CN106093878A - A kind of interference noise covariance matrix based on probability constraints reconstruct robust method - Google Patents

Abstract

The invention belongs to Array Signal Processing field, relate generally to interference noise covariance matrix based on the probability constraints reconstruct robust algorithm robustness to interference signal guide Random Vector error.The present invention provides a kind of interference noise covariance matrix based on probability constraints reconstruct robust algorithm (IPNCMR PC), introduce and preset outage probability foundation interference signal guide vector error model based on probability constraints, obtain equivalent random error norm constraint upper limit parameter based on probability constraints, use RCB algorithm that power and the steering vector of interference signal are effectively estimated, improve its estimated accuracy further, obtain interference noise covariance matrix more accurately, thus improve the interference noise covariance matrix restructing algorithm robustness to interference signal guide vector error further.

Description

A kind of interference noise covariance matrix based on probability constraints reconstruct robust method

Technical field

The invention belongs to Array Signal Processing field, relate generally to interference noise covariance matrix weight based on probability constraints The structure robust algorithm robustness to interference signal guide Random Vector error.

Background technology

Capon adaptive beam-forming algorithm can make array under conditions of ensureing output undistorted to desired signal Output is minimum, improves output Signal to Interference plus Noise Ratio (Signal-to-Interference-plus-Noise to greatest extent Ratio, SINR), improve array gain to greatest extent, there is preferable azimuth resolution and stronger interference rejection capability. But, Capon Wave beam forming is built upon desired signal steering vector and interference noise covariance matrix the most accurately known On the basis of imagination, sensitive to the application condition of desired signal steering vector and interference noise covariance matrix, and should in reality In with, interference noise covariance matrix is usually difficult to obtain, and often carrys out generation with array received data sample covariance matrix Replace.In the case of the fast umber of beats of array received data is limited, the performance of Capon adaptive beam-forming algorithm can be inevitably Decline, especially when array received data include desired signal, being particularly acute of hydraulic performance decline.

To this, Gershman et al. proposed worst optimized performance (Worst-Case based on Capon in 2003 Performance Optimization, WCPO) Beamforming Method, its core concept assumes that the true guiding of desired signal Vector a (θ₁) with preset steering vectorBetween there is estimation difference, and error norm has the upper limit I.e. assume true steering vector a (θ₁) belong to oval uncertain collectionIts design Criterion is to make the wave beam output SINR under worst condition the highest, i.e. For battle array Row receive the sample covariance matrix of data, and the steering vector solution that WCPO obtains is designated asIn order to improve further based on The performance of the robust adaptive beamforming algorithm of difference optimized performance, Sergiy A. etc. proposed based on probability in 2008 The Robust Minimum Variance beamforming algorithm of constraint, introduces the outage probability p preset and represents that random error reaches worst condition Probability, use a kind of statistical to replace determining mode, set up steering vector error model based on probability constraints, structure Optimization problem based on probability constraintsThus further increase Robustness to desired signal steering vector random error.But, because this two classes algorithm uses sample covariance matrixAnd It not interference noise covariance matrix R_i+nCarry out computing array weighting, and sample covariance matrix include desired signal composition, I.e.Especially in the case of the fast umber of beats of array received data is limited, by mistake by true desired signal as interference letter Number carry out zero and fall into (i.e. " falling into from zero "), when especially desired signal input signal-to-noise ratio SNR is relatively big, thus cause array to export SINR progressively off-target SINR.

In order to effectively solve this problem, Gu Yujie etc. proposed a kind of interference covariance matrix restructing algorithm in 2012 (Interference-plus-Noise Covariance Matrix Reconstruction, IPNCMR), this IPNCMR weight The core concept of structure algorithm is first to carry out Capon spectral integral in the angular interval not comprising desired signal arrival bearing to obtain Interference noise covariance matrix, is then based on this matrix and sets up the quadratic constraints secondary rule about desired signal steering vector error The problem of drawing, thus obtain Wave beam forming weights, it is greatly improved the performance of adaptive beam-forming algorithm.But this IPNCMR calculates There is the deficiency that some are intrinsic in method, this algorithm needs the interference noise structure of accurately known array, and interference signal is led the most accurately To vector, and in actual applications, the steering vector of interference signal is unknown, needs employing to be similar to desired signal and guides arrow The method that amount is estimated is estimated.Therefore, this IPNCMR algorithm is more sensitive to interference signal guide vector error, especially leads To Random Vector error.

For improving such algorithm robustness to interference signal guide vector error, Yuan Xiaolei etc. carried in 2015 Go out a kind of interference covariance matrix restructing algorithm (IPNCMR-for the most random steering vector based on WCPO criterion WCPO), be similar to the modeling of desired signal steering vector error, build interference signal guide vector error based on worst performance The error model of the criterion of optimalityD=2,3 ..., D, use robust Capon Wave beam forming (Robust Capon Beamforming, RCB) estimates the power of the d interference signalAnd guiding VectorThe architectural characteristic utilizing interference noise covariance matrix reconstructs and considers the dry of interference signal guide vector error Disturb noise covariance matrixImprove interference noise covariance matrix restructing algorithm to disturbing the steady of signal guide vector error Strong property.This algorithm is in the case of desired signal low input SNR, it is thus achieved that preferably export SINR than IPNCMR algorithm；But, When high input SNR, its output SINR still distance optimum output SINR has a certain distance.Therefore, further research for The interference noise robust variance-covariance matrix restructing algorithm of interference signal guide vector error is necessary.

Summary of the invention

It is an object of the invention to provide a kind of interference noise covariance matrix based on probability constraints reconstruct robust algorithm (A Robust Algorithm for Interference-plus-Noise Covariance Matrix Reconstruction Based on Probability Constraints, IPNCMR-PC), introduce default outage probability and build Be based on the interference signal guide vector error model of probability constraints, it is thus achieved that equivalent random error norm based on probability constraints is about Bundle upper limit parameter, uses RCB algorithm effectively to estimate power and the steering vector of interference signal, improves it further and estimate Meter precision, it is thus achieved that interference noise covariance matrix more accurately, thus improve the reconstruct of interference noise covariance matrix further and calculate The method robustness to interference signal guide vector error.

The thinking of the present invention is: present invention architectural characteristic based on preferable interference noise covariance matrix It is the steering vector of the d interference signal, d=2,3 ..., D,It is its power, σ²It is array received white Gaussian noise power, I_NIt is N × N unit matrix), it is firstly introduced into default outage probability p_dRepresent the d interference signal guide Random Vector error Reach the probability of worst condition, set up steering vector error model based on probability constraints And assume random error δ_dBe a zero-mean, variance be C_δ-dMultiple symmetrical Gaussian stochastic variable, thus obtain based on probability about Equivalent random error norm constraint upper limit ε of bundle_d-e.Then RCB algorithm is used to estimate the power of the d interference signalWith Steering vectorSimultaneously to sample covariance matrixCarry out Eigenvalues Decomposition (EVD) and estimate array received white Gaussian noise PowerThus utilize the architectural characteristic of interference noise covariance matrix to obtain the interference noise covariance matrix of reconstructFinally useReplace sample covariance matrixSet up desired signal based on The steering vector error model of probability constraintsThe minimum variance ripple of structure probability constraints Bundle forms optimization problemAnd assume random error δ₁It it is one Zero-mean, variance are C_δ-1Multiple symmetrical Gaussian stochastic variable, thus obtain Wave beam forming weighted value, so can carry further The high interference noise covariance matrix restructing algorithm robustness to interference signal guide vector error.

A kind of interference noise covariance matrix based on probability constraints reconstruct robust method, specifically comprises the following steps that

S1, the even linear array being made up of M array element receive D the signal from far field information source, the incoming wave of each signal Direction is respectively θ_d, d=1 ..., D, without loss of generality, it is assumed that the 1st signal is desired signal, remaining D-1 is interference letter Number, and assume between each signal orthogonal, and the most orthogonal between signal and noise, then n-th take array soon and connect Receipts data are designated as

$x\left(n\right)=a\left({\mathrm{\θ}}_1\right)s_1\left(n\right)+\underset{d=2}{\overset{D}{\Σ}}a\left({\mathrm{\θ}}_d\right)s_d\left(n\right)+v\left(n\right)=As\left(n\right)+v\left(n\right)$

Wherein, A=[a (θ₁),…,a(θ_D)] it is array manifold matrix, s (n) is the signal source vector that array received arrives, v N () represents the noise vector that array received arrives, it is assumed that it is zero mean Gaussian white noise.The N number of fast beat of data that array received arrives It is represented by following vector form:

X=[x (1) ..., x (N)]=AS+V

S=[s (1) ..., s (N)]

V=[v (1) ..., v (N)]

The sample covariance matrix of array received data can be obtained by array received data matrix X

${\hat{R}}_x=\frac{1}{N}{\mathrm{XX}}^H=\frac{1}{N}\underset{n=1}{\overset{N}{\Σ}}x\left(n\right)x^H\left(n\right)$

In general, it is expected that the true steering vector of signal and interference signal is unknown, estimated by corresponding DOA algorithm Meter obtains, and this most inevitably introduces certain estimation difference.Assume signal d, d=1,2 ..., the pre-estimation steering vector of D ForReal signal guide vector a (θ_d) it is positioned at the uncertain set of following ellipse D=1 ..., in D, ε_dRepresent signal d pre-estimation steering vectorWith true steering vector a (θ_dEstimation difference δ between)_d's The norm upper bound.

S2, utilize the sample covariance matrix of array received dataEstimate array received white Gaussian noise powerRightCarry out Eigenvalues Decomposition (EVD) and obtain its eigenvalue (by arrangement from big to small) D the source signal part that wherein D big eigenvalue arrives corresponding to array received, remaining M-D little eigenvalue is corresponding to battle array The noise section that row receive, so noise power can be estimated with following formula:

S3, architectural characteristic based on preferable interference noise covariance matrix, set up interference signal d, d=2,3 ..., D based on The steering vector error model of probability constraintsObtain equivalence based on probability constraints with Chance error difference norm constraint upper limit ε_d-e, use RCB algorithm to estimate the power of D-1 interference signal respectively on this basisd =2 ..., D and steering vectorD=2 ..., D.

S31, interference signal d, d=2,3 ..., the pre-estimation steering vector of D isReal signal guide vector a (θ_d) it is positioned at oval uncertain setIn, introduce outage probability p_dRepresent d Interference signal guide Random Vector error reaches the probability of worst condition, sets up steering vector error model based on probability constraintsBuild optimization problem based on probability constraints

If S32 assumes steering vector random error δ_dObey zero-mean, covariance matrix is C_δ-dGaussian random distribution, the most at random Variable w^Hδ_dObey zero-mean, covariance matrix isGauss distribution, it is assumed that stochastic variable w^Hδ_dReal part and imaginary part be mutual Statistical iteration, then its amplitude | w^Hδ_d| Rayleigh distributed, it is hereby achieved that The most available by certain conversionThen optimization based on probability constraints is asked Topic can be converted toThe WCPO wave beam that analogy is original Formation optimization problem understands, when covariance matrix isTime, the random error norm constraint higher limit of equivalence is

S33, utilize sample covariance matrixBuild interference signal d RCB Wave beam forming optimization problem:

Necessarily arrange and be converted to following Semidefinite Programming afterwards:

$\begin{array}{cc}\underset{a\left({\mathrm{\θ}}_d\right),{\mathrm{\σ}}_d^2}{min}& 1/{\mathrm{\σ}}_d^2\end{array}$

Use existing SeDuMi software or CVX software to solve, can obtain disturbing the power of signal dAnd guiding Vector

S32, take d=2 respectively ..., D, repeats step S31 and i.e. can get the interference signal in interference noise covariance matrix ?In combination with the array received white Gaussian noise power estimated in step S2Can be examined Consider the interference noise covariance matrix reconstruct of interference signal guide vector error

S4, the pre-estimation steering vector of desired signal areIts true steering vector a (θ₁) it is positioned at oval uncertain collection CloseIntroduce outage probability p₁Represent that desired signal steering vector random error reaches To the probability of worst condition, set up steering vector error model based on probability constraints Utilize the interference noise covariance matrix estimated in step S3 simultaneouslyReplace sample covariance matrixStructure probability is about The minimum variance Wave beam forming optimization problem of bundle:

$\begin{array}{ccc}\underset{w}{min}{w}^H{\hat{R}}_{i+n}w,& s.t.& \mathrm{Pr}\left\{\right|w^H{\mathrm{\δ}}_1|\≤|w^H\hat{a}\left({\mathrm{\θ}}_1\right)|-1\}\≥p_1\end{array}$

Necessarily arrange and be converted to following Second-order cone programming problem afterwards:

$\begin{array}{ccc}\underset{w}{min}\left|\right|Vw\left|\right|& s.t.& w^H\hat{a}\left({\mathrm{\θ}}_1\right)\≥1+\sqrt{-ln(1-p_1)}\left|\right|C_{\mathrm{\δ}-1}^{1/2}w|{|}^2,{\hat{R}}_{i+n}=V^{H}V\end{array}$

Use existing SeDuMi software or CVX software to solve, obtain its sane array weight w_IPNCMR-PC。

The invention has the beneficial effects as follows:

It is firstly introduced into default outage probability and represents that interference signal random error reaches the probability of worst condition, use one Statistical replaces determining mode, sets up steering vector error model based on probability constraints, obtains based on probability constraints Equivalence random error norm constraint upper limit parameter, then uses RCB algorithm to estimate the power of D-1 interference signal respectivelyd =2 ..., D and steering vectorD=2 ..., D, improves its estimated accuracy, it is thus achieved that interference noise association more accurately further Variance matrix, can be effectively improved wave beam effectively for existing intrinsic deficiency based on the reconstruct of interference noise covariance matrix The robustness of formation algorithm.

S3 step of the present invention carrys out estimating interference noise covariance matrix according to the definition of interference noise covariance matrix, builds The steering vector error model based on probability constraints of vertical all interference signals, obtains equivalent random error based on probability constraints The norm constraint upper limit, on this basis use RCB algorithm estimate respectively all interference signals power and and steering vector, Estimated accuracy can be improved further, it is thus achieved that more accurate interference noise covariance matrix, improve and interference signal guide is vowed The robustness of amount random error.

Accompanying drawing explanation

Fig. 1 is the flow chart of the inventive method.

Fig. 2 is the wave beam of the present invention output SINR change curve with desired signal input SNR.

Fig. 3 is the wave beam of the present invention output SINR change curve with the fast umber of beats of array received data.

Detailed description of the invention

Below in conjunction with embodiment and accompanying drawing, describe technical scheme in detail.

As shown in Figure 1:

S1, the even linear array being made up of M array element receive D the signal from far field information source, the incoming wave of each signal Direction is respectively θ_d, d=1 ..., D, without loss of generality, it is assumed that the 1st signal is desired signal, remaining D-1 is interference letter Number, and assume between each signal orthogonal, and the most orthogonal between signal and noise, then n-th take array soon and connect Receipts data are designated as

$x\left(n\right)=a\left({\mathrm{\θ}}_1\right)s_1\left(n\right)+\underset{d=2}{\overset{D}{\Σ}}a\left({\mathrm{\θ}}_d\right)s_d\left(n\right)+v\left(n\right)=As\left(n\right)+v\left(n\right)$

Wherein, A=[a (θ₁),…,a(θ_D)] it is array manifold matrix, s (n) is the signal source vector that array received arrives, v N () represents the noise vector that array received arrives, it is assumed that it is zero mean Gaussian white noise.The N number of fast beat of data that array received arrives It is represented by following vector form:

X=[x (1) ..., x (N)]=AS+V

S=[s (1) ..., s (N)]

V=[v (1) ..., v (N)]

The sample covariance matrix of array received data can be obtained by array received data matrix X

${\hat{R}}_x=\frac{1}{N}{\mathrm{XX}}^H=\frac{1}{N}\underset{n=1}{\overset{N}{\Σ}}x\left(n\right)x^H\left(n\right)$

In general, it is expected that the true steering vector of signal and interference signal is unknown, carried out by corresponding DOA algorithm Estimation obtains, and this most inevitably introduces certain estimation difference.Assume signal d, d=1,2 ..., the pre-estimation of D guides Vector isReal signal guide vector a (θ_d) it is positioned at the uncertain set of following ellipsed =1 ..., in D, ε_dRepresent signal d pre-estimation steering vectorWith true steering vector a (θ_dEstimation difference δ between)_dModel The number upper bound.

S2, utilize the sample covariance matrix of array received dataEstimate array received white Gaussian noise power RightCarry out Eigenvalues Decomposition (EVD) and obtain its eigenvalue (by arrangement from big to small) D the source signal part that wherein D big eigenvalue arrives corresponding to array received, remaining M-D little eigenvalue is corresponding to battle array The noise section that row receive, so noise power can be estimated with following formula:

S3, architectural characteristic based on preferable interference noise covariance matrix, set up interference signal d, d=2,3 ..., D based on The steering vector error model of probability constraintsObtain equivalence based on probability constraints with Chance error difference norm constraint upper limit ε_d-e, use RCB algorithm to estimate the power of D-1 interference signal respectively on this basisd =2 ..., D and steering vectorD=2 ..., D.

S31, interference signal d, d=2,3 ..., the pre-estimation steering vector of D isReal signal guide vector a (θ_d) it is positioned at oval uncertain setIn, introduce outage probability p_dRepresent d Interference signal guide Random Vector error reaches the probability of worst condition, sets up steering vector error model based on probability constraintsBuild optimization problem based on probability constraints

If S32 assumes steering vector random error δ_dObey zero-mean, covariance matrix is C_δ-dGaussian random distribution, the most at random Variable w^Hδ_dObey zero-mean, covariance matrix isGauss distribution, it is assumed that stochastic variable w^Hδ_dReal part and imaginary part be mutual Statistical iteration, then its amplitude | w^Hδ_d| Rayleigh distributed, it is hereby achieved that The most available by certain conversionThen optimization based on probability constraints is asked Topic can be converted toThe WCPO wave beam that analogy is original Formation optimization problem understands, when covariance matrix isTime, the random error norm constraint higher limit of equivalence is

S33, utilize sample covariance matrixBuild interference signal d RCB Wave beam forming optimization problem:

Necessarily arrange and be converted to following Semidefinite Programming afterwards:

$\begin{array}{cc}\underset{a\left({\mathrm{\θ}}_d\right),{\mathrm{\σ}}_d^2}{min}& 1/{\mathrm{\σ}}_d^2\end{array}$

Use existing SeDuMi software or CVX software to solve, can obtain disturbing the power of signal dAnd guiding Vector

S32, take d=2 respectively ..., D, repeats step S31 and i.e. can get the interference signal in interference noise covariance matrix ?In combination with the array received white Gaussian noise power estimated in step S2Can be examined Consider the interference noise covariance matrix reconstruct of interference signal guide vector error

S4, the pre-estimation steering vector of desired signal areIts true steering vector a (θ₁) it is positioned at oval uncertain collection CloseIntroduce outage probability p₁Represent that desired signal steering vector random error reaches The probability of worst condition, sets up steering vector error model based on probability constraintsWith The interference noise covariance matrix estimated in Shi Liyong step S3Replace sample covariance matrixStructure probability constraints Minimum variance Wave beam forming optimization problem:

$\begin{array}{ccc}\underset{w}{min}{w}^H{\hat{R}}_{i+n}w,& s.t.& \mathrm{Pr}\left\{\right|w^H{\mathrm{\δ}}_1|\≤|w^H\hat{a}\left({\mathrm{\θ}}_1\right)|-1\}\≥p_1\end{array}$

Necessarily arrange and be converted to following Second-order cone programming problem afterwards:

$\begin{array}{ccc}\underset{w}{min}\left|\right|Vw\left|\right|& s.t.& w^H\hat{a}\left({\mathrm{\θ}}_1\right)\≥1+\sqrt{-ln(1-p_1)}\left|\right|C_{\mathrm{\δ}-1}^{1/2}w|{|}^2,{\hat{R}}_{i+n}=V^{H}V\end{array}$

Use existing SeDuMi software or CVX software to solve, obtain its sane array weight w_IPNCMR-PC。

Embodiment 1,

The even linear array being made up of 10 array elements receives the narrow band signal that 3 far field information sources are launched, it is desirable to presetting of signal Arrival bearing is θ₁=5 °, its steering vector estimation difference isIt is that a zero-mean, variance areMultiple symmetrical Gaussian stochastic variable, its outage probability is preset as p₁.The default arrival bearing of two interference signals It is respectively θ₂=-30 °, θ₃=40 °, then its steering vector estimation difference isBe a zero-mean, Variance isMultiple symmetrical Gaussian stochastic variable, its outage probability is preset as p₂,p₃, input signal-to-noise ratio SNR is 30dB. To desired signal, σ is set_δ-1=0.3, p₁=0.95, and its input signal-to-noise ratio SNR excursion is-10～40dB；To two Interference signal, arranges σ_δ-2=σ_δ-3=0.3, p₂=p₃=0.95.The fast umber of beats of array received data is 200, carries out 500 times Monte Carlo Experiment.In each Monte Carlo Experiment, it is desirable to signal and interference signal guide Random Vector error can model For

${\mathrm{\δ}}_d=\frac{{\mathrm{\ξ}}_d}{\sqrt{M}}{\[e^{{\mathrm{j\φ}}_1^d},e^{{\mathrm{j\φ}}_2^d},...,e^{{\mathrm{j\φ}}_M^d}\]}^T,d=1,2,3$

Wherein, stochastic variable ξ_dObey interval [0, σ_δ-dBeing uniformly distributed on], andM=1,2 ..., the phase place of MIt is Obey interval [0,2 π] upper equally distributed stochastic variable.

Specific as follows:

1. the covariance matrix of array received data, is obtained by array received data matrix XIt is carried out EVD obtain Array received white Gaussian noise power

2. the Gauss distribution, according to each disturbing signal guide Random Vector error and outage probability thereof, calculate its equivalence Random error norm constraint higher limit beUtilize sample covariance matrix simultaneouslyCarry out structure Build the RCB Wave beam forming optimization problem of interference signal d, obtain disturbing the power of signal dAnd steering vectorThus To the interference noise covariance matrix reconstruct considering interference signal guide vector error

3. the interference noise covariance matrix that reconstruct obtains, is utilizedBuild the structure probability constraints of desired signal Minimum variance Wave beam forming optimization problemIt is carried out certain arrangement obtain Following Second-order cone programming problemAdopt Solve with existing SeDuMi software or CVX software, obtain its sane array weight w_IPNCMR-PC。

4., change input signal signal to noise ratio snr, repeat the most 3., obtain interference noise covariance based on probability constraints Matrix reconstruction robust algorithm output Signal to Interference plus Noise Ratio SINR is with the change curve of desired signal input signal-to-noise ratio SNR.

Carry out IPNCMR-PC weighting design according to the method for the present invention, obtain its wave beam output SINR defeated with desired signal Enter the change curve of SNR as shown in Figure 2.In fig. 2, contrast IPNCMR-PC Yu IPNCMR, two kinds of algorithms of IPNCMR-WCPO, can To see, the IPNCMR-PC beamforming algorithm utilizing the present invention to propose exports SINR and approaches optimal output when low signal-to-noise ratio SINR, is far superior to IPNCMR.

Although along with the increase of SNR, output SINR can be gradually deviated from and most preferably export SINR, but substantially with IPNCMR performance phase When；No matter low signal-to-noise ratio or high s/n ratio situation, the performance of the IPNCMR-PC beamforming algorithm that the present invention proposes is superior to IPNCMR-WCPO algorithm, this also demonstrates IPNCMR-PC beamforming algorithm has more preferably interference signal guide vector error Robustness.

Embodiment 2,

The even linear array being made up of 10 array elements receives the narrow band signal that 3 far field information sources are launched, it is desirable to presetting of signal Arrival bearing is θ₁=5 °, its steering vector estimation difference isIt is that a zero-mean, variance are's Multiple symmetrical Gaussian stochastic variable, its outage probability is preset as p₁.The default arrival bearing of two interference signals is respectively θ₂=- 30°,θ₃=40 °, then its steering vector estimation difference isIt is that a zero-mean, variance areMultiple symmetrical Gaussian stochastic variable, its outage probability is preset as p₂,p₃, input signal-to-noise ratio SNR is 30dB.To expectation Signal, arranges σ_δ-1=0.3, p₁=0.95, and its input signal-to-noise ratio SNR excursion is-10～40dB；To two interference letters Number signal, arranges σ_δ-2=σ_δ-3=0.3, p₂=p₃=0.95.Desired signal input SNR is 15dB, the fast umber of beats of array received data Excursion is 100～500, carries out 500 Monte Carlo Experiments.In each Monte Carlo Experiment, it is desirable to signal is with dry Disturb signal guide Random Vector error can be modeled as

${\mathrm{\δ}}_d=\frac{{\mathrm{\ξ}}_d}{\sqrt{M}}{\[e^{{\mathrm{j\φ}}_1^d},e^{{\mathrm{j\φ}}_2^d},...,e^{{\mathrm{j\φ}}_M^d}\]}^T,d=1,2,3$

Wherein, stochastic variable ξ_dObey interval [0, σ_δ-dBeing uniformly distributed on], andM=1,2 ..., the phase place of M It is to obey interval [0,2 π] upper equally distributed stochastic variable.

Specific as follows:

1. the covariance matrix of array received data, is obtained by array received data matrix XIt is carried out EVD obtain Array received white Gaussian noise power

2. the Gauss distribution, according to each disturbing signal guide Random Vector error and outage probability thereof, calculate its equivalence Random error norm constraint higher limit beUtilize sample covariance matrix simultaneouslyCarry out structure Build the RCB Wave beam forming optimization problem of interference signal d, obtain disturbing the power of signal dAnd steering vectorThus To the interference noise covariance matrix reconstruct considering interference signal guide vector error

3. the interference noise covariance matrix that reconstruct obtains, is utilizedBuild the structure probability constraints of desired signal Minimum variance Wave beam forming optimization problemIt is carried out certain arrangement obtain Following Second-order cone programming problemAdopt Solve with existing SeDuMi software or CVX software, obtain its sane array weight w_IPNCMR-PC。

4., change the fast umber of beats of array received data, repeat the most 3., obtain interference noise covariance based on probability constraints Matrix reconstruction robust algorithm output Signal to Interference plus Noise Ratio SINR is with the change curve of the fast umber of beats of array received data.

Carry out IPNCMR-PC weighting design according to the method for the present invention, obtain its wave beam output SINR with array received number According to fast umber of beats change curve as shown in Figure 3.In figure 3, contrast IPNCMR-PC Yu IPNCMR, two kinds of algorithms of IPNCMR-WCPO, The IPNCMR-PC beamforming algorithm utilizing the present invention to propose exports SINR and just basically reaches stable when fast umber of beats is less, and And under identical fast umber of beats, INCMR-PC output SINR is better than two kinds of algorithms of IPNCMR, IPNCMR-WCPO, and this also absolutely proves The effectiveness of IPNCMR-PC beamforming algorithm.

Claims (1)

1. interference noise covariance matrix based on a probability constraints reconstruct robust algorithm, it is characterised in that include walking as follows Rapid:

S1, the even linear array being made up of M array element receive D the signal from far field information source, the arrival bearing of each signal It is respectively θ_d, d=1 ..., D, without loss of generality, it is assumed that the 1st signal is desired signal, remaining D-1 is interference signal, And assume between each signal orthogonal, and the most orthogonal between signal and noise, then n-th take array received number soon According to being designated as

$x\left(n\right)=a\left({\mathrm{\θ}}_1\right)s_1\left(n\right)+\underset{d=2}{\overset{D}{\Σ}}a\left({\mathrm{\θ}}_d\right)s_d\left(n\right)+v\left(n\right)=As\left(n\right)+v\left(n\right)$

Wherein, A=[a (θ₁),…,a(θ_D)] it is array manifold matrix, s (n) is the signal source vector that array received arrives, v (n) table Show the noise vector that array received arrives, it is assumed that it is zero mean Gaussian white noise.Array received to N number of fast beat of data can represent Vector form for following:

X=[x (1) ..., x (N)]=AS+V

S=[s (1) ..., s (N)]

V=[v (1) ..., v (N)]

The sample covariance matrix of array received data can be obtained by array received data matrix X

${\hat{R}}_x=\frac{1}{N}{\mathrm{XX}}^H=\frac{1}{N}\underset{n=1}{\overset{N}{\Σ}}x\left(n\right)x^H\left(n\right)$

In general, it is expected that the true steering vector of signal and interference signal is unknown, carried out by corresponding DOA algorithm Estimation obtains, and this most inevitably introduces certain estimation difference.Assume signal d, d=1,2 ..., the pre-estimation of D guides Vector isReal signal guide vector a (θ_d) it is positioned at the uncertain set of following ellipse| |δ_d||₂≤ε_d, d=1 ..., in D, ε_dRepresent signal d pre-estimation steering vectorWith true steering vector a (θ_dEstimate between) Meter error delta_dThe norm upper bound.

S2, utilize the sample covariance matrix of array received dataEstimate array received white Gaussian noise powerRight Carry out Eigenvalues Decomposition (EVD) and obtain its eigenvalue (by arrangement from big to small)Its D the source signal part that middle D big eigenvalue arrives corresponding to array received, remaining M-D little eigenvalue is corresponding to array The noise section received, so noise power can be estimated with following formula:

S3, architectural characteristic based on preferable interference noise covariance matrix, set up interference signal d, d=2,3 ..., D is based on probability The steering vector error model of constraintObtain equivalence based on probability constraints with chance error Difference norm constraint upper limit ε_d-e, use RCB algorithm to estimate the power of D-1 interference signal respectively on this basisAnd steering vector

S31, interference signal d, d=2,3 ..., the pre-estimation steering vector of D isReal signal guide vector a (θ_d) position In oval uncertain set||δ_d||₂≤ε_dIn }, introduce outage probability p_dRepresent that d is done Disturb signal guide Random Vector error and reach the probability of worst condition, set up steering vector error model based on probability constraintsBuild optimization problem based on probability constraints

If S32 assumes steering vector random error δ_dObey zero-mean, covariance matrix is C_δ-dGaussian random distribution, then stochastic variable w^Hδ_dObey zero-mean, covariance matrix isGauss distribution, it is assumed that stochastic variable w^Hδ_dReal part and imaginary part be mutual statistical Independent, then its amplitude | w^Hδ_d| Rayleigh distributed, it is hereby achieved that The most available by certain conversionThen optimization problem based on probability constraints Can be converted toThe WCPO wave beam shape that analogy is original Optimization problem is become to understand, when covariance matrix isTime, the random error norm constraint higher limit of equivalence is

S33, utilize sample covariance matrixBuild interference signal d RCB Wave beam forming optimization problem:

$\begin{array}{cccc}\underset{a\left({\mathrm{\θ}}_d\right),{\mathrm{\σ}}_d^2}{max}& {\mathrm{\σ}}_d^2& s.t.& {\hat{R}}_x\≥{\mathrm{\σ}}_d^{2}a\left({\mathrm{\θ}}_d\right)a^H\left({\mathrm{\θ}}_d\right),\left|\right|a\left({\mathrm{\θ}}_d\right)-\hat{a}\left({\mathrm{\θ}}_d\right)|{|}_2\≤{\mathrm{\ϵ}}_{d-e}\end{array}$

Necessarily arrange and be converted to following Semidefinite Programming afterwards:

$\begin{array}{cc}\underset{a\left({\mathrm{\θ}}_d\right),{\mathrm{\σ}}_d^2}{\min }& 1/{\mathrm{\σ}}_d^2\end{array}$

$\begin{array}{cc}s.t.& \left[\begin{array}{cc}{\hat{R}}_x& a\left({\mathrm{\θ}}_d\right)\\ a^H\left({\mathrm{\θ}}_d\right)& 1/{\mathrm{\σ}}_d^2\end{array}\right]\≥0\end{array}$

$\left[\begin{array}{cc}{\mathrm{\ϵ}}_{d-e}I& a\left({\mathrm{\θ}}_d\right)-\hat{a}\left({\mathrm{\θ}}_d\right)\\ {\left(a\right({\mathrm{\θ}}_d)-\hat{a}({\mathrm{\θ}}_d\left)\right)}^H& 1\end{array}\right]>0$

Use existing SeDuMi software or CVX software to solve, can obtain disturbing the power of signal dAnd steering vector

S32, take d=2 respectively ..., D, repeats step S31 and i.e. can get the interference signal terms in interference noise covariance matrixIn combination with the array received white Gaussian noise power estimated in step S2May be accounted The interference noise covariance matrix reconstruct of interference signal guide vector error

S4, the pre-estimation steering vector of desired signal areIts true steering vector a (θ₁) it is positioned at oval uncertain setIntroduce outage probability p₁Represent that desired signal steering vector random error reaches The probability of worst condition, sets up steering vector error model based on probability constraintsWith The interference noise covariance matrix estimated in Shi Liyong step S3Replace sample covariance matrixStructure probability constraints Minimum variance Wave beam forming optimization problem:

$\begin{array}{ccc}\underset{w}{min}{w}^H{\hat{R}}_{i+n}w,& s.t.& \mathrm{Pr}\left\{\right|w^H{\mathrm{\δ}}_1|\≤|w^H\hat{a}\left({\mathrm{\θ}}_1\right)|-1\}\≥p_1\end{array}$

Necessarily arrange and be converted to following Second-order cone programming problem afterwards:

$\begin{array}{ccc}\underset{w}{\min }\left|\right|Vw\left|\right|& s.t.& w^H\hat{a}\left({\mathrm{\θ}}_1\right)\≥1+\sqrt{-ln(1-p_1)}\left|\right|C_{\mathrm{\δ}-1}^{1/2}w|{|}^2,{\hat{R}}_{i+n}=V^{H}V\end{array}$

Use existing SeDuMi software or CVX software to solve, obtain its sane array weight w_IPNCMR-PC。