CN106443569A - Robust adaptive beamforming method based on steering vector correction - Google Patents

Abstract

The invention relates to a robust adaptive beamforming method based on steering vector correction. The method comprises: calculating a sampling covariance matrix Rx of a system; obtaining a reference matrix C distinguishing the desired signal airspace feature according to a priori desired signal wave angle of arrival range and a steering vector determined by a array model; subjecting the Rx to characteristic decomposition; subjecting the C to the characteristic decomposition and ordering characteristic values in a descending order, constructing a projection matrix by the preceding characteristic values; solving a detection matrix; subjecting the detection matrix to characteristic decomposition and determining signal strength according to the maximum characteristic value; performing optimization according to the signal strength; and solving a beamforming vector. The method can overcome signal-oriented vector mismatch, and forms a beam aligned in the direction of the incoming wave by adaptively adjusting the complex weighted value of an array sensor, and may provide a large array gain for signal reception.

Description

A kind of robust adaptive beamforming method based on steering vector correction

Technical field

The invention belongs to digital processing field, the beam-forming technology being related in Array Signal Processing field.

Background technology

Adaptive beamformer technology is an important research contents in Array Signal Processing field, radio communication, The fields such as Underwater acoustic signal processing, imaging of medical, space radio, Radar Signal Processing have a wide range of applications [1] [2] [3] [4] [5].However, the performance of adaptive beam former is easy to be affected [6] by steering vector error.Steering vector error Produce and generally caused by DOA estimate error and formation error.When there is error in steering vector, traditional adaptive beam Shaper can suppress desired signal as interference, and its performance drastically can decline, and this phenomenon is referred to as desired signal and offsets. Therefore, the sane beam-forming technology of steering vector error is overcome to become the study hotspot [6] [7] [8] [9] of the problem.? In these researchs, minimum variance is undistorted (Minimum Variance Distortionless Response:MVDR) wave beam Formation technology gets most of the attention, and document [10] summarizes the design criteria of some robust M VDR beam-forming technologies, such as sidelobe cancellation, Diagonal loading, principal space projection etc..

Based on MVDR beam-forming technology, it is to improve its robustness, the innovatory algorithm for having some outstanding is proposed [7] successively [8][9].A kind of robust ada- ptive beamformer algorithm based on worst condition optimization thought is proposed in document [7], to multiple mismatch feelings Condition has robustness.Document [8] proposes a kind of method of iterated revision steering vector, by the orthogonal of optimized choice steering vector Vector, overcomes steering vector error.Document [9] is based on document [8], and research uses minimum information realization robust ada- ptive beamformer. These beam-forming technologies based on MVDR utilize the blur estimation to desired signal direction of arrival, by revising leading for desired signal Robustness to vector strengthening system.Correction to desired signal generally searches for local by optimization problem in restriction range Optimal solution is obtained.One of constraint is the scope of desired signal direction of arrival, the fuzzy local optimum that can cause to obtain of this scope Solution performance is undesirable, and then affects robustness of the system to steering vector error.

List of references

[1]VAN VEEN B.D.and BUCKLEY K.M.,Beamforming:a versatile approach to spatial filtering[J].IEEEASSPMagazine,19885(2):4-24.

[2] Liu Fengcong. robust adaptive beamforming algorithm [M]. Xi'an:Publishing house of Xian Electronics Science and Technology University, 2012.

[3] Yan Shefeng, Ma Yuanliang. the design of sensor array beam optimization and application [M]. Beijing:Science Press, 2009.

[4] Cheng Jing, Tang Liang, Zheng Min, the robust adaptive beamforming algorithm [J] based on angle spread. computer utility, 2014,34(S1):15-17.

[5] Zeng Hao, Zheng Fang, Yuan Angfei, Huang Tiancong, the target identification method [J] in multi-user digital Wave beam forming, calculate Machine application, 201131 (1):229-231.

[6]VOROBYOV S.A.,GERSHMAN A.B.,and LUO Z.Q.,Robust adaptive beamforming using worst-case performance optimization:A solution to the signal mismatch problem[J],IEEE Transactions on SignalProcessing,2003 51(2): 313-324.

[7]STOICA P.,WANG Z.and LI J.,Robust capon beamforming[J].IEEE Signal processing letters,2003 10(6):172-175.

[8]HASSANIEN A.,VOROBYOV S.A.,and WONG K.M.,Robust Adaptive Beamforming Using Sequential Quadratic Programming:An Iterative Solution to the Mismatch Problem[J].IEEE SignalProcessingLetters,2008 15:733-736.

[9]KHABBAZIBAMENJ A.,VOROBYOV S.A.,and HASSANIEN A.,Robust Adaptive Beamforming Based on Steering Vector Estimation With as Little as Possible Prior Information[J].IEEETransactions on SignalProcessing,2012 60(6):2974- 2987

[10]VOROBYOV S.A.,Principles ofminimum variance robust adaptive beamforming design[J].SignalProcessing,2013 93:3264-3277.

Content of the invention

It is an object of the invention to provide a kind of sane adaptive beam that can overcome DOA estimate error and formation error Forming method.The present invention adaptive can distinguish desired signal power, and the constraints of adjust automatically most having problem, to not There can be good Wave beam forming effect with the desired signal of intensity.Technical scheme is as follows：

A kind of robust adaptive beamforming method based on steering vector correction, comprises the following steps：

Step one：The sample covariance matrix of computing system, obtains the reception signal x for being sampled by n times snap_nBuild sensing The covariance matrix R of device array received signal_x；

Step 2：The steering vector d (θ) for determining according to desired signal direction of arrival scope Θ of priori and by Array Model, Obtain distinguishing the R-matrix C of desired signal spatial feature；

Step 3：To R_xFeature decomposition is carried out, estimates number K of incoming wave signal_R, and by R_xMaximum K_RIndividual eigenvalue Corresponding characteristic vector is arranged in matrix B；

Step 4：Feature decomposition is carried out to C and by descending for eigenvalue arrangement, take front K_CIndividual characteristic vector is arranged in square Battle array D, can obtain projection matrix P_D=D^HD, wherein, ()^HIt is Hermitian transposition computing, K_CNumber is determined by Array Model；

Step 5：Ask for detecting matrix P=BB^H(DD^HBB^H)¹⁰；

Step 6：Feature decomposition is carried out to detection matrix P, signal strength is judged according to eigenvalue of maximum, if which is maximum special Value indicative is more than 0.5, then be judged to strong signal；If 0.5 is less than, it is judged to weak signal；

Step 7：Ask for constraint matrix Tried to achieve by corresponding characteristic vector p of eigenvalue of maximum by P,

Step 8：If it is determined that being weak signal, A is asked for using following optimization problem：

S.t.Tr (A)=M

A±0

Step 9：If it is determined that being strong signal, A is asked for using following optimization problem：

S.t.Tr (A)=M

A±0

Step 10：Revised steering vector a is obtained by A, this obtains in two kinds of situation：First, when the order of A is for for the moment, a is The unique features vector of A；Second, when the order of A is more than for the moment, decompose A=YY^H, ask for intermediary matrix as the following formula

Then a should be the vector of all characteristic vector sums composition for being orthogonal to E, try to achieve a accordingly；

Step 11：Wave beam forming vector is asked for as follows：

The sane type Beamforming Method that signal guide vector mismatch can be overcome proposed by the present invention, by self-adaptative adjustment The wave beam for being added with weights, forming alignment arrival bearing of sensor array, can receive for signal and provide larger array gain.This Invention improves the not strong problem of its binding effect for the Beamforming Method for proposing in [9].Increasing in new constraints Pretending under using, not only possesses the few feature of required prior information, Beam Forming System is more enhanced to formation error, arrival bearing The robustness of estimation difference, under conditions of larger input signal-to-noise ratio, achieves than former algorithm better performance.

The present invention requires no knowledge about accurate arrival bearing, it is only necessary to know arrival bearing's approximate range.The present invention is not required to It is to be understood that amount of interference, can be in interference position adaptive generation null.The fast umber of beats of the sampling substantially array element that the present invention needs The two of number can just reach preferable performance to three times, have the characteristics that with fast umber of beats fast convergence rate of sampling.The present invention can be preferable Overcome the performance loss for bringing because of formation error and steering vector ambiguous estimation, with good robustness.

Description of the drawings

Fig. 1 is the structural representation of M for array number.

Specific embodiment

Step one：The sample covariance matrix of computing system.The reception signal x for being sampled by n times snap_nBuild sensor array Row receive the covariance matrix of signal：

Step 2：Calculate the R-matrix for distinguishing desired signal spatial feature.Desired signal direction of arrival model according to priori Enclose the Θ and steering vector d (θ) for being determined by Array Model, obtain R-matrix C and

Wherein,It is supplementary set of the Θ in [- pi/2, pi/2].

Step 3：To R_xFeature decomposition is carried out, and number K of incoming wave signal is roughly estimated with L-curve method [3]_R, and by R_x Maximum K_RThe corresponding characteristic vector of individual eigenvalue is arranged in matrix B.

Step 4：Feature decomposition is carried out to C and by descending for eigenvalue arrangement, take front K_CIndividual characteristic vector is arranged in square Battle array D, can obtain projection matrix P_D=DD^H, wherein ()^HIt is Hermitian transposition computing.Wherein, K_CCan be obtained with priori.To K_CFirst Being described as follows of the property tested：

P_DIt is capable by selecting to angular regions Θ, because ‖ is P_DValue of d (θ) ‖ in the range of θ ∈ Θ is very big, and to otherThen value is less.Meanwhile, K_CNumber difference, P_DTo angular selectivity (‖ P_DD (θ) ‖ takes the scope of higher value) it is different [9].K_CBigger, P_DThe angular range of selection is bigger.Because angular range Θ is priori, K_CNumber completely by array Model determines.So it is believed that K_CIt is priori.For example, when the width of Θ is 10 °, for the sensor array of 10 array elements Row, the spaced even linear array of half-wavelength, K_COptimum selection is 3.

Step 5：Ask for " detection " matrix P=BB^H(DD^HBB^H)¹⁰.The effect of the detection matrix is to judge desired signal Strong and weak.The true scope to desired signal steering vector can be extracted further using detection matrix to constrain (see step 7 and step Nine).

Step 6：Feature decomposition is carried out to " detection " matrix P, signal strength is judged according to eigenvalue of maximum.If which is maximum Eigenvalue is more than 0.5, then be judged to strong signal；If 0.5 is less than, it is judged to weak signal.(that is, strong and weak herein differentiation is phase For P eigenvalue of maximum.)

Step 7：Ask for " constraint " matrix Tried to achieve by corresponding characteristic vector p of eigenvalue of maximum by P, P with reference to described in step 4_DSelectivity to angle,To angle and selective, while P can be compared_DThe angle of selection Degree scope is less, closer to true desired signal direction of arrival.Therefore this property constraint can be utilized to steering vector search Scope.

Step 8：If it is determined that being weak signal, A is asked for using following optimization problem：

S.t.Tr (A)=M

A±0

Step 9：If it is determined that being strong signal, the optimal conditions two that changes in step 8 areThen walk Optimization problem in rapid eight is changed into：

S.t.Tr (A)=M

A±0

Step 10：Revised steering vector a is obtained by A.This obtains in two kinds of situation.First, when the order of A is for for the moment, a is The unique features vector of A；Second, when the order of A is more than for the moment, decompose A=YY^H, ask for intermediary matrix as the following formula

Then a should be orthogonal to the vector of all characteristic vector sums composition of E.A is tried to achieve accordingly.

Step 11：Ask for Wave beam forming vector as follows (i.e. each array element is added with the arrangement of weights).

Claims (1)

1. a kind of robust adaptive beamforming method based on steering vector correction, comprises the following steps：

Step one：The sample covariance matrix of computing system, obtains the reception signal x for being sampled by n times snap_nBuild sensor array Row receive the covariance matrix R of signal_x；

Step 2：The steering vector d (θ) for determining according to desired signal direction of arrival scope Θ of priori and by Array Model, obtains Distinguish the R-matrix C of desired signal spatial feature；

Step 3：To R_xFeature decomposition is carried out, estimates number K of incoming wave signal_R, and by R_xMaximum K_RIndividual eigenvalue is corresponding Characteristic vector is arranged in matrix B；

Step 4：Feature decomposition is carried out to C and by descending for eigenvalue arrangement, take front K_CIndividual characteristic vector is arranged in matrix D, Projection matrix P can be obtained_D=D^HD, wherein, ()^HIt is Hermitian transposition computing, K_CNumber is determined by Array Model；

Step 5：Ask for detecting matrix P=BB^H(DD^HBB^H)¹⁰；

Step 6：Feature decomposition is carried out to detection matrix P, signal strength is judged according to eigenvalue of maximum, if its eigenvalue of maximum More than 0.5, then it is judged to strong signal；If 0.5 is less than, it is judged to weak signal；

Step 7：Ask for constraint matrix Tried to achieve by corresponding characteristic vector p of eigenvalue of maximum by P,

Step 8：If it is determined that being weak signal, A is asked for using following optimization problem：

$\underset{A}{\min }\mathrm{Tr}\left({R_x}^{-1}A\right)$

S.t.Tr (A)=M

$Tr\left(\right(I-P_D\left)A\right)\≤\underset{\mathrm{\θ}\∈\mathrm{\Θ}}{max}{d}^H\left(\mathrm{\θ}\right)(I-P_D)d^H\left(\mathrm{\θ}\right)$

A±0

Step 9：If it is determined that being strong signal, A is asked for using following optimization problem：

$\underset{A}{min}Tr\left({R_x}^{-1}A\right)$

S.t.Tr (A)=M

$Tr\left(\right(I-\tilde{P}\left)A\right)\≤0.3$

A±0

Step 10：Revised steering vector a is obtained by A, this obtains in two kinds of situation：First, when the order of A is for for the moment, a is A Unique features vector；Second, when the order of A is more than for the moment, decompose A=YY^H, ask for intermediary matrix as the following formula

$E=\frac{1}{M}{Y}^{H}Y-\frac{Y^{H}CY}{Tr\left(Y^{H}CY\right)},$

Then a should be the vector of all characteristic vector sums composition for being orthogonal to E, try to achieve a accordingly；

Step 11：Wave beam forming vector is asked for as follows：

$w=\frac{R_x^{-1}a}{a^H{R}_x^{-1}a}.$