CN107907854B - DOA estimation method under impulse noise environment - Google Patents

DOA estimation method under impulse noise environment Download PDF

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CN107907854B
CN107907854B CN201711040857.6A CN201711040857A CN107907854B CN 107907854 B CN107907854 B CN 107907854B CN 201711040857 A CN201711040857 A CN 201711040857A CN 107907854 B CN107907854 B CN 107907854B
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李丽
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Abstract

In order to better inhibit impulse noise and interference of a same-frequency band signal, the invention defines a new circular correlation function, provides a new MUSIC algorithm based on Sigmoid circular correlation, and applies the algorithm to DOA estimation under stable distributed noise. Simulation results show that compared with a classical MUSIC algorithm, a CRCO-MUSIC algorithm based on class correlation entropy and a FLOM-MUSIC algorithm based on base fraction low-order moment, the SCC-MUSIC algorithm provided by the invention can obtain a better estimation result, and has more obvious advantages particularly in a high impulse noise environment.

Description

DOA estimation method under impulse noise environment
Technical Field
The invention belongs to the field of communication and information systems, and particularly relates to a DOA estimation method in an impulse noise environment.
Background
Doa (direction of arrival) estimation is one of the basic problems in array signal processing, and is widely used in the fields of radar, sonar, radio communication, and the like. Multiple Signal Classification (MUSIC) algorithms can achieve super-resolution estimation of DOA, but traditional algorithms mostly assume that background noise follows gaussian distribution. In fact, the noise may be strongly impulsive due to the influence of natural factors (such as atmospheric noise, sea clutter, etc.) and artificial factors (such as electromagnetic devices such as motors, etc.), and it is more appropriate to describe the noise by using Alpha stable distribution. Unlike gaussian-distributed random variables, Alpha-stably-distributed random variables do not have finite second moments, and the conventional MUSIC method is no longer applicable.
To suppress the effect of Alpha stable distributed noise, zhangjinfeng et al proposed a DOA estimation method based on Fractional low Order Statistics (flo). Although the method obtains a good estimation effect, the method has certain limitations: firstly, the order p must satisfy 1 < p < alpha or 0 < p < alpha/2, secondly, if the prior knowledge of alpha is not available or the value can not be correctly estimated, the improper value of the order can cause the performance of the algorithm to be reduced or even fail, and therefore, the estimation effect of the characteristic index alpha can influence the performance of the algorithm. In order to overcome the limitations, Zhang jin Feng et al propose a DOA estimation method based on class M estimation and a CRCO-MUSIC algorithm based on class correlation entropy. Although the algorithm has better anti-noise performance and signal applicability, the algorithm has better weak impulse suppression effect, and if the algorithm is in a high impulse noise environment with alpha less than 1, the algorithm performance is obviously reduced.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: in the working environment of systems such as wireless communication and the like, various noises and interferences exist, so that a target signal received by a receiver is often submerged in the noises and the interferences, and in order to better inhibit the influence of impulse noises and same-frequency interferences and improve the robustness of a DOA estimation algorithm, the invention provides a DOA estimation method in an impulse noise environment.
The technical scheme adopted by the invention for solving the technical problem is as follows: a DOA estimation method based on Sigmoid cyclic correlation under an impulse noise environment is provided, and the method comprises the following steps:
step 1: establishing a signal receiving model
Considering that L far-field narrow-band signals are incident on a uniform linear array with an array element number of M, under the assumption that a signal source is a narrow band, a mathematical model of a received signal can be expressed as:
X(t)＝A(θ)S(t)+N(t) (1)
wherein x (t) ═ x1(t),...,xM(t)]TIs an observed signal vector; s (t) ═ s1(t),s2(t),…sKa(t)]TFor an incident signal vector of cyclic frequency epsilon, Ka< L, other L-KaThe individual signals have different cyclic frequencies or do not have a cyclostationary property; a (θ) ═ a (θ)1),a(θ2),…,a(θKa)]Is the incident signal direction vector of interest, and
Figure GDA0002904094450000021
θkthe angle of incidence of the kth signal source is, and d is the distance between array elements; n (t) ═ n1(t),n2(t),…nM(t)]TThe array noise is an M multiplied by 1 dimensional noise data vector of the array, the noise is additive noise which follows S alpha S distribution, the noise of each array element is independent, and the noise and the signal are independent;
step 2: Sigmoid-Cyclic Correlation-MUSIC algorithm
Defining a cyclic correlation function based on the characteristic elicitation of the cyclostationary signal, which is recorded as
Figure GDA0002904094450000022
The definition formula is as follows:
Figure GDA0002904094450000023
wherein the content of the first and second substances,<·>trepresents a time average;
two ends of the formula (1) are subjected to Sigmoid cyclic correlation to obtain a Sigmoid cyclic covariance matrix of the received signal
Figure GDA0002904094450000024
Figure GDA0002904094450000031
Wherein the content of the first and second substances,
Figure GDA0002904094450000032
sigmoid cyclic autocorrelation array, sigma, for the incident signal2Is the ambient noise power; since the incident signal is not circularly correlated with the noise and the noise does not have a cyclostationary property, i.e. the noise contributes zero to the circular autocorrelation matrix, i.e. σ2I ═ 0, where I is the identity matrix;
equation (3) can be obtained by singular value decomposition:
Figure GDA0002904094450000033
the unitary matrix U, V represents left and right singular matrices, respectively, the corresponding singular vectors being obtained from column vectors in the singular matrix, the singular values being obtained from elements on the diagonal in the diagonal matrix S, and the signal and noise being circularly uncorrelated
Figure GDA0002904094450000034
Namely, it is
Figure GDA0002904094450000035
In only KaA non-zero singular value, the rest M-KaThe singular values are zero, correspondingly dividing unitary matrix U, V into two parts:
U＝[US UN] V＝[VS VN] (5)
wherein U isSAnd VSFrom KaSingular vector components, U, corresponding to non-zero singular valuesNAnd VNThe singular vectors corresponding to zero singular values form; by USOr VSThe subspace formed by the column vectors is a signal subspace consisting of UNOr VNThe subspace formed by the column vectors of (a) is a noise subspace; the signal subspace and the noise subspace satisfy an orthogonal relationship, then:
Figure GDA0002904094450000036
the direction vector a (θ) is linearly uncorrelated, and the steering vector of the signal subspace obtained from equations (3) and (6) is also orthogonal to the noise space, that is:
aH(θ)UN＝0 (7)
a (theta) and U due to the presence of noiseNCan not be completely orthogonal, so that the DOA estimation is actually realized by spectral peak search, namely the spectral estimation formula of the Sigmoid Cyclic correction MUSIC algorithm is
Figure GDA0002904094450000041
Performing a spectrum search on equation (8) can result in a DOA estimate based on the SCC-MUSIC algorithm.
The invention provides a DOA estimation method in an impulse noise environment. The algorithm is simple and effective, can simultaneously resist the influence of Alpha stable distribution noise and same frequency interference, and can still realize accurate estimation of DOA under strong pulse noise.
Drawings
FIG. 1 is a graph of algorithm performance as a function of GSNR;
FIG. 2 is a graph of algorithm performance versus fast beat number;
FIG. 3 is a graph of algorithm performance versus characteristic index;
fig. 4 is the angular resolution of the algorithm.
Wherein: (a) the DOA estimation success rate is all; (b) both are DOAs to estimate RMSE.
Detailed Description
The invention is further described with reference to the following figures and detailed description of embodiments.
A DOA estimation method under impulse noise environment comprises the following steps:
step 1: establishing a signal receiving model
Considering that L far-field narrow-band signals are incident on a uniform linear array with an array element number of M, under the assumption that a signal source is a narrow band, a mathematical model of a received signal can be expressed as:
X(t)＝A(θ)S(t)+N(t) (1)
wherein x (t) ═ x1(t),...,xM(t)]TIs an observed signal vector;
Figure GDA0002904094450000042
for an incident signal vector of cyclic frequency epsilon, Ka< L, other L-KaThe individual signals have different cyclic frequencies or do not have a cyclostationary property;
Figure GDA0002904094450000043
is the incident signal direction vector of interest, and
Figure GDA0002904094450000051
θkthe angle of incidence of the kth signal source; n (t) ═ n1(t),n2(t),…nM(t)]TThe array noise is an M multiplied by 1 dimensional noise data vector of the array, the noise is additive noise which follows S alpha S distribution, the noise of each array element is independent, and the noise and the signal are independent;
step 2: Sigmoid-Cyclic Correlation-MUSIC algorithm
The Sigmoid transform is a common nonlinear transform and has wide application, and is defined as follows:
Figure GDA0002904094450000052
the Sigmoid transform has the following properties with respect to the S α S distribution with the position parameter μ ═ 0.
Properties 1: if x (t) follows an S α S distribution with the position parameter μ ═ 0, Sigmoid [ x (t) ] is a symmetric distribution with zero mean.
Properties 2: if x (t) follows a distribution of S α S with a position parameter μ ═ 0 and the dispersion coefficient γ > 0, then: i Sigmoid [ x (t)]||α> 0, and Sigmoid [ x (t)]The mean value is zero.
Properties 3: if x (t) obeys the S α S distribution with the position parameter μ ═ 0, Sigmoid [ x (t) ] has limited second-order statistics and the mean is zero (i.e., Sigmoid [ x (t) ] is a second-order moment process).
Conventional delay estimation methods suffer performance degradation when there is interference in the received signal that overlaps the source signal spectrum. In view of the fact that many signals used in communication systems are cyclostationary signals, scholars have proposed a DOA estimation method based on the cyclostationary characteristics of the signals. Generally, because the interference and the signal have different cyclic frequencies and the noise does not have the cyclostationary characteristic, the cyclic DOA estimation method based on the cyclostationary characteristic has stronger anti-noise and same-frequency-band interference capability than the traditional DOA estimation method, and has better estimation effect even under the condition of low signal-to-noise ratio related interference. Therefore, based on the characteristic elicitation of the cyclostationary signal, a new Cyclic Correlation (SCC) function is defined and recorded as
Figure GDA0002904094450000053
The definition formula is as follows:
Figure GDA0002904094450000054
wherein the content of the first and second substances,<·>trepresenting a time average.
Obtaining Sigmoid cyclic correlation at both ends of equation (1) andsigmoid cyclic covariance matrix capable of obtaining received signal
Figure GDA0002904094450000061
Figure GDA0002904094450000062
Wherein the content of the first and second substances,
Figure GDA0002904094450000063
sigmoid cyclic autocorrelation array, sigma, for the incident signal2Is the ambient noise power; since the incident signal is not circularly correlated with the noise and the noise does not have a cyclostationary property, i.e. the noise contributes zero to the circular autocorrelation matrix, i.e. σ2I＝0；
The Sigmoid cyclic correlation MUSIC algorithm is different from the conventional MUSIC algorithm, the Sigmoid cyclic autocorrelation matrix of the observed signal does not meet the Hamilter matrix, and the singular value decomposition is generally used for replacing the characteristic value decomposition of the conventional MUSIC algorithm to obtain the noise subspace and the signal subspace of the signal.
Equation (3) can be obtained by singular value decomposition:
Figure GDA0002904094450000064
the unitary matrix U, V represents left and right singular matrices, respectively, the corresponding singular vectors being obtained from column vectors in the singular matrix, the singular values being obtained from elements on the diagonal in the diagonal matrix S, and the signal and noise being circularly uncorrelated
Figure GDA0002904094450000065
Namely, it is
Figure GDA0002904094450000066
In only KaA non-zero singular value, the rest M-KaThe singular values are zero, correspondingly dividing unitary matrix U, V into two parts:
U＝[US UN] V＝[VS VN] (5)
wherein U isSAnd VSFrom KaSingular vector components, U, corresponding to non-zero singular valuesNAnd VNThe singular vectors corresponding to zero singular values form; by USOr VSThe subspace formed by the column vectors is a signal subspace consisting of UNOr VNThe subspace formed by the column vectors of (a) is a noise subspace; the signal subspace and the noise subspace satisfy an orthogonal relationship, then:
Figure GDA0002904094450000067
the direction vector a (θ) is linearly uncorrelated, and the steering vector of the signal subspace obtained from equations (3) and (6) is also orthogonal to the noise space, that is:
aH(θ)UN＝0 (7)
a (theta) and U due to the presence of noiseNCan not be completely orthogonal, so that the DOA estimation is actually realized by spectral peak search, namely the spectral estimation formula of the Sigmoid Cyclic MUSIC algorithm is
Figure GDA0002904094450000071
By performing spectrum search on equation (8), a DOA estimate based on the SCC-MUSIC algorithm can be obtained.
The beneficial effects of the invention can be further illustrated by the following simulations:
the experimental conditions are as follows:
alpha stable distribution noise has no finite second moment, so the signal-to-noise ratio of the S alpha S process in the invention adopts generalized signal-to-noise ratio
Figure GDA0002904094450000072
To describe. Wherein γ (γ > 0) represents the dispersion coefficient of the S.alpha.S noise,
Figure GDA0002904094450000073
representing the signal power. The experiment adopts 8 array element uniform linear arrays, the array element spacing is c/2 epsilon, and epsilon is the cycle frequency. The incident source is two far-field BPSK signals, the incident angle of a target Signal (SOI) is 10 degrees, the carrier frequency is 150MHz, the incident angle of an interference Signal (SNOI) is 50 degrees, and the carrier frequency is 100 MHz.
The invention uses two indexes to evaluate the performance of the algorithm: DOA estimation success rate and Root Mean Square Error (RMSE). This DOA estimation is considered successful when the incidence angle estimation errors of 2 sources do not exceed 3 °. The estimation success rate is the ratio of the number of estimation successes to the number of random experiments. RMSE of DOA estimation is defined as
Figure GDA0002904094450000074
Where L is the number of estimated successes,
Figure GDA0002904094450000075
and
Figure GDA0002904094450000076
is the parameter theta1And theta2An estimate of (d). The results are statistically obtained from 300 random experiments.
The invention simultaneously compares the classic MUSIC algorithm, the FLOM-MUSIC algorithm based on fractional low-order moment, the CRCO-MUSIC algorithm based on similar correlation entropy and the SCC-MUSIC algorithm.
The experimental contents are as follows:
experiment 1: effect of GSNR on algorithm performance. Fig. 1 shows the estimation results at different GSNRs. The noise characteristic index α is 1.5, and the snapshot number N is 100. It can be seen that all algorithms improve significantly with increasing GSNR. Compared with other 4 algorithms, the classical MUSIC algorithm has poorer performance in a stable distributed noise environment. Under the environment of low signal-to-noise ratio, the SCC-MUSIC algorithm and the CRCO-MUSIC algorithm can obtain higher estimation success rate, and the SCC-MUSIC algorithm has lower estimation error; and under the environment of high signal-to-noise ratio, the SCC-MUSIC algorithm has better performance.
Experiment 2: impact of fast beat number on algorithm performance. Fig. 2 shows the effect of the number of snapshots N on the performance of the algorithm. The S α S noise characteristic index α is set to 1.5, and GSNR is set to 4 dB. It can be found that in addition to the classical MUSIC algorithm, the RMSE of 4 other algorithms decreases with the increase of the fast beat number, wherein the estimation success probabilities of the SCC-MUSIC, CRCO-MUSIC and ACO-MUSIC 3 algorithms are similar, but the SCC-MUSIC algorithm can obtain a lower estimation error.
Experiment 3: the influence of the noise figure of merit is stably distributed. Fig. 3 shows the estimation results of the algorithm under different noise characteristic indexes, wherein the fast beat number N is 100, and the GSNR is 4 dB. It can be seen that the algorithm herein has very significant advantages in high impulsive noise environments. Furthermore, consistent with the phenomena of fig. 2 and 3, the noise figure a has less impact on the performance of the algorithm herein.
Experiment 4: angular resolution. Fig. 4 shows the angular resolution of the different algorithms. Angle of incidence theta of source 11Changing from 0 to 18, the angle of incidence of the source 2 is fixed at θ 220 °, noise figure α is 1.5, and GSNR is 4 dB. As can be seen from the figure, the minimum angular difference that the algorithm can resolve is 6 °, which is superior to other algorithms. Furthermore, it can be found that the estimation success rate of the method is higher when the angle difference between the two sources is small, and the method has a weak advantage in RMSE when the angle difference between the two sources is large.

Claims (1)

1. A DOA estimation method under an impulse noise environment is characterized by comprising the following steps:
step 1: establishing a signal receiving model
Considering that L far-field narrow-band signals are incident on a uniform linear array with an array element number of M, under the assumption that a signal source is a narrow band, a mathematical model of a received signal can be expressed as:
X(t)＝A(θ)S(t)+N(t) (1)
wherein x (t) ═ x1(t),...,xM(t)]TIs an observed signal vector;
Figure FDA0002904094440000011
for an incident signal vector of cyclic frequency epsilon, Ka< L, other L-KaThe individual signals have different cyclic frequencies or do not have a cyclostationary property; a (θ) ═ a (θ)1),a(θ2),…,a(θKa)]Is the incident signal direction vector of interest, and
Figure FDA0002904094440000012
θkthe angle of incidence of the kth signal source is, and d is the distance between array elements; n (t) ═ n1(t),n2(t),…nM(t)]TThe array noise is an M multiplied by 1 dimensional noise data vector of the array, the noise is additive noise which follows S alpha S distribution, the noise of each array element is independent, and the noise and the signal are independent;
step 2: Sigmoid-Cyclic Correlation-MUSIC algorithm
Defining a cyclic correlation function based on the characteristic elicitation of the cyclostationary signal, which is recorded as
Figure FDA0002904094440000013
The definition formula is as follows:
Figure FDA0002904094440000014
wherein the content of the first and second substances,<·>trepresents a time average;
sigmoid cyclic correlation is obtained at two ends of the formula (1), and a Sigmoid cyclic covariance matrix of the received signal can be obtained
Figure FDA0002904094440000015
Figure FDA0002904094440000016
Wherein the content of the first and second substances,
Figure FDA0002904094440000017
sigmoid cyclic autocorrelation array, sigma, for the incident signal2Is the ambient noise power; since the incident signal is not circularly correlated with the noise and the noise does not have a cyclostationary property, i.e. the noise contributes zero to the circular autocorrelation matrix, i.e. σ2I ═ 0, where I is the identity matrix;
the formula (3) can be obtained through singular value decomposition:
Figure FDA0002904094440000021
the unitary matrix U, V represents left and right singular matrices, respectively, the corresponding singular vectors being obtained from column vectors in the singular matrix, the singular values being obtained from elements on the diagonal in the diagonal matrix S, and the signal and noise being circularly uncorrelated
Figure FDA0002904094440000022
Namely, it is
Figure FDA0002904094440000023
In only KaA non-zero singular value, the rest M-KaThe singular values are zero, correspondingly dividing unitary matrix U, V into two parts:
U＝[US UN] V＝[VS VN] (5)
wherein U isSAnd VSFrom KaSingular vector components, U, corresponding to non-zero singular valuesNAnd VNThe singular vectors corresponding to zero singular values form; by USOr VSThe subspace formed by the column vectors is a signal subspace consisting of UNOr VNThe subspace formed by the column vectors of (a) is a noise subspace; the signal subspace and the noise subspace satisfy an orthogonal relationship, then:
Figure FDA0002904094440000024
the direction vector a (θ) is linearly uncorrelated, and the steering vector of the signal subspace is also orthogonal to the noise space, which can be obtained from equations (3) and (6), that is:
aH(θ)UN＝0 (7)
a (theta) and U due to the presence of noiseNCan not be completely orthogonal, so that the DOA estimation is actually realized by spectral peak search, namely the spectral estimation formula of the Sigmoid Cyclic correction MUSIC algorithm is
Figure FDA0002904094440000025
By performing spectrum search on equation (8), a DOA estimate based on the SCC-MUSIC algorithm can be obtained.
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