap signal then received on Subarray is
Xin_sub(t)=THXin(t) (5)
Then the covariance matrix of Subarray is
2. the normalization of covariance matrix
The output of each submatrix is normalized first, normalization passes through matrix TLComplete
Wherein
U=N0+N1+…+Nl-1-J0-J1-…-Jl-1+1
Q=N0+N1+…+Nl-J0-J1-…-Jl-1
NiThe array number included for i-th (0≤i≤L-1) individual submatrix, JiFor i-th (0≤i≤L-2) individual submatrix and i+1
The overlapping array number of individual submatrix.
Interference plus noise covariance matrix after normalization is
Pass through normalized so that the noise power of each submatrix is consistent, so that MDL criterions can be applicable.
Step 2: estimation interference space
To normalized covariance matrix Rsub_normCarry out Eigenvalues Decomposition
In formula, λi(i=1,2 ..., L) it is covariance matrix Rsub_normCharacteristic value,For with eigenvalue λiCorresponding spy
Levy vector, λiDescending arrangement
The number of interference signal source is estimated using MDL criterions, and then estimates interference space.
The function of MDL criterions is
Wherein
From MDL criterions, when d numerical value change, when formula (11) takes minimum value, corresponding d value is interference letter
The number P in number source, selected characteristic vectorPreceding P Column vector groups into interference space Us, i.e.,By
Mathematical knowledge understands vectorWith vector a (θ1),a(θ2),…,a(θp) open into same vector space, i.e.,：
Wherein, span { } represents the space of vector,As interference space is estimated
Meter.
Step 3: solving the adaptive weight vector of innovatory algorithm
The interference space estimated using step 2, using rectangular projection Adaptive beamformer method, is solved and changed
Enter the adaptive weight vector of algorithm.
The thought of algorithm is thrown using conventional orthogonal, by static weight vector wq_subThe interference space estimated into step 2
UsOrthogonal complement space projection, the adaptive weight vector for obtaining innovatory algorithm is
In formula, I is that L × L ties up unit matrix, and η is a constant, wq_subFor static weight vector, and each element is 1 L dimensions
Column vector,Effect be make antenna main beam direction gain keep it is constant.
Step 4, Adaptive beamformer is carried out to the echo received
After adaptive weight vector is obtained, processing can be weighted to the echo data of reception：
Y=WHX(t) (13)
In formula, X (t) is the echo-signal received, and noise is disturbed and weaken so as to effectively removes, and letter is expected in enhancing
Number.
Since then, just complete a kind of based on the normalized sub- Adaptive beamformer of Subarray rectangular projection of covariance matrix
Processing of the method to echo data.
It is proposed by the present invention a kind of based on the normalized adaptive ripple of Subarray rectangular projection of covariance matrix in order to verify
Beam forming method, carries out the emulation of adaptive beam directional diagram and output Signal to Interference plus Noise Ratio (SINR), and emulation uses arrowband uniform line
Battle array, simulation parameter is as shown in table 1.Algorithm is the sampling snap signal of Subarray directly using rectangular projection (OP) algorithm before improving
Calculate adaptive weight vector.
The simulation parameter of table 1 is set
Fig. 2 and Fig. 3 are the comparison (emulation 1 of adaptive beam directional diagram of the innovatory algorithm of the present invention with improving preceding algorithm
It is secondary), fast umber of beats of sampling is respectively 20 and 100, and beam position angle is 0 °, it can be seen that it is adaptive that the preceding algorithm of improvement is obtained
Answer the deformation of beam pattern main lobe and sidelobe level is seriously raised；The adaptive beam major lobe of directional diagram that algorithm is obtained after improvement is protected
Shape and sidelobe level is relatively low, close to static beam pattern, performance is greatly improved compared with before-improvement.
Fig. 4 is that desired signal angle is 0 °, and input signal-to-noise ratio is 0dB, other emulation bars under the conditions of different sampling snaps
The comparison of the output Signal to Interference plus Noise Ratio (SINR) of algorithm before the same Fig. 2 of part, innovatory algorithm of the present invention and improvement.Can by simulation result
Know, the output SINR of algorithm is higher after improvement, and restrain quickly；And the output SINR of algorithm is relatively low before improving, convergence is slower, and
With the increase of fast umber of beats, output SINR has declined, because fast umber of beats of sampling is higher, the accuracy of the interference space of estimation
Reduction, interference can not be effectively suppressed, and cause the SINR of output can degradation.
Fig. 5 is innovatory algorithm of the present invention and the output Signal to Interference plus Noise Ratio for improving preceding algorithm in different beams orientation angle
(SINR) comparison, input signal-to-noise ratio is 0dB, other same Fig. 2 of simulated conditions, it can be seen that algorithm can effectively suppress after improvement
Interference, and the SINR of output is higher.
It can be obtained from Fig. 2~Fig. 5, innovatory algorithm of the present invention can strengthen desired signal, with good anti-interference
Can, it is a kind of sane Subarray adaptive beam-forming algorithm.
In summary, presently preferred embodiments of the present invention is these are only, is not intended to limit the scope of the present invention.
Within the spirit and principles of the invention, any modification, equivalent substitution and improvements made etc., should be included in the present invention's
Within protection domain.
Claims (1)
1. one kind is based on the normalized Subarray rectangular projection Beamforming Method of covariance matrix, it is characterised in that including such as
Lower step：
Step 1, receive signal to Subarray to be normalized, calculate the interference plus noise covariance matrix after normalization
Rsub_norm：Wherein, Rin_sub is the covariance matrix of Subarray；TL is normalization matrix：Wherein, L is submatrix number,
<mrow>
<msub>
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<mo>=</mo>
<mfenced open='{' close=''>
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<mi>&Sigma;</mi>
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</mrow>
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</msub>
</munderover>
<msubsup>
<mi>w</mi>
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</msubsup>
<mo>)</mo>
</mrow>
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<mo>/</mo>
<mn>2</mn>
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<mi>l</mi>
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Wi is
The weight coefficient of i-th of array element, U=N0+N1+ ...+Nl-1-J0-J1- ...-Jl-1+1, Q=N0+N1+ ...+Nl-J0-J1- ...-Jl-1,
Ni is the array number that i-th (0≤i≤L-1) individual submatrix is included, and Ji is i-th (0≤i≤L-2) individual submatrix and i+1 submatrix
Overlapping array number；() H represents complex conjugate transposition；
Step 2, interference space is estimated using MDL criterions：
Step 2.1, to the interference plus noise covariance matrix R after normalizationsub_normCarry out Eigenvalues Decomposition, obtain characteristic value and
Its corresponding characteristic vector, and characteristic value is carried out to descending arrangement；
Step 2.2, using MDL criterions estimate interference signal source number be P, then in step 2.1 characteristic vector it is preceding P arrange
Vector composition interference space；
Step 3, the interference space estimated using step 2, using rectangular projection Adaptive beamformer method, solution is come from
Adapt to weight vector；
Step 4, the adaptive weight vector obtained using step 3, processing is weighted to the echo data of reception, obtains adaptive
Wave beam.
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| CN106054142B (en) * | 2016-05-13 | 2018-08-03 | 西安电子科技大学 | A kind of airborne MIMO radar main lobe smart munition suppressing method and system |
| CN106199547B (en) * | 2016-06-30 | 2019-01-11 | 西安电子科技大学 | Weak target detection method at a slow speed based on external illuminators-based radar |
| CN107064884B (en) * | 2017-01-05 | 2020-01-31 | 西安电子科技大学 | Self-adaptive beam forming method based on regular overlapping subarrays |
| CN116112323B (en) * | 2021-11-10 | 2024-06-07 | 大唐移动通信设备有限公司 | Interference suppression method, device, equipment and storage medium |
| CN114609651B (en) * | 2022-03-28 | 2023-06-16 | 电子科技大学 | Space domain anti-interference method of satellite navigation receiver based on small sample data |
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| CN102830387B (en) * | 2012-08-23 | 2014-05-07 | 北京理工大学 | Data preprocessing based covariance matrix orthogonalization wave-beam forming method |
| CN103885045B (en) * | 2014-04-09 | 2016-02-10 | 西安电子科技大学 | Based on the circulation associating Adaptive beamformer method of Subarray partition |
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