CN107330425A - A kind of robust array beamses forming method perceived based on compression covariance matrix - Google Patents
A kind of robust array beamses forming method perceived based on compression covariance matrix Download PDFInfo
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Abstract
A kind of robust array beamses forming method perceived based on compression covariance matrix, the present invention relates to the robust array beamses forming method perceived based on compression covariance matrix.The present invention is modeled as existing beamforming algorithm beam space under the conditions of SIRV models and non-ideal compressed sensing to solve array error and composes main secondary lobe than not high, and Adaptive beamformer exports the problem of SINR value is low.The present invention includes：One：Construct signal covariance matrix RxExpression formula, solve signal covariance matrix R using sample covariance matrix and signal guide vector matrix and interference steering vector matrix, and using beam space methodx；Two：Optimize and solve robust adaptive beamforming algorithm model, obtain Beam-former weight w；Three：By signal covariance matrix RxBeam-former weight w is as initial value iteration optimization, until convergence, obtains final Beam-former weight wopt.The present invention is used for intelligent antenna technology field.
Description
Technical field
The present invention relates to intelligent antenna technology field, and in particular to robust array beamses forming method.
Background technology
For decades, Adaptive beamformer technology has attracted the sight of many researchers, this technology extensive use
In radar, communication, navigation, aerospace and biomedicine.According to the difference of computational methods, Adaptive beamformer technology is generally
Two classes can be divided into.One class is the algorithm based on reference signal, such as LMS algorithm (Widrow B, Mantey P E, Griffiths
L J,and Goode B B.Adaptive antenna systems.Proc.IEEE,1967,55:2143-2159.Gitlin
R D,Weinstein S D.On the design of gradient algorithms for digitally
implemented adaptive filters.IEEE Trans on CT,1973,2:125-136.[3]Nagumo J I,
and Noda A.A learning method for system identification.IEEE
Trans.Autom.Control,1967,12:282-287) with DMI algorithms (Albert A E, and Gardner L
S.Stochastic Approximation and Nonlinear Regression.MIT Press.1967.Widrow B,
MeCool J,Ball M.The complex LMS algorithm.Proceedings of the IEEE,1975,4(63):
719-720.).Another kind of is the algorithm estimated based on DOA, the MVDR beamforming algorithms (Dentino that such as Capon is proposed
M,McCool J,etc.Adaptive filtering in the frequency domain[J].IEEE Proc,1978,
12(66):1658-1659), LCMV algorithms (Xiaofei Zhang, Dazhuan Xu.Frequency Domain LMS
Based Adaptive Beamforming Algorithm.Chinese Space Science and
Technology.2005,2:41-58) and MSC algorithms (Reed I S.Rapid convergence rate in
adaptive antenna.Aerospace and Electronic Systems,1974,10(6):853-863).However, examining
Consider actual conditions, real system has various errors and non-ideal factor (O.Besson and P.Stoica.Decoupled
estimation of doa and angular spread for a spatially distributed source.IEEE
Transaxtions on Signal Processing,2000,48:1872-1882), this requires algorithm to have enough Shandongs
Rod.Document (S.A.Vorobyov, Y.Rong, A.B.Gershman.Robust adaptive beamforming using
probability-constrained optimization.In Proceedings of IEEE Workshop on
Statistical Signal Processing.2005:934-939.S.A.Vorobyov,Y.C.Eldar,
A.Nemirovski,and A.B.Gershman.Probability-constrained approach to estimation
of random gaussian parameters.In Proceedings of First IEEE Inter.Workshop on
Computational Advances in Multi-Sensor Adaptive Processing,2005:101-
104.S.A.Vorobyov,Y.C.Eldar,A.Nemirovski,and A.B.Gershman.Probabilistically-
constrained estimation random parameters with unknown distribution.In
Proceedings of 4th IEEE Sensor Array and Multi-channel Signal Processing
Workkshop,SAM'06,2006:Proposed in 54-57) estimation gaussian random parameter or robust adaptive beamforming it is general
Rate constrained procedure.Document (C é sar C.Gaudes, Ignacio Santamar í a, Javier V í a.Robust Array
Beamforming With Sidelobe Control Using Support Vector Machines[J].IEEE
Transactions on Signal Processing,2007,55(2):574-584.Manel Martínez-Ramón,
Christos Christodoulou.Support Vector Machines for Antenna Array Processing
and Electromagnetics[M].Morgan&Claypool Publishers,2006,ch3:33-40.Amina El
Gonnouni,Manel Martínez-Ramón,JoséLuis Rojo-A Support Vector Machine
MUSIC Algorithm[J].IEEE Transactions on Antennas and Propagation,2012,60(10):
4901-4910) SVMs (the support vector machines, SVM) is applied and formed in robust array beamses
In.In some scenes, compressed sensing can substantially reduce traffic load, and this technology is effectively utilized sparse signal and with one
Individual sample frequency sampling (ALI CAFER GURBUZ, VOLKAN CEVHER, JAMES far below Nyquist rate
H.McCLELLAN.Bearing Estimation via Spatial Sparsity using Compressive
Sensing.IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS.2012,2(48):
1358-1369.Jian Jin,Yuantao Gu,and Shunliang Mei.A Stochastic Gradient
Approach on Compressive Sensing Signal Reconstruction Based on Adaptive
Filtering Framework.IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL
PROCESSING.2010,4(2):409-420.Emmanuel J.Candès,Michael B.Wakin.An
Introduction to Compressive Sampling.IEEE SIGNAL PROCESSING MAGAZINE.2008,
(3):21-30).Candes is in document (E Candes.Compressive sampling [A] .Proceedings of the
International Congress of Mathematicians[C].Madrid,Spain,2006,3:In 1433-1452)
If it is sparse in an orthogonal intersection space to demonstrate signal, then this signal can be sampled with low frequency but can be with the extensive of high probability
It is multiple.Document (E Candes, J Romberg, Terence Tao.Robust uncertainty principles:Exact
signal reconstruction from highly incomplete frequency information[J].IEEE
Trans.on Information Theory,2006,52(2):489-509.E Candès.The restricted
isometry property and its implications for compressed sensing[J].Acadèmie des
sciences,2006,346(I):In 598-592), the sufficient and necessary condition that Candes demonstrates this restoration methods presence is
Perceive matrix and meet RIP (Restricted Isometry Property).Based on MP algorithms, OMP (J A Tropp and A
C Gilbert.Signal Recovery from Partial Information by Orthogonal Matching
Pursuit[OL].April2005,www.personal.umich.edu/_jtropp/papers/TG05-Signal-
Recovery.pdf), TMP (C La, M N Do.Signal reconstruction using sparse tree
representation[A].Proceedings of SPIE[C].San Diego,CA,United States:
International Society for Optical Engineering.2005.5914:1-11) and StOMP (D L
Donoho,Y Tsaig,I Drori,etc.Sparse solution of underdetermined linear
equations by stagewise orthogonal matching pursuit[R].Technical Report,2006)
It is suggested in succession etc. various signal recovery algorithms.However, in some scenes, compressed sensing matrix is simultaneously unsatisfactory for RIP, and this is claimed
For non-ideal compressed sensing.
The content of the invention
The invention aims to solve array error to be modeled as under the conditions of SIRV models and non-ideal compressed sensing now
There is beamforming algorithm beam space to compose main secondary lobe than not high, and Adaptive beamformer exports the problem of SINR value is low, and
Propose a kind of robust array beamses forming method perceived based on compression covariance matrix.
A kind of robust array beamses forming method perceived based on compression covariance matrix is comprised the following steps：
Step one：Sampling front-rear space smooth algorithm and MUSIC algorithms estimation signal and interference radiating way, build signal and lead
To vector matrix and interference steering vector matrix；
Step 2：Construct signal covariance matrix RxExpression formula, built using sample covariance matrix and step one
Signal guide vector matrix and interference steering vector matrix, and solve signal covariance matrix R using beam space methodx；
Step 3：Set up robust adaptive beamforming algorithm model；
Step 4：The signal guide vector matrix and interference steering vector matrix and step 2 built using step one is obtained
Signal covariance matrix Rx, optimize the robust adaptive beamforming algorithm model that simultaneously solution procedure three is set up, obtain wave beam
Shaper weight w；
Step 5：The signal covariance matrix R that step 2 is obtainedxAnd the Beam-former weight w that step 4 is obtained is made
For initial value iteration optimization, until restraining, final Beam-former weight w is obtainedopt。
Beneficial effects of the present invention are：
In the present invention, the error modeling for being directed to vector is the constant random vector of ball (spherically invariant
Random vector, SIRV), for the directional interference of direction time-varying, it is proposed that the inventive method.First, when setting up direction
Become interference and SIRV array error models, give the signal model expression formula under conditions of Signal Compression.Adaptive beam shape
Estimated data or interference covariance matrix are generally wanted into method, and when compressed sensing matrix and when being unsatisfactory for RIP, it is impossible to accurate weight
Signal is built, therefore is difficult to obtain accurate interference covariance matrix.Therefore, the thought that compression covariance matrix is perceived is introduced,
And SVR and the Beamforming Method based on probability constraintses are combined, give the SVM- probability perceived based on compression covariance matrix
Constrain the optimization problem expression formula of robust array beamses formation.By contrasting the simulation analysis result of several distinct methods, show
Institute's extracting method of the present invention has preferably output Signal to Interference plus Noise Ratio.
Under the conditions of array error is modeled as SIRV and non-ideal compressed sensing, inventive algorithm output signal beam space
Compose main sidelobe level difference big, and with input signal signal to noise ratio (SNR) lifting, Adaptive beamformer output Signal to Interference plus Noise Ratio
(SINR) it is obviously improved compared to other methods, 6dB can be lifted with respect to MVDR algorithms maximum.
Brief description of the drawings
Fig. 1 is SNR distinct methods array pattern comparison diagrams when 20dB, interference are -3 °；SNR is input signal noise
Than SVR is Support vector regression；
Fig. 2 is SNR distinct methods array pattern comparison diagrams when 20dB, interference are -40 °；
Fig. 3 be interference be -3 ° when distinct methods under output signal SINR value with SNR situation of change figure；SINR is output
Signal Signal to Interference plus Noise Ratio；
Fig. 4 be interference be -40 ° when distinct methods under output signal SINR value with SNR situation of change figure.
Embodiment
Embodiment one：It is a kind of based on compression covariance matrix perceive robust array beamses forming method include with
Lower step：
Signal model
The estimation of the covariance matrix of coherent signal and interference is discussed, these signals and interference are by with the equal of N number of array element
Even linear array is received.Array element spacing is d.In t, there are K arrowband coherent signal and P arrowband coherent interference, respectively
It is expressed as s1(t),s2(t),…,sKAnd J (t)1(t),J2(t),…,JP(t), their wavelength is λ.Echo signal incoming wave side
To for θ1,θ2,…,θK, interference radiating way isWherein interference radiating way is time-varying, is represented by：
WhereinThe center of interference radiating way is represented,The absolute magnitude of excursion is represented, rand (t) is represented
The random number of even variation between [- 1,1].In the case where error is not present in the steering vector of array, by array steering vector
It is expressed as a, its expression formula is
A=[1, ej2πdsinθ/λ,…,ej2π(N-1)dsinθ/λ] (2)
Wherein θ is arrival bearing.Then n-th of array element receipt signal model is
In formula, ξn(t) it is the noise item of n-th of array element, is that average is that zero variance isWhite Gaussian noise.Signal source and
Interference source distance arrays are remote enough, therefore can regard plane wave as.
In invention, it is considered to which the steering vector of array has error, and the error meets SIRV
(Spherically Invariant Random Vector) model.It is assumed that it is 0 that error z, which obeys average, variance isSIRV
Distribution, has
SIRV is described as independent multiple Gauss vector δ~N that a positive stochastic variable τ root mean square and a M are tieed up in formula
(0M, C) product, have
Then array array steering vector is rewritable into a+z.
Consider under conditions of Signal Compression, n-th of array element is received into signal and is write as vector xn, its expression formula is
It is t comprising the time started0, NtIndividual sample, sampling rate is FS, wherein FSLess than Nyquist sampling frequency.Using
Compression sensing method, can be by each array element signals xnLinear projection is to another group of base vector φnmIn, m=1,2 ..., M, length is
Nt, matrix form can be written as：
yn=Φnxn=ΦnΨnΘ (7)
In formula, vector theta represents orientation sample, is combined into by discrete angular collection, ΨnFor wordbook, its column vector is believed for source
Number time-varying part, corresponding angle set Θ index, ΦnIt is φ for a column vectornmM × NtCalculation matrix is tieed up, and has M
×Nt.Consider matrix ΦnIt is unsatisfactory for RIP (J A Tropp and A C Gilbert.Signal Recovery from
Partial Information by Orthogonal Matching Pursuit[OL].April2005,
Www.personal.umich.edu/_jtropp/papers/TG05-Signal-Recove ry.pdf) situation, then its be
Non-ideal compressed sensing, signal (the J A Tropp and A C Gilbert.Signal that can not now rebuild completely before compression
Recovery from Partial Information by Orthogonal Matching Pursuit[OL]
.April2005,www.personal.umich.edu/_jtropp/papers/TG05-Signal-Recovery.pdf)。
Under these conditions, it is considered to Adaptive beamformer problem.According to classical Adaptive beamformer method
(Widrow B,MeCool J,Ball M.The complex LMS algorithm.Proceedings of the IEEE,
1975,4(63):719-720.Dentino M,McCool J,etc.Adaptive filtering in the frequency
domain[J].IEEE Proc,1978,12(66):1658-1659), optimization problem can be written as：
The Adaptive beamformer method of the SVM- probability constraintses perceived based on compression covariance matrix
Adaptive beamformer method generally wants estimated data or interference covariance matrix, and works as compressed sensing matrix not
When meeting RIP, it is impossible to accurate reconstruction signal, therefore it is difficult to obtain accurate interference covariance matrix.In this case, it is of the invention
Employ document (Ahmed O.Nasif, Zhi Tian, Qing Ling.High-dimensional Sparse
Covariance Estimation for Random Signals.Daniel Romero,Geert Leus.Compressive
Covariance Sampling) in compression covariance matrix perceive thought, the covariance matrix of estimation is expressed as：
In formula, RiI-th of the interference covariance matrix (i=0 ..., I-1) estimated is represented, I represents the association side of estimation
The total number of poor matrix,Represent the weight of linear combination.
In order to improve the robustness under the conditions of array error and control sidelobe level amplitude, document (Manel Mart í nez-
Ramón,Christos Christodoulou.Support Vector Machines for Antenna Array
Processing and Electromagnetics[M].Morgan&Claypool Publishers,2006,ch3:33-40)
Middle use SVR-MVDR methods.In document ([S.A.Vorobyov, Y.Rong, A.B.Gershman.Robust adaptive
beamforming using probability-constrained optimization.In Proceedings of IEEE
Workshop on Statistical Signal Processing.2005:934-939.S.A.Vorobyov,
Y.C.Eldar,A.Nemirovski,and A.B.Gershman.Probability-constrained approach to
estimation of random gaussian parameters.In Proceedings of First IEEE
Inter.Workshop on Computational Advances in Multi-Sensor Adaptive Processing,
2005:In 101-104), it is contemplated that when array steering vector error modeling is that random Gaussian is distributed, apply based on probability constraintses
Adaptive beamformer method.With reference to both approaches, and the thought perceived using compression covariance matrix, it is of the invention by Shandong
The Adaptive beamformer method of rod is written as optimization problem：
In formula, Pr () is probable value, and w is MVDR Beam-former weights, RxFor data covariance matrix,To be oriented to matrix, y is mapping value vector, includingSituation.
Because z obeys SIRV distributions, have：
Obviously, the probability constraintses in formula (10) are w non-convex complex function, then the optimization problem in formula (10) is also difficult to resolve
Non-convex optimization problem.Therefore, can by convex approximate method (S.A.Vorobyov, Y.Rong,
A.B.Gershman.Robust adaptive beamforming using probability-constrained
optimization.In Proceedings of IEEE Workshop on Statistical Signal
Processing.2005:934-939) simplify constraint, have：
Then optimization problem is converted to：
According toReal part and imaginary part are met respectively
By document (S.A.Vorobyov, Y.Rong, A.B.Gershman.Robust adaptive beamforming
using probability-constrained optimization.In Proceedings of IEEE Workshop on
Statistical Signal Processing.2005:934-939) understand, the optimization problem of formula (13) is exactly that convex optimization is asked
Topic.
There is identical structure in view of two probability constraintses in formula (13) optimization problem, only need to analyze one of them.For
Optimal solution is obtained, problem is converted into following form：
It is assumed that z Follow Weibull Distributions and its probability density function is：
Probability-distribution function is：
Substitution formula (15), is obtained：
This method is applied in second constraint, the determination expression formula of second constraint can be obtained.Then whole optimization problem
It can be written as：
Using Cauchy Schwartz inequality, have：
|wH(a+z)|≥||wHa|-|wHz|| (20)
Then：
Formula (21) can regard as Pr (| wH(a+z) | >=1) lower bound.Probability constraintses are replaced with the lower bound, then in formula (10)
Optimization problem can be written as：
According toWe haveNormalize wHZ, is obtained：
It is assumed that z is Weibull distributions, as one kind of SIRV non-gaussian distribution, then wHZ also Follow Weibull Distributions.And
When form parameter is 2, wHZ is changed into rayleigh distributed.When form parameter is not 2, probability density function is formula (16), probability point
Cloth function is formula (17).
Then have：
Convolution (24) and formula (25) can obtain below qualitative constraint really：
Or, more compactly, have
Because the change of w phases has no effect on the cost function of formula (24), then w may be selected following formula is set up：
Then probability constrained problems can be converted into：
In order to solve this problem, second order cone optimization method can be used.
Defined variable t is allowed to meet：
Constraints in probability constrained problems (29) can be converted into：
Have：
Then optimization problem (29) can be converted into：
If t, it is known that and meet t ＞ 0, formula (33) is a second order cone optimization problem.If t can be calculated most
Figure of merit topt, solution formula (33) is then substituted into, best initial weights are with regard to that can obtain.Asked used here as a simple approximation method
Solve topt。
According to following publicity：
It is a t upper bound to understand 1- α, it is replaced t, in the hope of (33) and then can obtain best initial weights solution.
Due to optimal value toptCertain small boundary thereon.In order to more accurately be solved, using the method for iteration.
Initialization：Weights are obtained using second order cone optimization method and are treated as initial value w0。
Iterative process：The w obtained by formula (33)k-1Estimation is worth to the t of renewalk
Utilize tkSolving-optimizing problem (33).Repeat the above steps until convergence.
Although tk＞ 0, but estimate wk, k=1,2 ... still may not be in feasible zone, when this is due to each iteration, only
Have：
It is met.
The present invention proposes algorithm combination SVR optimizations and optimized with probability constraintses, and is perceived using based on compression covariance matrix
Thought wave beam null width is carried out it is optimal widen, it is final to improve so as to realize the optimal construction to interference covariance matrix
Export Signal to Interference plus Noise Ratio.Step is as follows：
Step one：Using front-rear space smooth algorithm and MUSIC algorithms estimation signal and interference radiating way, build signal and lead
To vector matrix and interference steering vector matrix；
Step 2：Construct signal covariance matrix RxExpression formula, built using sample covariance matrix and step one
Signal guide vector matrix and interference steering vector matrix, and solve signal covariance matrix R using beam space methodx；
Step 3：Set up robust adaptive beamforming algorithm model；
Step 4：The signal guide vector matrix and interference steering vector matrix and step 2 built using step one is obtained
Signal covariance matrix Rx, optimize the robust adaptive beamforming algorithm model that simultaneously solution procedure three is set up, obtain wave beam
Shaper weight w；
Step 5：The signal covariance matrix R that step 2 is obtainedxAnd the Beam-former weight w that step 4 is obtained is made
For initial value iteration optimization, until restraining, final Beam-former weight w is obtainedopt。
Embodiment two：Present embodiment from unlike embodiment one：Letter is constructed in the step 2
Number covariance matrix RxExpression formula be specially：
Wherein RiI-th of the covariance matrix estimated is represented, i=0 ..., I-1, I represent the covariance matrix of estimation
Total number,Represent the weight of linear combination.
With formula (9) and document (Ahmed O.Nasif, Zhi Tian, Qing Ling.High-dimensional
Sparse Covariance Estimation for Random Signals.Daniel Romero,Geert
Leus.Compressive Covariance Sampling) in method construct sample covariance matrix.
Other steps and parameter are identical with embodiment one.
Embodiment three：Present embodiment from unlike embodiment one or two：Ripple described in step 2
Wave beam subspace number and beam angle in beam space law are specially：
Wherein RnumberFor wave beam subspace number, RnullFor beam angle, pmaxMain lobe value, p are composed for beam spacesubmaxFor
Beam space composes maximum side petal.
Other steps and parameter are identical with embodiment one or two.
Embodiment four：Unlike one of present embodiment and embodiment one to three：The step 3
In set up robust adaptive beamforming algorithm model and be specially：
Wherein Pr (| wH(a+z) | >=1) it is probable value, w is Beam-former weights, wHIt is w conjugate transposition, RxFor letter
Number covariance matrix,For steering vector matrix, y is mapping value vector, includingFeelings
Condition, a is array steering vector, and z is array steering error, and α is factor of influence (artificial to set, value is 0.3-0.5),
Subject to implication is " being satisfied with it ".
Other steps and parameter are identical with one of embodiment one to three.
Embodiment five：Unlike one of present embodiment and embodiment one to four：The step 4
The signal covariance that the signal guide vector matrix and interference steering vector matrix and step 2 that middle utilization step one is built are obtained
Matrix Rx, optimize the robust adaptive beamforming algorithm model that simultaneously solution procedure three is set up, obtain Beam-former weight w
Detailed process is：
Step 4 one：Using the MVDR Beamforming Methods optimized based on SVM, Beam-former weight w is tried to achieve, and will ask
The Beam-former weight w obtained is used as initial value w0；MVDR is minimum variance distortionless response；
Step 4 two：If k>1 is kth time iteration, wkFor the result of kth time iteration, intermediate variable t is defined,tkFor the intermediate variable of kth time iteration；
If wk-1MeetThen pass throughMeter
Calculate tk；
If wk-1It is unsatisfactory forConstant beta >=1 is then selected, makes β wk-1MeetAnd use β wk-1Substitute wk-1Substitute intoCalculate tk；
WhereinFor Weibull probability-distribution functions,For SIRV ((spherically invariant
Random vector, SIRV)) distribution variance,It is wkConjugate transposition；
Step 4 three：Work as tk＞ 0, then utilizeSolve
wk, by wkIt is used as new wk-1, step 4 two and step 4 three are re-executed, until wkConvergence, obtains final iteration result
wmid；
Work as tk≤ 0, perform step 4 four；
Step 4 four：By diagonal loading algorithm and appropriate load factor is selected to obtain wmid。
Other steps and parameter are identical with one of embodiment one to four.
Embodiment six：Unlike one of present embodiment and embodiment one to five：The step 5
The middle signal covariance matrix R for obtaining step 2xAnd the Beam-former weight w that step 4 is obtained is excellent as initial value iteration
Change, until convergence, obtains final Beam-former weight woptDetailed process be：
Step 5 one：If l is the l times iteration,For RxThe result of the l times iteration, wlFor the result of the l times iteration, if
Put initial valueFor the R obtained by step 2x, initial value w(0)The w obtained for step 4mid；
Step 5 two：UtilizeAnd formulaTry to achieve w(l+1)；Utilize w(l+1)、And formulaTry to achievePath optimizing is：
Step 5 three：Repeat step five or two, until Δ p (w(l+1)) andRestrain, the condition of convergence is：
Wherein δ is convergence factor；
Δp(w(l+1))=p (w(l+1))max-p(w(l+1))submax
Wherein Δ p (w(l+1)) represent p (w in the l+1 times iteration(l+1))maxWith p (w(l+1))submaxDifference, p (w(l+1))max
It is w for Beam-former weights(l+1)When beam space spectrum main lobe value, p (w(l+1))submaxIt is w for Beam-former weights(l+1)
When beam space spectrum maximum side petal,Represent in the l+2 times iterationWith's
Difference,It is for signal covariance matrixWhen beam space spectrum main lobe value,For signal
Covariance matrix isWhen beam space spectrum maximum side petal.
Other steps and parameter are identical with one of embodiment one to five.
Embodiment one：
In order to verify the validity and superiority of inventive algorithm, emulated, and give conclusion.Simulated conditions
For：Array number is 32, and adjacent array element interval and signal wavelength ratio are 1/2, and degree of rarefication is 8, and original signal strength is 512, pressure
Sample number after contracting is 20, and desired signal direction is 0 °, it is considered to which interference signal direction is -3 ° and -40 ° of both of these cases.
Fig. 1 and Fig. 2 give the contrast of distinct methods array pattern under disturbance direction.From analogous diagram, institute
There is method main lobe direction to be directed to desired signal direction, and null is upwardly formed in disturber.But MVDR beamforming algorithm masters
Secondary lobe is than low, and interference radiating way null is narrower.SVR algorithms and probability constraintses algorithm improve main secondary lobe ratio, but interference radiating way null
It is still narrow.Nulling widening algorithm interference radiating way null has widened one fixed width in both sides to the left and right, not only broadens null width,
Also null depth has been deepened, has coped with the inaccurate situation of interference radiating way estimation, enhance algorithm robustness, but its beam space
The main secondary lobe of spectrum is not than still high.Algorithm is carried for the present invention, simulation result shows, array beamses formation output is met simultaneously
Beam space spectrum main secondary lobe is higher, null wider width and null depth are deeper, thus make an uproar with output letter is dry well
Than.Therefore, we are verified using SINR figures.
Fig. 3 and Fig. 4 give the situation of change of distinct methods output signal SINR value under disturbance direction with SNR.By
Analogous diagram is visible, and inventive algorithm Adaptive beamformer output Signal to Interference plus Noise Ratio (SINR) is obviously improved compared to other methods,
When inputting SNR for 20dB, 6dB can be lifted compared with MVDR algorithms., demonstrate the superiority and validity of optimized algorithm.
The present invention can also have other various embodiments, in the case of without departing substantially from spirit of the invention and its essence, this area
Technical staff works as can make various corresponding changes and deformation according to the present invention, but these corresponding changes and deformation should all belong to
The protection domain of appended claims of the invention.
Claims (6)
1. a kind of robust array beamses forming method perceived based on compression covariance matrix, it is characterised in that：It is described to be based on pressure
The robust array beamses forming method that contracting covariance matrix is perceived comprises the following steps：
Step one：Using front-rear space smooth algorithm and MUSIC algorithms estimation signal and interference radiating way, signal guide arrow is built
Moment matrix and interference steering vector matrix；
Step 2：Construct signal covariance matrix RxExpression formula, the signal built using sample covariance matrix and step one led
Signal covariance matrix R is solved to vector matrix and interference steering vector matrix, and using beam space methodx；
Step 3：Set up robust adaptive beamforming algorithm model；
Step 4：The letter that the signal guide vector matrix and interference steering vector matrix and step 2 built using step one is obtained
Number covariance matrix Rx, optimize the robust adaptive beamforming algorithm model that simultaneously solution procedure three is set up, obtain Wave beam forming
Device weight w；
Step 5：The signal covariance matrix R that step 2 is obtainedxAnd the Beam-former weight w that step 4 is obtained is as initial
It is worth iteration optimization, until convergence, obtains final Beam-former weight wopt。
2. a kind of robust array beamses forming method perceived based on compression covariance matrix according to claim 1, its
It is characterised by：Signal covariance matrix R is constructed in the step 2xExpression formula be specially：
<mrow>
<msub>
<mi>R</mi>
<mi>x</mi>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>I</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<msubsup>
<mi>&sigma;</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
</mrow>
Wherein RiI-th of the covariance matrix estimated is represented, i=0 ..., I-1, I represent total of the covariance matrix of estimation
Number,Represent the weight of linear combination.
3. a kind of robust array beamses forming method perceived based on compression covariance matrix according to claim 2, its
It is characterised by：Wave beam subspace number in beam space method and beam angle described in step 2 are specially：
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mi>n</mi>
<mi>u</mi>
<mi>m</mi>
<mi>b</mi>
<mi>e</mi>
<mi>r</mi>
</mrow>
</msub>
<mo>=</mo>
<munder>
<mi>arg</mi>
<msub>
<mi>R</mi>
<mrow>
<mi>n</mi>
<mi>u</mi>
<mi>m</mi>
<mi>b</mi>
<mi>e</mi>
<mi>r</mi>
</mrow>
</msub>
</munder>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
<mo>&lsqb;</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>s</mi>
<mi>u</mi>
<mi>b</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mi>n</mi>
<mi>u</mi>
<mi>l</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>=</mo>
<munder>
<mi>arg</mi>
<msub>
<mi>R</mi>
<mrow>
<mi>n</mi>
<mi>u</mi>
<mi>l</mi>
<mi>l</mi>
</mrow>
</msub>
</munder>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
<mo>&lsqb;</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>p</mi>
<mrow>
<mi>s</mi>
<mi>u</mi>
<mi>b</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
</mrow>
Wherein RnumberFor wave beam subspace number, RnullFor beam angle, pmaxMain lobe value, p are composed for beam spacesub maxFor wave beam
Spatial spectrum maximum side petal.
4. a kind of robust array beamses forming method perceived based on compression covariance matrix according to claim 3, its
It is characterised by：Robust adaptive beamforming algorithm model is set up in the step 3 is specially：
<mrow>
<munder>
<mi>min</mi>
<mrow>
<mi>w</mi>
<mo>,</mo>
<msub>
<mi>R</mi>
<mi>x</mi>
</msub>
</mrow>
</munder>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msup>
<mi>w</mi>
<mi>H</mi>
</msup>
<msub>
<mi>R</mi>
<mi>x</mi>
</msub>
<mi>w</mi>
<mi> </mi>
<mi>s</mi>
<mi>u</mi>
<mi>b</mi>
<mi>j</mi>
<mi>e</mi>
<mi>c</mi>
<mi>t</mi>
<mi> </mi>
<mi>t</mi>
<mi>o</mi>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mi>W</mi>
<mi>H</mi>
</msup>
<mi>A</mi>
<mo>=</mo>
<mi>y</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>Pr</mi>
<mrow>
<mo>(</mo>
<mo>|</mo>
<mrow>
<msup>
<mi>w</mi>
<mi>H</mi>
</msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>a</mi>
<mo>+</mo>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>|</mo>
<mo>&GreaterEqual;</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>&GreaterEqual;</mo>
<mn>1</mn>
<mo>-</mo>
<mi>&alpha;</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein Pr (| wH(a+z) | >=1) it is probable value, w is Beam-former weights, wHIt is w conjugate transposition, RxAssisted for signal
Variance matrix, A is steering vector matrix, and y is mapping value vector, and a is array steering vector, and z is array steering error, and α is shadow
Ring the factor.
5. a kind of robust array beamses forming method perceived based on compression covariance matrix according to claim 4, its
It is characterised by：The signal guide vector matrix and interference steering vector matrix and step built in the step 4 using step one
Two obtained signal covariance matrix Rx, optimize the robust adaptive beamforming algorithm model that simultaneously solution procedure three is set up, obtain
Detailed process to Beam-former weight w is：
Step 4 one：Using the MVDR Beamforming Methods optimized based on SVM, try to achieve Beam-former weight w, and will try to achieve
Beam-former weight w is used as initial value w0；
Step 4 two：If k>1 is kth time iteration, wkFor the result of kth time iteration, intermediate variable t is defined,tkFor the intermediate variable of kth time iteration；
If wk-1MeetThen pass throughCalculate tk；
If wk-1It is unsatisfactory forConstant beta >=1 is then selected, makes β wk-1MeetAnd use β wk-1Substitute wk-1Substitute intoCalculate tk；
WhereinFor Weibull probability-distribution functions,The variance being distributed for SIRV,It is wkConjugate transposition；
Step 4 three：Work as tk＞ 0, then utilizeSolve wk, by wk
It is used as new wk-1, step 4 two and step 4 three are re-executed, until wkConvergence, obtains final iteration result wmid；
Work as tk≤ 0, perform step 4 four；
Step 4 four：By diagonal loading algorithm and select obtain wmid。
6. a kind of robust array beamses forming method perceived based on compression covariance matrix according to claim 5, its
It is characterised by：The signal covariance matrix R for obtaining step 2 in the step 5xAnd the Beam-former power that step 4 is obtained
Value w is as initial value iteration optimization, until convergence, obtains final Beam-former weight woptDetailed process be：
Step 5 one：If l is the l times iteration,For RxThe result of the l times iteration, wlFor the result of the l times iteration, set just
Initial valueFor the R obtained by step 2x, initial value w(0)The w obtained for step 4mid；
Step 5 two：UtilizeAnd formulaTry to achieve w(l+1)；Utilize w(l+1)、And formulaTry to achieve
Step 5 three：Repeat step five or two, until Δ p (w(l+1)) andRestrain, the condition of convergence is：
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
<mfenced open = "(" close = ")">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>&Delta;</mi>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>w</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msup>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>&Delta;</mi>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>R</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>+</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>></mo>
<mi>&delta;</mi>
</mrow>
Wherein δ is convergence factor；
Δp(w(l+1))=p (w(l+1))max-p(w(l+1))submax
<mrow>
<mi>&Delta;</mi>
<mi>p</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>R</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>+</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>p</mi>
<msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>R</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>+</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>-</mo>
<mi>p</mi>
<msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>R</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>+</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mrow>
<mi>s</mi>
<mi>u</mi>
<mi>b</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
</mrow>
Wherein Δ p (w(l+1)) represent p (w in the l+1 times iteration(l+1))maxWith p (w(l+1))submaxDifference, p (w(l+1))maxFor ripple
Beamformer weights are w(l+1)When beam space spectrum main lobe value, p (w(l+1))submaxIt is w for Beam-former weights(l+1)When
Beam space composes maximum side petal,Represent in the l+2 times iterationWithDifference
Value,It is for signal covariance matrixWhen beam space spectrum main lobe value,Assisted for signal
Variance matrix isWhen beam space spectrum maximum side petal.
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