Bayes steady beam forming method under steady interference environment
1. A Bayes robust beam forming method under a stationary interference environment is characterized by comprising the following steps:
step 1: establishing an array received signal model;
step 2: establishing a Bayesian probability model, wherein the specific contents are as follows:
suppose an interference + noise vector n at each sampling instant in the array received signal modelkIndependent of each other, and obey a complex Gaussian distribution with a mean value of 0 and a precision matrix of Λ, then nkCan be expressed as
In the formula, Λ is an NxN dimensional matrix;
from the above probability model, it can be known that the likelihood function of the array observation data follows a multivariate Gaussian distribution
p(Y|s,v,Λ)＝π-NK|Λ|Ketr{-(Y-vsH)HΛ(Y-vsH)}
Where Y is the data received by the array of K sample times YkK is 1, …, K is an N × K dimensional matrix, s is s1,…,sK]TThe vector is composed of amplitude information of K snapshots of the expected signal waveform, and etr {. is used for carrying out exponential operation on a matrix trace;
suppose the precision matrix Λ obeys the Wishart prior distribution as follows
p(Λ)＝W(Λ|W,ν)∝|Λ|ν-Netr{-W-1Λ}
Where ∈ denotes a proportional ratio, W denotes a mean matrix, and ν denotes a degree of freedom;
amplitude vector of desired signal waveformThe elements in s are assumed to be independent of each other and all obey the following mean value of 0 and the precision ofComplex gaussian distribution of
In the formula (I), the compound is shown in the specification,obeying a gamma prior distribution
Wherein, gamma function is represented by gamma, a > 0 represents shape parameter, b > 0 represents expansion parameter;
suppose that the desired signal steering vector v obeys a complex Watson distribution as follows
In the formula, mu is equal to CSNIs the nominal steering vector in the complex unit sphere,is a focusing parameter; this distribution is symmetric about μ space; regularization factor cp(λ) can be represented as
In the formula (I), the compound is shown in the specification,representing kummer confluent hypergeometryThe function of the function is that of the function,represents a liter factor;
order toIts prior probability obeys the following Wishart distribution
In the formula, W2Representing the mean matrix, v2Representing a degree of freedom;
by collectionsAll unknown variables in the probability model are represented, and the statistical characteristics of the unknown variables are combined with the distribution of the observation data Y to obtain the following combined probability density
And step 3: using a variation inference method to obtain an update formula of posterior distribution parameters of each variable in theta, wherein the specific contents are as follows:
(1) initializing probabilistic model parameters, i.e. making v ═ vpWherein v ispA vector is directed for a preset desired signal,v＝v2＝N，a＝b＝10-6，s＝1K×1，W＝W2＝10+6·IN×Nin which 1 isK×1Is a K x 1 dimensional full 1 vector, IN×NAn identity matrix of dimension NxN;
(2) definition of lnf (v) ═ ln [ p (v)/cp(λ)]And applying this formula in mode v0Performing Taylor expansion to obtain
In the formula (I), the compound is shown in the specification,a sea plug matrix of dimension N × N; the two ends of the above formula are indexed and normalized, so that the v approximately follows the following Gaussian prior distribution
In the formula, mode v0Can be iteratively calculated according to a Newton's descent method, and the iterative formula of the t +1 step is
In the formula, the calculation formulas of the gradient matrix and the sea plug matrix are respectively
(3) The posterior probability q (v) of the desired signal steering vector v obeys a complex gaussian distribution with the mean vector muvSum precision matrix ΛvThe iterative update formula of
Wherein < · > represents the mathematical expectation operation;
(4) definition ofThe posterior probability obeys the Wishart distribution, i.e.In this distribution, the degree of freedom v3And a scale matrix W3Is updated by the formula
v3＝ν2+1
(5) The posterior probability q(s) of the amplitude vector s of the desired signal waveform obeys a complex gaussian distribution with the mean vector musSum precision matrix ΛsThe iterative update formula of
(6) The posterior probability q (Λ) of the interference + noise precision matrix Λ follows the Wishart distribution, the scale matrix W of which1And degree of freedom v1Respectively of the iterative update formula
W1 -1＝W-1+YYH+<sHs><vvH>-2<v><s>H<Y>H
ν1＝K+ν
(7) The posterior probability of the accuracy of the desired signal obeys the gamma distribution, i.e.Wherein each distribution parameter is iteratively updated by the formula
a2＝K+a
(8) Iterating the processes (2) - (7) until a convergence condition is met;
and 4, step 4: solving Λ the convergence of the interference + noise accuracy matrix and the desired signal steering vectoroptAnd voptSubstitution formulaCalculating to obtain the optimal weight vector wopt。
2. The Bayesian robust beam forming method in the stationary interference environment according to claim 1, wherein the step 1 is as follows:
assuming that the fast array sampling rate is K, the array received data at each sampling time can be expressed as:
in the formula, ykV and nkAll vectors are Nx 1-dimensional vectors and respectively represent array output signals, target components and interference + noise components at sampling time k; skThe amplitude of the expected signal waveform at the sampling moment k; the target, interference and noise components are assumed to be independent of each other; v is a guide vector expressed asWherein λ0For the wavelength of the incident signal, { d1,d2,…,dNAnd the position coordinates of the array elements are shown, and theta is DOA of the expected signals.
3. The Bayesian robust beamforming method according to claim 1, wherein the convergence condition in step 3 isWhereinThe desired signal accuracy value calculated for the current step,the desired signal accuracy value calculated for the previous step.
4. A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of claim 1.
5. A computer-readable storage medium having stored thereon computer-executable instructions for, when executed, implementing the method of claim 1.
6. A computer program comprising computer executable instructions which when executed perform the method of claim 1.
Background
Adaptive beamforming is an important research content of array signal processing, and enhances signals in a desired incident direction and suppresses interference signals in other incident directions through spatial filtering. The Minimum Variance Distortionless Response (MVDR) algorithm is a representative adaptive beam forming method, and minimizes the beam output variance on the premise of constraining the response of the desired signal to be constant 1, so as to achieve the purpose of interference resistance. The MVDR beamformer has an output Signal-to-interference-plus-noise ratio (SINR) much higher than that of the conventional data-independent beamformers. However, the actual array observation data is often mixed with the desired signal, so that an ideal Interference-plus-noise covariance (INC) matrix is not easily obtained and can only be approximated by a sampling covariance matrix, and at this time, if there is a deviation in the preset desired signal steering vector, the MVDR beamformer may misunderstand the desired signal as Interference to suppress, thereby causing a signal self-cancellation effect.
A Robust Adaptive Beamforming (RAB) algorithm is an improved form of the MVDR beamforming algorithm, and provides an effective technical means for resisting mismatching of a steering vector and a covariance matrix in a stationary interference environment. A typical representation of the RAB algorithm is the worst case performance optimization algorithm (s.a. vorobyov, a.b. gershman, z. -q.luo, Robust adaptive beamforming using word-case performance optimization: a solution to the signal mismatch protocol, IEEE trans. signal process.51(2) (2003)313-324.), which eliminates the signal self-cancellation effect by constraining the array response within the desired signal steering vector uncertainty set to be constant 1, widening the beam main lobe. The algorithm has the defects of difficult selection of the optimal user parameters and high calculation complexity. Khabbazibasense et al propose a RAB algorithm (A. Khabbazibasense, S.A. Vorobyov, A. Hassanen, Robust adaptive beamforming based on propagating vector estimation with as little as possible in the information formation, IEEE Trans. Signal Process.60(6) (2012)2974-2987.) which can make the main lobe of the beam point to the real target by adaptively correcting the desired signal steering vector, and reduce the loss of array freedom. The algorithm is also based on the interior point method to solve the constructed convex optimization problem, so that the calculation complexity is higher, and the practical application range of the algorithm is limited. Zhang et al propose an INC matrix reconstruction method (Z.Zhang, W.Liu, W.Leng, A.Wang, H.Shi, Interference-plus-Noise correlation matrix reconstruction and Spatial power sampling for robust adaptive beamforming, IEEE Signal Process.Lett.23(1) (2016) 121-.
Furthermore, describing the statistical characteristics of the error of the steering vector of the expected signal by adopting the Bayesian viewpoint is an effective technical approach for improving the robustness of the beam former. The Bayesian beamformer concept (k.l. bell, y.ephraim, h.l. van Trees, a Bayesian approach to robust adaptive beamforming, IEEE trans. signal process.48(2) (2000)386-398.) was first proposed by k.l. bell et al, which can be regarded as a weighted sum of MVDR beamformers with a set of main lobe azimuths pointing at discrete points in an uncertain set of desired signal directions of arrival (DOAs), with weights determined by the posterior distribution of DOA sample points. However, this algorithm does not take into account the covariance matrix fitting error, and still uses the sampling covariance matrix instead of the INC matrix to calculate the beamforming weight vector, so the performance loss is severe at high input Signal-to-noise ratio (SNR). Unlike the uniform prior distribution applied to the DOA error of the desired signal by k.l.bell et al, c.j.lam et al proposes a Bayesian beamforming algorithm (c.j.lam, a.c.singer, Bayesian beamforming for DOA uncertainty: Theory and Implementation, IEEE trans.signal process.54(11) (2006)4435-4445.) based on the prior distribution of the gaussian DOA error, and uses fourier transform to reduce the computational complexity in the Implementation of the algorithm by k.bell. However, this algorithm still computes bayesian weight vectors based on a sampled covariance matrix and thus has the same performance limitations as the algorithm proposed by k.l.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a Bayes robust beam forming method under a stable interference environment. The invention aims at the array beam forming requirements in signal environments such as model mismatch, small samples, prior information loss and the like, establishes an array processing theory and method system based on an observation data multistage probability model by introducing a Bayesian machine learning technology, and applies the array processing theory and method system to solve the key problem of steady environment interference suppression in the field, so as to break through the bottleneck encountered by further developing and perfecting the array signal processing theory and solve the challenge suffered by the existing array signal processing method when applied to solving the array beam forming problem in increasingly complex signal environments.
Technical scheme
The Bayesian probability model can flexibly describe the statistical characteristics of each component in the array received signal, so that the waveform information of the expected signal can be accurately extracted. The invention estimates the posterior distribution of each hidden variable in the hierarchical probability model by using a Variational inference (Variational inference) criterion, corrects a preset expected signal guide vector according to an estimation result, and reconstructs an INC matrix to calculate a Bayes weight vector.
The expected signal and the interference signal are assumed to be far-field narrow-band signals, which are incident on a uniform linear array composed of N array elements, and the spacing between the array elements is half of the wavelength of the incident signal. When the receiving signal of the linear array is used for self-adaptive beam forming, the technical scheme adopted by the invention comprises the following steps:
step 1: establishing an array received signal model;
step 2: establishing a Bayesian probability model, wherein the specific contents are as follows:
assuming interference + noise at each sampling instant in the array received signal modelAcoustic vector nkIndependent of each other, and obey a complex Gaussian distribution with a mean value of 0 and a precision matrix of Λ, then nkCan be expressed as
In the formula, Λ is an NxN dimensional matrix;
from the above probability model, it can be known that the likelihood function of the array observation data follows a multivariate Gaussian distribution
p(Y|s，v，Λ)＝π-NK|Λ|Ketr{-(Y-vsH)HΛ(Y-vsH)}
Where Y is the data received by the array of K sample times YkK is 1, …, K is an N × K dimensional matrix, s is s1，…，sK]TThe vector is composed of amplitude information of K snapshots of the expected signal waveform, and etr {. is used for carrying out exponential operation on a matrix trace;
suppose the precision matrix Λ obeys the Wishart prior distribution as follows
p(Λ)＝W(Λ|W，v)∝|Λ|v-Netr{-W-1Λ}
Where ∈ denotes a proportional ratio, W denotes a mean matrix, and v denotes a degree of freedom;
the elements in the amplitude vector s of the expected signal waveform are assumed to be independent of each other and are subject to the following mean value of 0 and the precision ofComplex gaussian distribution of
In the formula (I), the compound is shown in the specification,obeying a gamma prior distribution
Wherein, gamma function is represented by gamma, a > 0 represents shape parameter, b > 0 represents expansion parameter;
suppose that the desired signal steering vector v obeys a complex Watson distribution as follows
In the formula, mu is equal to CSNIs the nominal steering vector in the complex unit sphere,is a focusing parameter; this distribution is symmetric about μ space; regularization factor cp(λ) can be represented as
In the formula (I), the compound is shown in the specification,representing the kummer confluent hyper-geometric function,represents a liter factor;
order toIts prior probability obeys the following Wishart distribution
In the formula, W2Representing the mean matrix, v2Representing a degree of freedom;
by collectionsAll unknown variables in the probability model are represented, and the statistical characteristics of the unknown variables are combined with the distribution of the observation data Y to obtain the following combined probability density
And step 3: using a variation inference method to obtain an update formula of posterior distribution parameters of each variable in theta, wherein the specific contents are as follows:
(1) initializing probabilistic model parameters, i.e. making v ═ vpWherein v ispA vector is directed for a preset desired signal,v＝v2＝N，a＝b＝10-6，s＝1K×1，W＝W2＝10+6·IN×Nin which 1 isK×1Is a K x 1 dimensional full 1 vector, IN×NAn identity matrix of dimension NxN;
(2) definition ln f (v) ═ ln [ p (v)/cp(λ)]And applying this formula in mode v0Performing Taylor expansion to obtain
In the formula (I), the compound is shown in the specification,a sea plug matrix of dimension N × N; the two ends of the above formula are indexed and normalized, so that the v approximately follows the following Gaussian prior distribution
In the formula, mode v0Can be iteratively calculated according to a Newton's descent method, and the iterative formula of the t +1 step is
In the formula, the calculation formulas of the gradient matrix and the sea plug matrix are respectively
(3) The posterior probability q (v) of the desired signal steering vector v obeys a complex gaussian distribution with the mean vector muvSum precision matrix ΛvThe iterative update formula of
Wherein < · > represents the mathematical expectation operation;
(4) definition ofThe posterior probability obeys the Wishart distribution, i.e.The degree of freedom v in this distribution3And a scale matrix W3Is updated by the formula
v3＝v2+1
(5) The posterior probability q(s) of the amplitude vector s of the desired signal waveform obeys a complex gaussian distribution with the mean vector musSum precision matrix ΛsThe iterative update formula of
(6) The posterior probability q (Λ) of the interference + noise precision matrix Λ follows the Wishart distribution, the scale matrix W of which1And degree of freedom v1Respectively of the iterative update formula
v1＝K+v
(7) The posterior probability of the accuracy of the desired signal obeys the gamma distribution, i.e.Wherein each distribution parameter is iteratively updated by the formula
a2＝K+a
(8) Iterating the processes (2) - (7) until a convergence condition is met;
and 4, step 4: solving Λ the convergence of the interference + noise accuracy matrix and the desired signal steering vectoroptAnd voptSubstitution formulaCalculating to obtain the optimal weight vector wopt。
The further technical scheme of the invention is as follows: the step 1 is as follows:
assuming that the fast array sampling rate is K, the array received data at each sampling time can be expressed as:
in the formula, ykV and nkAll vectors are Nx 1-dimensional vectors and respectively represent array output signals, target components and interference + noise components at sampling time k; skThe amplitude of the expected signal waveform at the sampling moment k; the target, interference and noise components are assumed to be independent of each other; v is a guide vector expressed asWherein λ0For the wavelength of the incident signal, { d1，d2，…，dNAnd the position coordinates of the array elements are shown, and theta is DOA of the expected signals.
The further technical scheme of the invention is as follows: the convergence condition in step 3 isWhereinThe desired signal accuracy value calculated for the current step,the desired signal accuracy value calculated for the previous step.
A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the above-described method.
A computer-readable storage medium having stored thereon computer-executable instructions for performing the above-described method when executed.
A computer program comprising computer executable instructions which when executed perform the method described above.
Advantageous effects
The Bayes steady beam forming method under the stationary interference environment provided by the invention establishes a steady beam forming theoretical framework aiming at high-precision spatial filter parameter estimation according to the advantages of Bayes machine learning technology in the reconstruction performance of each component feature in a mixed signal. The method introduces a step of probability modeling of each component spatial domain characteristic of a received signal, and the importance of the method is represented by the following two aspects: the layered probability modeling process of the observed data is substantially to achieve the best fitting of the observed data by utilizing a group of reasonable prior distribution, the process well utilizes the structural characteristics of each signal component in the observed data, and has a principle similar to a maximum likelihood method, but the calculation efficiency of the beam forming process can be obviously improved by using an efficient parameter estimation algorithm; the structural information of each signal component is contained in a layered probability model for spatial filter parameter estimation, and prior distribution parameters in the model can be adaptively adjusted according to actual signal environments, so that the array beam forming method can better adapt to the processing requirements in different signal environments. The beneficial effects are as follows:
(1) because the gaussian distribution assumption of the expected signal steering vector by the existing Bayesian beam forming method is not consistent with the actual probability model, the optimal target array manifold estimation precision is difficult to obtain. Therefore, the method introduces Watton distribution depending on the direction of the incident signal to realize accurate estimation of the expected signal guide vector, then applies reasonable prior distribution hypothesis on interference and noise components, and optimizes probability parameters by using observation data to obtain a distribution function fitting with a real model, thereby effectively improving the reconstruction precision of the interference + noise covariance matrix. The related method has the array structure adaptability and the output SINR which are obviously superior to those of the diagonal loading method and the existing Bayesian method.
(2) Aiming at the problem that the existing Bayes beam forming method can not infer parameters in a non-conjugate prior distribution model, the invention provides a filter parameter estimation method based on local variation inference, so that higher calculation efficiency than the traditional probability sampling method is obtained. Specifically, the Watson prior of the expected signal guide vector is subjected to second-order Taylor expansion at a mode point of the expected signal guide vector to obtain a probability density lower bound in a Gaussian form, and the approximate prior distribution and the array received data likelihood function meet the conjugate relation, so that the posterior distribution form can be accurately deduced by applying a variational criterion. The probability approximation and the variation inference process are called local variation inference methods. By continuously iterating to minimize the gap between the exact prior and the approximate prior, a computational accuracy comparable to that of conventional probabilistic sampling methods can be obtained.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
Fig. 1 is a graph showing the variation of the output SINR of the array with the input SNR obtained by the method of the present invention and five other robust beamforming methods in an implementation example under the situation of mismatching of the steering vector of the desired signal caused by the DOA estimation error, and a comparison graph between the output SINR and the optimal output SINR curve.
Fig. 2 is a graph showing the variation of the array output SINR with the input SNR obtained by the method of the present invention and five other robust beamforming methods in an implementation example under the condition of the mismatch of the desired signal steering vector caused by coherent local scattering, and a comparison graph of the output SINR with the optimal output SINR curve.
The basic principles and embodiments of the present invention were verified by computer numerical simulations.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The technical scheme adopted by the invention for solving the technical problem can be divided into the following 5 steps:
the method comprises the following steps: using array element position coordinates as d1，…，dNThe N-element uniform linear array is used as a receiving array to receive far-field narrow-band expected and interference signals. Each sensor array element on the linear array converts the received physical signal into an electric signal and obtains a discrete time domain signal through an amplifying circuit and a data acquisition unit.
Step two: assuming that the fast array sampling rate is K, the array received data at each sampling time can be expressed as:
in the formula, ykV and nkAll are N × 1 dimensional vectors, which respectively represent the array output signal, the target component and the interference + noise component at the sampling time k. skThe amplitude of the desired signal waveform at sampling instant k. The target, interference and noise components are assumed to be independent of each other. v is a guide vector expressed asWherein λ0For the wavelength of the incident signal, { d1，d2，…，dNAnd the position coordinates of the array elements are shown, and theta is DOA of the expected signals.
Step three: establishing a hierarchical probability framework according to the array received signal model established in the second step, wherein the hierarchical probability framework comprises the following sub-steps:
the first substep: assume the interference + noise vector n at each sampling instantkIndependent of each other, and obey a complex Gaussian distribution with a mean value of 0 and a precision matrix of Λ, then nkCan be expressed as
In the formula, Λ is an NxN dimensional matrix.
From the above probability model, it can be known that the likelihood function of the array observation data follows the following multivariate gaussian distribution:
p(Y|s，v，Λ)＝π-NK|Λ|Kctr{-(Y-vsH)HΛ(Y-vsH)}
where Y is the data received by the array of K sample times YkK is 1, …, K is an N × K dimensional matrix, s is s1，…，sK]TThe vector is composed of amplitude information of K snapshots of the expected signal waveform, and etr {. is used for carrying out exponential operation on a matrix trace;
and a second substep: suppose the precision matrix Λ obeys the Wishart prior distribution as follows
p(Λ)＝W(Λ|W，v)∝|Λ|v-Netr{-W-1Λ}
Where ∈ denotes a proportional ratio, W denotes a mean matrix, and v denotes a degree of freedom;
and a third substep: the elements in the amplitude vector s of the expected signal waveform are assumed to be independent of each other and are subject to the following mean value of 0 and the precision ofComplex gaussian distribution of
In the formula (I), the compound is shown in the specification,obeying a gamma prior distribution
Wherein, gamma function is represented by gamma, a > 0 represents shape parameter, b > 0 represents expansion parameter;
and a fourth substep: suppose that the desired signal steering vector v obeys a complex Watson distribution as follows
In the formula, mu is equal to CSNIs the nominal steering vector in the complex unit sphere,are focus parameters. This distribution is spatially symmetric about μ. Regularization factor cp(λ) can be represented as
In the formula (I), the compound is shown in the specification,representing the kummer confluent hyper-geometric function,indicating the liter factor.
Order toIts prior probability obeys the following Wishart distribution
In the formula, W2Representing the mean matrix, v2Representing a degree of freedom;
and a fifth substep: by collectionsAll unknown variables in the probability model are represented, and the statistical characteristics of the unknown variables are combined with the distribution of the observation data Y to obtain the following combined probability density
Step four: calculating posterior distribution parameters of each variable in theta by using a variational inference method, comprising the following substeps:
the first substep: initializing probabilistic model parameters, i.e. making v ═ vpWherein v ispA vector is directed for a preset desired signal,v＝v2＝N，a＝b＝10-6，s＝1K×1，W＝W2＝10+6·IN×Nin which 1 isK×1Is a K x 1 dimensional full 1 vector, IN×NAn identity matrix of dimension NxN;
and a second substep: definition ln f (v) ═ ln [ p (v)/cp(λ)]And applying this formula in mode v0Performing Taylor expansion to obtain
In the formula (I), the compound is shown in the specification,is a sea plug matrix of dimension N x N. The two ends of the above formula are indexed and normalized, so that the v approximately follows the following Gaussian prior distribution
In the formula, mode v0Can be iteratively calculated according to a Newton's descent method, and the iterative formula of the t +1 step is
In the formula, the calculation formulas of the gradient matrix and the sea plug matrix are respectively
And a third substep: the posterior probability q (v) of the desired signal steering vector v obeys a complex gaussian distribution with the mean vector muvSum precision matrix ΛvThe iterative update formula of
Wherein < · > represents the mathematical expectation operation;
and a fourth substep: definition ofThe posterior probability obeys the Wishart distribution, i.e.The degree of freedom v in this distribution3And a scale matrix W3Is updated by the formula
v3＝v2+1
And a fifth substep: the posterior probability q(s) of the amplitude vector s of the desired signal waveform obeys a complex gaussian distribution with the mean vector musSum precision matrix ΛsThe iterative update formula of
And a sixth substep: the posterior probability q (Λ) of the interference + noise precision matrix Λ follows the Wishart distribution, the scale matrix W of which1And degree of freedom v1Respectively of the iterative update formula
v1＝K+v
And a seventh substep: the posterior probability of the accuracy of the desired signal obeys the gamma distribution, i.e.Wherein each distribution parameter is iteratively updated by the formula
a2＝K+a
And a substep eight: iterating the sub-steps two-seven until a convergence condition is met, i.e.WhereinThe desired signal accuracy value calculated for the current step,the desired signal accuracy value calculated for the previous step.
Step five: solving Λ the convergence of the interference + noise accuracy matrix and the desired signal steering vectoroptAnd voptSubstitution formulaCalculating to obtain the optimal weight vector wopt。
And carrying out numerical simulation by using a computer to check the estimation performance of the method provided by the invention.
The simulation adopts a 10-element uniform linear array with half-wavelength array element spacing, the received noise of each array element obeys complex Gaussian distribution with the mean value of 0 and the variance of 1, and the complex Gaussian distribution is independent of each other. The total number of incident signals of the array is 3, wherein the number of expected signals is 1, the number of equal-power interference signals is 2, and each incident signal waveform obeys complex Gaussian distribution. The Interference-TO-noise ratio (INR) was set TO 30 dB. The interference signal incidence DOA is 30 ° and 50 °, respectively, and the preset value of the desired signal incidence DOA is 5 °. The number of Monte Carlo experiments is set as 100, and in each experiment, the position error of each array element obeys [ -0.05 lambda ]0，0.05λ0]A uniform distribution in the range, wherein0Is the wavelength of the incident signal.
1) When the DOA estimation error exists, the output SINR results of the method provided by the invention and the five existing stable beam forming methods are compared
Consider the situation of mismatching of the steering vector of the desired signal due to the DOA estimation error, i.e. the error between the preset value and the true value of the DOA of the desired signal follows a uniform distribution within the range of-3 °, 3 ° in each monte carlo experiment. The array sample fast beat number is 50. The method is utilized to solve the problems of the prior five methods, namely WORSCASE 1 method (S.A. Vorobyov, A.B. Gershman, Z. -Q.Luo, Robust adaptive beamforming using work-CASE performance optimization: a solution to the Signal mismatch process, IEEE Trans.Signal Process.51(2) (2003) 313-324), WORSCASE 2 method (A.Khabbabjen, S.A. Vorobyov, A.Hassanen, Robust adaptive beamforming with user with move-CASE performance enhancement with 12-CASE performance enhancement for information in IEEE transaction, IEEE transaction Trans.60 (6) (74. S.2987. S.J. J.S. J.12. 12. S.S.J.S.12), and the prior five methods, namely WORSCASE 1 method (S.A. Voroboro 1. V.1. V.S.S.S.S.S.S.P.S.S.S.S.S.S.S.P.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.74.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.P.S.S.P.P.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.S.P.P.P.P.S.S.S.S.S.S.S.S.S.S.S.S.S.S.P.P.P.P.S.S.P.P.S.S.P.P.P.P.S.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.S.S.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P.P., BAYESIAN 2 method (C.J.Lam, A.C.Singer, Bayesian beamforming for DOA university: thermal and implantation, IEEE Trans.Signal Process.54(11) (2006)4435-4445.) performs beamforming to plot an output SINR curve. Fig. 1 is a graph comparing the beamforming results of the six methods with the optimal SINR. As can be seen from the results shown in fig. 1, the array output SINR of the proposed method is closest to the optimal output SINR, and thus the interference suppression performance is better than that of the existing method.
2) When coherent local scattering exists, the output SINR results of the method provided by the invention and the five existing robust beam forming methods are compared
The true desired signal steering vector may be expressed asWhereinA vector is directed for a preset desired signal,representing coherent scatter paths, ηiAnd i is 1, 2, 3 and 4, which are corresponding phases on each path. In each Monte Carlo experiment, the parameter { theta }i}，{ηiIndependently of the same distribution, where { theta } isiSubject to a Gaussian distribution with a mean of 3 and a variance of 1 [ { η }iObey [0, 2 pi ]]Uniformly distributed therein. Setting the fast beat number to be 50, selecting five methods of worst case 1, worst case 2, SPSS-INC, Bayesian 1 and Bayesian 2 as comparison objects of the method provided by the invention, and respectively calculating the beam output SINR obtained by each method under different input SNR conditions. Fig. 2 shows the output SINR and the optimum SINR versus input SNR curves of the above six methods. From the results shown in fig. 2, it can be seen that the proposed method has interference suppression performance superior to other existing methods, which reflects that the proposed method can effectively utilize the hierarchical probability model to avoid crosstalk between different signal components, and better suppress interference components while realizing accurate reconstruction of desired signal waveforms.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.
