CN109375154B - Coherent signal parameter estimation method based on uniform circular array in impact noise environment - Google Patents
Coherent signal parameter estimation method based on uniform circular array in impact noise environment Download PDFInfo
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- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
- G01S3/14—Systems for determining direction or deviation from predetermined direction
Abstract
The invention belongs to the field of array signal processing parameter estimation, and particularly relates to a coherent signal parameter estimation method based on a uniform circular array in an impact noise environment, which comprises the following steps of: carrying out snapshot sampling on D information source signals in the space; performing impact-removing pretreatment on snapshot sampling data; performing mode excitation transformation on the array output data; constructing a sparse reconstruction dictionary set; sparse reconstruction is carried out to obtain a coherent information source azimuth angle; judging whether the maximum iteration times are reached, if so, executing a step seven; if not, let t=t+1, return to step five; and obtaining a sparse reconstruction result, obtaining information of the azimuth angle of the information source by using the index set U, and outputting a coherent information source direction of arrival estimation result. The method solves the problem of coherent signal parameter estimation based on a uniform circular array in an impact noise environment, adopts the mode excitation transformation and compressed sensing sparse heavy conception as the basis of parameter estimation, and has the advantages of low calculation complexity, short calculation time and high robustness.
Description
Technical Field
The invention belongs to the field of array signal processing parameter estimation, and particularly relates to a coherent signal parameter estimation method based on a uniform circular array in an impact noise environment.
Background
Spatial spectrum estimation is a key technology in the fields of short wave direction finding, radio reconnaissance, radar target positioning tracking, intelligent antennas and the like, and accurate direction of arrival (DOA) estimation has important significance for improving the performance of a communication system. Because of simple structure and convenient analysis, the early spatial spectrum estimation algorithm and application are proposed based on the linear array, but the linear array can only provide azimuth angle estimation deviating from the array axis. Compared with a linear array, the circular array can provide 360-degree omnibearing and non-fuzzy azimuth angle estimation, has approximately the same resolution in each azimuth, can simultaneously provide azimuth angle and pitch angle two-dimensional angle estimation, and has more practical value. The particularity of the uniform circular array structure makes the array flow pattern of the uniform circular array structure not have the vandermonde structure of the linear array, so that many excellent estimation schemes suitable for the linear array cannot be directly applied to the circular array. The beam space transformation based on the phase mode excitation is an effective proposal for the uniform circular array, and the array flow pattern of the uniform circular array can be transformed into a form similar to a vandermonde matrix through the beam space transformation.
Smart antennas exploit the spatial differences between mobile users to achieve capacity multiplication, and in an actual mobile environment, multipath signals formed by the same mobile user signal passing through various reflectors are generally considered coherent. The common high-resolution signal estimation method has better resolution performance under the condition of independent sources, but the estimation performance is obviously deteriorated under the coherent source environment, and even the estimation performance is completely invalid and cannot be estimated. Due to the presence of coherent signals, neither the conventional multiple signal classification (MUSIC) algorithm nor the rotation invariant subspace (ESPRIT) algorithm can estimate the direction of arrival of the signal correctly. For uniform linear arrays, although spatial smoothing algorithms can process coherent signal sources, these decorrelation algorithms cannot be directly applied to uniform circular arrays. The uniform circular array is converted into a virtual uniform linear array, and the obtained virtual uniform linear array has translational invariance like a common linear array, so that spatial smoothing decoherence can be applied, but the calculated amount is increased while the spatial smoothing is performed.
The traditional high-resolution direction-finding estimation schemes all consider a Gaussian white noise signal model, and in practical cases, background environments are not ideal Gaussian white noise, and impact noise conditions expressed by a symmetrical alpha stable distribution process (Salpha S) exist. Because the impulse noise does not have the second-order moment or the higher-order moment, the direction of arrival estimation problem under the impulse noise can not be directly transplanted into the target parameter estimation scheme under the Gaussian noise, otherwise, the algorithm performance can be drastically reduced or even disabled. The conventional MUSIC method based on co-transformation and fractional low-order moment can solve the DOA estimation problem under the condition of impact noise, but the multi-dimensional search brings higher calculated amount, and the performance is obviously reduced under the condition of fewer snapshots. The DOA estimation problem of a coherent signal source based on a uniform circular array under impact noise is solved by firstly establishing a uniform circular array data receiving model under the impact noise environment, designing an impact-removing preprocessing scheme and utilizing a new parameter estimation method.
Through the search of the prior art documents, the mode space matrix reconstruction algorithm based on the uniform circular array is utilized in the mode space matrix reconstruction algorithm published in the journal of electronics and information (2007, vol.29, no.12, pp.2832-2835) of high book, etc., the Toeplitz matrix is reconstructed, the incoming wave direction of a coherent source is successfully estimated, but under the background of impact noise, the method performance is seriously deteriorated to cause failure. Han Xiaodong et al, in DOA estimation of a uniform circular array coherent source under an impact noise background published in application science and technology (2012, vol.39, no.1, pp.35-39), are based on the ideas of a mode spatial transformation algorithm and a spatial smoothing algorithm, and combine with the ROC-MUSIC algorithm and the FLOM-MUSIC algorithm to realize DOA estimation of the uniform circular array coherent source under the impact noise background, but the required calculation time is long, the performance is deteriorated under the conditions of low signal-to-noise ratio and few snapshot sampling, and the DOA estimation speed and the accuracy problem of the coherent source under the impact noise environment cannot be solved.
Compressed sensing is used as a new signal acquisition and processing theory, can fully utilize the sparsity of signals, and is widely applied to various fields such as signal processing. The compressed sensing theory extracts interesting target information from a small amount of observed data, designs an observed matrix to reduce the required data dimension, and can accurately recover the parameter information of the original signal from fewer observed data. Therefore, when the problem of DOA estimation of a coherent signal source is solved under the condition of impact noise, a de-impact pretreatment scheme is designed, and mode excitation is carried out on an output signal of a uniform circular array to form a virtual array in a mode space, on the basis, the required parameters are estimated by utilizing a small amount of measured values through orthogonal matching sparse reconstruction based on sparsity of the signal, and the problem of target parameter estimation under the severe noise environment is effectively solved. Simulation results show that the coherent signal parameter estimation method based on the uniform circular array in the impact noise environment can ensure the accuracy of estimation, can provide 360-degree azimuth information, has strong resolution, reduces the calculated amount caused by space smoothing, and has obvious advantages especially under the conditions of fewer snapshot sampling numbers and low signal to noise ratio.
In summary, in the prior art, the estimation performance is obviously degraded in a coherent source environment, and even the estimation performance is completely invalid and cannot be estimated; only the azimuth angle estimation deviating from the array axis can be provided, and the calculation amount is too large.
Disclosure of Invention
The invention aims to provide a coherent information source DOA estimation method based on a uniform circular array in an impact noise environment with higher effectiveness and robustness.
A coherent signal parameter estimation method based on a uniform circular array in an impact noise environment comprises the following steps:
(1) Carrying out snapshot sampling on D information source signals in the space;
(2) Performing impact-removing pretreatment on snapshot sampling data;
(3) Performing mode excitation transformation on the array output data;
(4) Constructing a sparse reconstruction dictionary set;
(5) Sparse reconstruction is carried out to obtain a coherent information source azimuth angle;
(6) Judging whether the maximum iteration times are reached, if so, executing a step seven; if not, let t=t+1, return to step five;
(7) And obtaining a sparse reconstruction result, obtaining information of the azimuth angle of the information source by using the index set U, and outputting a coherent information source direction of arrival estimation result.
The snapshot sampling of the space D information source signals comprises:
the antenna array is a circular array with radius r on xy plane, M isotropic array elements are uniformly distributed on circumference, the center of circle of the circular array antenna is used as reference point, D far-field narrowband signals are distributed in azimuth angle { theta } 1 ,θ 2 ,…,θ D Incident on a uniform circular array with azimuth angle θ d ∈[0,360°](d=1, 2, …, D) refers to the angle between the projection of the origin to source line on the xy plane and the x axis in the counterclockwise direction, and the source is coplanar with the array;
the array receives the kth snapshot sample data as:
X(k)＝A(θ)S(k)+N(k)
wherein X (k) = [ X ] 1 (k),x 2 (k),…,x M (k)] T A received data vector for the array;
A(θ)＝[a(θ 1 ) a(θ 2 ) … a(θ D )]is a signal steering vector matrix, θ= (θ) 1 ,θ 2 ,…,θ D ) Is the angle vector, θ d Is the incoming wave direction of the D-th source, d=1, 2, …, D; s (k) = [ S ] 1 (k),s 2 (k),…,s D (k)] T A received signal vector for a received antenna reference point; n (k) = [ N ] 1 (k),n 2 (k),…,n M (k)] T For the impact noise vector which is independently and uniformly distributed and meets the S alpha S distribution, determining the impact degree of noise by the characteristic index alpha;
d-th steering vector:
a(θ d )＝[exp(jk 0 rcos(θ d -γ 0 )),exp(jk 0 rcos(θ d -γ 1 )),…,exp(jk 0 rcos(θ d -γ M-1 ))] T
wherein d=1, 2, …, D; k (k) 0 Represents wave number, k 0 =2pi/λ; lambda is the wavelength of the incident signal; gamma ray m ＝2πm/MM=0, 1,2, …, M-1, represents the angle of the M-th element of the array with the x-axis.
The impact-removing pretreatment for the snapshot sampling data comprises the following steps:
taking single snapshot sampling data as a unit, constructing the upper limit max { |x of the amplitude of the kth snapshot sampling data 1 (k)|,|x 2 (k)|,…,|x M (k) I } to
The received data is normalized for a standard, wherein the value of q is determined from the characteristic index α of the impact noise sαs distribution.
The performing mode excitation transformation on the array output data comprises:
wherein t=j -1 C v F/M，F＝[w -l ,w -l+1 ,…,w l ] H ，l＝-h,…,0,…,h，
w l ＝[1,exp(j2πl/M),…,exp(j2πl(M-1)/M)] H ，
J＝diag{J -h (β),…,J -1 (β),J 0 (β),J 1 (β),…,J h (β)}，
C v ＝diag{j -h ,…,j -1 ,j 0 ,j 1 ,…,j h And h is equal to 2 pi r/lambda which is the maximum mode number of mode excitation, J l (β), l= -h, …,0, …, h, is a first class bessel function of order l.
The constructing a sparse reconstruction dictionary set includes:
under the condition of K-time snapshot sampling, the output signal data matrix is
Define covariance matrix of output signal +.>
For covariance matrix->
Performing eigenvalue decomposition, wherein the eigenvectors corresponding to the D large eigenvalues are v respectively 1 ,v 2 ,…,v D By E S ＝span{v 1 ,v 2 ,…v D Construction of Signal subspace E S The method comprises the steps of carrying out a first treatment on the surface of the Dividing the possible range (0, 360 DEG) of the source at equal intervals, phi= (phi) 1 ,φ 2 ,…,φ P ) Wherein the value of P is determined by the dividing precision, P is larger than the far-field narrowband signal number D, and a signal guide vector sparse dictionary set B (phi) = [ B (phi) 1 ) b(φ 2 ) … b(φ P )]，b(φ p ) For sparse dictionary set atoms, p=1, 2, …, P, b (Φ) p )＝exp(jlφ p ) L= -h, …,0, …, h; signal subspace E S Initial residual r defined as sparse reconstruction 0 Setting t as the iteration number of sparse reconstruction, t=1, 2, …, D, setting t=1 for initial values, setting an index set U, and setting the initial index set as an empty set.
The sparse reconstruction obtains a coherent source azimuth angle, which comprises the following steps:
respectively calculating residual errors r in the t-th iteration process t-1 At each signal steering vector sparse dictionary set atom b (phi) p ) (p=1, 2, …, P) recording the atom corresponding to the maximum projection coefficient
Adding the index set U into the index set; reconstructing an original signal using an index set U, an approximation solution s of the original signal t ＝U + r t-1 ＝(U T U) -1 U T r t-1 And updates the residual to +.>
The invention has the beneficial effects that:
(1) The method solves the problem of coherent signal parameter estimation based on a uniform circular array in an impact noise environment, adopts the mode excitation transformation and compressed sensing sparse heavy conception as the basis of parameter estimation, and has the advantages of low calculation complexity, short calculation time and high robustness.
(2) Compared with the existing coherent signal parameter estimation method based on the uniform circular array, the method can solve the problem of the coherent signal source direction of arrival in the impulse noise environment by combining the mode excitation transformation and the compressed sensing sparse heavy conception through the de-impulse pretreatment, and the provided parameter estimation scheme is also suitable for the problem of the coherent signal source direction of arrival estimation in the Gaussian noise environment, so that the designed method is wider in applicability.
(3) The method for estimating the direction of arrival of the coherent signal source by using the mode excitation transformation and the compressed sensing sparse conception can obtain an estimated value with higher accuracy in a shorter time, and the method for estimating the robust parameters can rapidly and effectively estimate the direction of arrival under the conditions of small snapshot sampling number and low signal to noise ratio.
Drawings
FIG. 1 is a schematic diagram of a coherent signal parameter estimation method based on a uniform circular array in an impulse noise environment;
fig. 2 is a graph of the variation of the success probability of coherent signal arrival direction estimation based on a uniform circular array with signal to noise ratio by using mode excitation transformation and compressed sensing sparse reconstruction when the characteristic index α=1.5;
fig. 3 is a graph of the variation of the success probability of coherent signal arrival direction estimation based on a uniform circular array with signal to noise ratio using mode excitation transformation and compressed sensing sparse reconstruction when the characteristic index α=0.8;
fig. 4 is a graph of the success probability of coherent signal arrival direction estimation based on a uniform circular array with the mode excitation transformation and compressed sensing sparse reconstruction concept when the characteristic index α=1.5;
fig. 5 is a graph of the success probability of coherent signal arrival direction estimation based on a uniform circular array with the mode excitation transformation and compressed sensing sparse reconstruction concept when the characteristic index α=0.8;
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Coherent signal parameter estimation method based on uniform circular array in impact noise environment
The invention relates to a method for carrying out robust estimation on the direction of arrival of a coherent signal based on a uniform circular array under the impact noise environment by jointly realizing mode excitation and a sparse reconstruction mechanism, belonging to the field of array signal processing parameter estimation.
Spatial spectrum estimation is a key technology in the fields of short wave direction finding, radio reconnaissance, radar target positioning tracking, intelligent antennas and the like, and accurate direction of arrival (DOA) estimation has important significance for improving the performance of a communication system. Because of simple structure and convenient analysis, the early spatial spectrum estimation algorithm and application are proposed based on the linear array, but the linear array can only provide azimuth angle estimation deviating from the array axis. Compared with a linear array, the circular array can provide 360-degree omnibearing and non-fuzzy azimuth angle estimation, has approximately the same resolution in each azimuth, can simultaneously provide azimuth angle and pitch angle two-dimensional angle estimation, and has more practical value. The particularity of the uniform circular array structure makes the array flow pattern of the uniform circular array structure not have the vandermonde structure of the linear array, so that many excellent estimation schemes suitable for the linear array cannot be directly applied to the circular array. The beam space transformation based on the phase mode excitation is an effective proposal for the uniform circular array, and the array flow pattern of the uniform circular array can be transformed into a form similar to a vandermonde matrix through the beam space transformation.
Smart antennas exploit the spatial differences between mobile users to achieve capacity multiplication, and in an actual mobile environment, multipath signals formed by the same mobile user signal passing through various reflectors are generally considered coherent. The common high-resolution signal estimation method has better resolution performance under the condition of independent sources, but the estimation performance is obviously deteriorated under the coherent source environment, and even the estimation performance is completely invalid and cannot be estimated. Due to the presence of coherent signals, neither the conventional multiple signal classification (MUSIC) algorithm nor the rotation invariant subspace (ESPRIT) algorithm can estimate the direction of arrival of the signal correctly. For uniform linear arrays, although spatial smoothing algorithms can process coherent signal sources, these decorrelation algorithms cannot be directly applied to uniform circular arrays. The uniform circular array is converted into a virtual uniform linear array, and the obtained virtual uniform linear array has translational invariance like a common linear array, so that spatial smoothing decoherence can be applied, but the calculated amount is increased while the spatial smoothing is performed.
The traditional high-resolution direction-finding estimation schemes all consider a Gaussian white noise signal model, and in practical cases, background environments are not ideal Gaussian white noise, and impact noise conditions expressed by a symmetrical alpha stable distribution process (Salpha S) exist. Because the impulse noise does not have the second-order moment or the higher-order moment, the direction of arrival estimation problem under the impulse noise can not be directly transplanted into the target parameter estimation scheme under the Gaussian noise, otherwise, the algorithm performance can be drastically reduced or even disabled. The conventional MUSIC method based on co-transformation and fractional low-order moment can solve the DOA estimation problem under the condition of impact noise, but the multi-dimensional search brings higher calculated amount, and the performance is obviously reduced under the condition of fewer snapshots. The DOA estimation problem of a coherent signal source based on a uniform circular array under impact noise is solved by firstly establishing a uniform circular array data receiving model under the impact noise environment, designing an impact-removing preprocessing scheme and utilizing a new parameter estimation method.
Through the search of the prior art documents, the mode space matrix reconstruction algorithm based on the uniform circular array is utilized in the mode space matrix reconstruction algorithm published in the journal of electronics and information (2007, vol.29, no.12, pp.2832-2835) of high book, etc., the Toeplitz matrix is reconstructed, the incoming wave direction of a coherent source is successfully estimated, but under the background of impact noise, the method performance is seriously deteriorated to cause failure. Han Xiaodong et al, in DOA estimation of a uniform circular array coherent source under an impact noise background published in application science and technology (2012, vol.39, no.1, pp.35-39), are based on the ideas of a mode spatial transformation algorithm and a spatial smoothing algorithm, and combine with the ROC-MUSIC algorithm and the FLOM-MUSIC algorithm to realize DOA estimation of the uniform circular array coherent source under the impact noise background, but the required calculation time is long, the performance is deteriorated under the conditions of low signal-to-noise ratio and few snapshot sampling, and the DOA estimation speed and the accuracy problem of the coherent source under the impact noise environment cannot be solved.
Compressed sensing is used as a new signal acquisition and processing theory, can fully utilize the sparsity of signals, and is widely applied to various fields such as signal processing. The compressed sensing theory extracts interesting target information from a small amount of observed data, designs an observed matrix to reduce the required data dimension, and can accurately recover the parameter information of the original signal from fewer observed data. Therefore, when the problem of DOA estimation of a coherent signal source is solved under the condition of impact noise, a de-impact pretreatment scheme is designed, and mode excitation is carried out on an output signal of a uniform circular array to form a virtual array in a mode space, on the basis, the required parameters are estimated by utilizing a small amount of measured values through orthogonal matching sparse reconstruction based on sparsity of the signal, and the problem of target parameter estimation under the severe noise environment is effectively solved. Simulation results show that the coherent signal parameter estimation method based on the uniform circular array in the impact noise environment can ensure the accuracy of estimation, can provide 360-degree azimuth information, has strong resolution, reduces the calculated amount caused by space smoothing, and has obvious advantages especially under the conditions of fewer snapshot sampling numbers and low signal to noise ratio.
The invention aims to provide a coherent information source DOA estimation method based on a uniform circular array in an impact noise environment with higher effectiveness and robustness.
The invention is realized in the following way:
step one, performing snapshot sampling on space D information source signals;
the antenna array is a circular array with the radius r on the xy plane, M isotropic array elements are uniformly distributed on the circumference, and the circle center of the circular array antenna is a reference point; d far-field narrowband signals are distributed in azimuth angle { theta } 1 ,θ 2 ,…,θ D Incident on a uniform circular array where azimuth angle θ d ∈[0,360°](d=1, 2, …, D) means that the projection of the origin-to-source line on the xy plane is inverse to the x-axisThe included angle on the hour hand is the same plane as the array, namely the included angle between the connecting line from the specified origin to the source and the z-axis is 90 degrees; the array receives the kth snapshot sample data as X (k) =a (θ) S (k) +n (k), where X (k) = [ X ] 1 (k),x 2 (k),…,x M (k)] T A (θ) = [ a (θ 1 ) a(θ 2 ) … a(θ D )]Is a signal steering vector matrix, where θ= (θ) 1 ,θ 2 ,…,θ D ) Is the angle vector, θ d Is the incoming wave direction of the D-th source, d=1, 2, …, D, S (k) = [ S ] 1 (k),s 2 (k),…,s D (k)] T For receiving a received signal vector of an antenna reference point, N (k) = [ N ] 1 (k),n 2 (k),…,n M (k)] T For the impact noise vector which is independently and uniformly distributed and meets the S alpha S distribution, determining the impact degree of noise by the characteristic index alpha; the d-th steering vector a (θ d )＝[exp(jk 0 rcos(θ d -γ 0 )),exp(jk 0 rcos(θ d -γ 1 )),…,exp(jk 0 rcos(θ d -γ M-1 ))] T D=1, 2, …, D, where k 0 Represents wave number, k 0 =2pi/λ, λ is the wavelength of the incident signal, γ m =2πm/M, m=0, 1,2, …, M-1, representing the angle between the M-th element of the array and the x-axis;
step two, performing impact removal pretreatment on snapshot sampling data;
taking single snapshot sampling data as a unit, constructing the upper limit max { |x of the amplitude of the kth snapshot sampling data 1 (k)|,|x 2 (k)|,…,|x M (k) -max is a maximum function; to be used for
Normalizing the received data for a standard, wherein the value of q is determined according to the characteristic index alpha of the impact noise S alpha S distribution;
step three, performing mode excitation transformation on the array output data;
J＝diag{J -h (β),…,J -1 (β),J 0 (β),J 1 (β),…,J h (β)}，C v ＝diag{j -h ,…,j -1 ,j 0 ,j 1 ,…,j h In the formula, h is about 2 pi r/lambda is the maximum mode number of mode excitation, J l (β), l= -h, …,0, …, h, is a first class bessel function of order l;
step four, constructing a sparse reconstruction dictionary set;
consider that under the condition of K-time snapshot sampling, the output signal data matrix is
Define covariance matrix of output signal +.>
For covariance matrix->
Performing eigenvalue decomposition, wherein the eigenvectors corresponding to the D large eigenvalues are v respectively 1 ,v 2 ,…,v D By E S ＝span{v 1 ,v 2 ,…v D Construction of Signal subspace E S The method comprises the steps of carrying out a first treatment on the surface of the Dividing the possible range (0, 360 DEG) of the source at equal intervals, phi= (phi) 1 ,φ 2 ,…,φ P ) Wherein the value of P is determined by the dividing precision, P is far greater than the far-field narrowband signal number D, and a signal guide vector sparse dictionary set B (phi) = [ B (phi) 1 ) b(φ 2 ) … b(φ P )]，b(φ p ) For sparse dictionary set atoms, p=1, 2, …, P, where b (φ p )＝exp(jlφ p ) L= -h, …,0, …, h; signal subspace E S Initial residual r defined as sparse reconstruction 0 Setting t asThe iteration times of sparse reconstruction, t=1, 2, …, D, initial value setting t=1, index set U, initial index set being empty set;
step five, sparse reconstruction is carried out to obtain a coherent information source azimuth angle;
respectively calculating residual errors r in the t-th iteration process t-1 At each signal steering vector sparse dictionary set atom b (phi) p ) (p=1, 2, …, P) recording the atom corresponding to the maximum projection coefficient
Adding the index set U into the index set; reconstructing an original signal using an index set U, an approximation solution s of the original signal t ＝U + r t-1 ＝(U T U) -1 U T r t-1 And updates the residual to +.>
Step six, judging whether the maximum iteration times are reached, if so, executing a step seven; if not, let t=t+1, return to step five;
and seventhly, obtaining a sparse reconstruction result, obtaining information source azimuth angle information by using the index set U, and outputting a coherent information source direction of arrival estimation result.
(1) The method solves the problem of coherent signal parameter estimation based on a uniform circular array in an impact noise environment, adopts the mode excitation transformation and compressed sensing sparse heavy conception as the basis of parameter estimation, and has the advantages of low calculation complexity, short calculation time and high robustness.
(2) Compared with the existing coherent signal parameter estimation method based on the uniform circular array, the method can solve the problem of the coherent signal source direction of arrival in the impulse noise environment by combining the mode excitation transformation and the compressed sensing sparse heavy conception through the de-impulse pretreatment, and the provided parameter estimation scheme is also suitable for the problem of the coherent signal source direction of arrival estimation in the Gaussian noise environment, so that the designed method is wider in applicability.
Experimental results show that the method for estimating the direction of arrival of the coherent signal source by using the mode excitation transformation and the compressed sensing sparse conception can obtain an estimated value with higher accuracy in a shorter time, and the method for estimating the robust parameters can rapidly and effectively estimate the direction of arrival under the conditions of small snapshot sampling number and low signal to noise ratio.
Fig. 1 is a schematic diagram of a coherent signal parameter estimation method based on a uniform circular array in an impulse noise environment.
Fig. 2 shows the variation of the success probability of coherent signal arrival direction estimation based on a uniform circular array with the signal-to-noise ratio by using the mode excitation transformation and the compressed sensing sparse reconstruction when the characteristic index α=1.5.
Fig. 3 shows the variation of the success probability of coherent signal arrival direction estimation based on a uniform circular array with the signal to noise ratio by using the mode excitation transformation and the compressed sensing sparse reconstruction when the characteristic index α=0.8.
Fig. 4 shows the variation of the success probability of coherent signal arrival direction estimation based on a uniform circular array with the number of snapshot samples when using the mode excitation transformation and the compressed sensing sparse reconstruction concept at the characteristic index α=1.5.
Fig. 5 shows the variation of the success probability of coherent signal arrival direction estimation based on a uniform circular array with the number of snapshot samples when using the mode excitation transform and the compressed sensing sparse reconstruction concept at the characteristic index α=0.8.
The invention provides a method for realizing robust estimation of a signal direction of arrival based on a uniform circular array in a complex noise environment and a severe direction finding background, aiming at the defects of the prior method for estimating the direction of arrival of a coherent source signal in an impact noise environment. The method comprises the steps of firstly establishing a data receiving model of a uniform circular array in an impact noise environment, then designing a de-impact pretreatment method, and utilizing mode excitation transformation and compressed sensing sparse heavy conception to want to solve the signal arrival direction. In engineering application, when the characteristic index of the impact noise is 2, the Gaussian noise distribution function form is satisfied, so the method provided by the invention can also solve the signal direction of arrival estimation problem of the Gaussian noise environment, and can ensure the coherent source signal azimuth estimation with low calculation complexity and high success probability under the conditions of small snapshot sampling number and low signal to noise ratio.
The invention is realized by the following technical scheme, which mainly comprises the following steps:
step one, performing snapshot sampling on space D information source signals;
the antenna array is a circular array with the radius r on the xy plane, M isotropic array elements are uniformly distributed on the circumference, and the circle center of the circular array antenna is a reference point; d far-field narrowband signals are distributed in azimuth angle { theta } 1 ,θ 2 ,…,θ D Incident on a uniform circular array where azimuth angle θ d ∈[0,360°](d=1, 2, …, D) means that the projection of the origin-to-source line on the xy plane is at an angle to the x-axis that is counter-clockwise and the source is coplanar with the array, i.e. the angle between the z-axis and the origin-to-source line is specified to be 90 °; the array receives the kth snapshot sample data as X (k) =a (θ) S (k) +n (k), where X (k) = [ X ] 1 (k),x 2 (k),…,x M (k)] T A (θ) = [ a (θ 1 ) a(θ 2 ) … a(θ D )]Is a signal steering vector matrix, where θ= (θ) 1 ,θ 2 ,…,θ D ) Is the angle vector, θ d Is the incoming wave direction of the D-th source, d=1, 2, …, D, S (k) = [ S ] 1 (k),s 2 (k),…,s D (k)] T For receiving a received signal vector of an antenna reference point, N (k) = [ N ] 1 (k),n 2 (k),…,n M (k)] T For the impact noise vector which is independently and uniformly distributed and meets the S alpha S distribution, determining the impact degree of noise by the characteristic index alpha; the d-th steering vector a (θ d )＝[exp(jk 0 rcos(θ d -γ 0 )),exp(jk 0 rcos(θ d -γ 1 )),…,exp(jk 0 rcos(θ d -γ M-1 ))] T D=1, 2, …, D, where k 0 Represents wave number, k 0 =2pi/λ, λ is the wavelength of the incident signal, γ m =2πm/M, m=0, 1,2, …, M-1, representing the angle between the M-th element of the array and the x-axis;
step two, performing impact removal pretreatment on snapshot sampling data;
taking single snapshot sampling data as a unit, constructing the upper limit max { |x of the amplitude of the kth snapshot sampling data 1 (k)|,|x 2 (k)|,…,|x M (k) -max is a maximum function; to be used for
Normalizing the received data for a standard, wherein the value of q is determined according to the characteristic index alpha of the impact noise S alpha S distribution;
step three, performing mode excitation transformation on the array output data;
step four, constructing a sparse reconstruction dictionary set;
consider that under the condition of K-time snapshot sampling, the output signal data matrix is
Define covariance matrix of output signal +.>
For covariance matrix->
Performing eigenvalue decomposition, wherein the eigenvectors corresponding to the D large eigenvalues are v respectively 1 ,v 2 ,…,v D By E S ＝span{v 1 ,v 2 ,…v D Construction of Signal subspace E S The method comprises the steps of carrying out a first treatment on the surface of the Dividing the possible range (0, 360 DEG) of the source at equal intervals, phi= (phi) 1 ,φ 2 ,…,φ P ) Wherein the value of P is determined by the dividing precision, P is far greater than the far-field narrowband signal number D, and a signal guide vector sparse dictionary set B (phi) = [ B (phi) 1 ) b(φ 2 ) … b(φ P )]，b(φ p ) For sparse dictionary set atoms, p=1, 2, …, P, where b (φ p )＝exp(jlφ p ) L= -h, …,0, …, h; signal subspace E S Initial residual r defined as sparse reconstruction 0 Setting t as the iteration times of sparse reconstruction, t=1, 2, … and D, setting t=1 for initial values, setting an index set U, and setting the initial index set as an empty set;
step five, sparse reconstruction is carried out to obtain a coherent information source azimuth angle;
respectively calculating residual errors r in the t-th iteration process t-1 At each signal steering vector sparse dictionary set atom b (phi) p ) (p=1, 2, …, P) recording the atom corresponding to the maximum projection coefficient
Adding the index set U into the index set; reconstructing an original signal using an index set U, an approximation solution s of the original signal t ＝U + r t-1 ＝(U T U) -1 U T r t-1 And updates the residual to +.>
/>
Step six, judging whether the maximum iteration times are reached, if so, executing a step seven; if not, let t=t+1, return to step five;
and seventhly, obtaining a sparse reconstruction result, obtaining information source azimuth angle information by using the index set U, and outputting a coherent information source direction of arrival estimation result.
According to the method, the estimation speed and the estimation precision of the coherent source signal arrival direction based on the uniform circular array are considered in an impact noise environment, and the compressed sensing sparse weight concept is utilized to solve the signal azimuth information contained in the virtual linear array formed after the impact removal pretreatment and the mode excitation conversion. The designed method can also determine parameter information with lower calculation complexity under the conditions of small snapshot sampling number and low signal to noise ratio, so that the designed coherent source signal direction of arrival estimation method based on the uniform circular array meets higher performance requirements.
In the experiment, a uniform circular array with the array element number of 10 is used, the array element radius is 1.5lambda/pi, 2 coherent incident signals exist, the azimuth angles are 60 degrees and 200 degrees respectively, the background noise is an impact noise vector which is independently and uniformly distributed and satisfies S alpha S distribution, and the Monte Carlo experiment times are 100 times. In the implementation of the parameter estimation scheme, the generalized signal-to-noise ratio expression is
Wherein gamma represents the dispersion coefficient of impact noise, gamma=1, the parameter q=1.7 in the de-impact pretreatment process, the maximum mode number h is calculated to be h=3, 7 phase modes can be excited, and the search interval in the sparse reconstruction process is [0 DEG, 360 DEG ]]，P＝361。
Under the condition that the snapshot sampling number is 1024, the change situation of success probability of the signal arrival direction of the coherent signal source to be solved by utilizing mode excitation transformation and compressed sensing sparse reconstruction under different impact noise environments is shown as a figure 2 and a figure 3. Under the condition of generalized signal-to-noise ratio gsnr=15 dB, the conditions of success probability of solving the signal arrival direction of the coherent signal source by using mode excitation transformation and compressed sensing sparse reconstruction under different impact noise environments are shown in fig. 4 and fig. 5.
As can be seen from fig. 2 and 3, the probability of success in attempting to solve the direction of arrival of the coherent signal source signal using the proposed modal excitation transformation and compressed sensing sparse re-concept increases with increasing signal-to-noise ratio. The method can also ensure the success probability of the coherent signal source signal arrival direction estimation scheme based on the uniform circular array to a certain extent under the strong impact noise environment with the characteristic index smaller than 1. Simulation results prove that the scheme of carrying out coherent signal source signal arrival direction estimation based on a uniform circular array by using mode excitation transformation and compressed sensing sparse re-conception in the patent is suitable for direction-finding environments with complex environmental noise, low signal-to-noise ratio and the like.
As can be seen from fig. 4 and 5, the probability of success in attempting to solve the direction of arrival of the coherent signal source signal using the proposed modal excitation transformation and compressed sensing sparse re-concept increases with increasing number of samples. Under the condition of small snapshot sampling, the scheme can still solve the signal arrival direction of the coherent signal source based on the uniform circular array with higher success probability. Simulation results prove that the scheme of carrying out coherent signal source signal arrival direction estimation based on a uniform circular array by using mode excitation transformation and compressed sensing sparse re-conception in the patent is suitable for direction-finding environments such as complex environmental noise, small snapshot sampling and the like.
The coherent signal parameter estimation method based on the uniform circular array in the impact noise environment is characterized by comprising the following comprehensive characteristics: (1) The method for pre-processing the array received data in the impact noise environment comprises the following steps of (1) processing the data received by the array; (2) A mode excitation conversion method for processing array receiving data of a uniform circular array; (3) And utilizing compressed sensing sparse conception to want to solve the arrival angle information of the coherent signal source. The method for removing the impact pretreatment designed in the impact noise environment normalizes the snapshot sampling data with a special value due to the impact of the impact noise by setting a threshold, fully considers the characteristics of the impact noise, can be used for solving the signal parameter estimation problem in the impact noise environment, has good robustness and higher estimation accuracy in the strong impact noise environment, and has practical application value. The mode excitation transformation processing provided for the array receiving data of the uniform circular array utilizes a virtual array formed by mode space transformation as the basis of subsequent parameter estimation, fully considers the structural characteristics of the array, can be used for providing 360-degree azimuth information, and ensures a signal direction-of-arrival estimation scheme with high resolution and low computational complexity. The method utilizes the compressed sensing sparse conception to solve the azimuth angle information of the coherent signal source, fully considers the characteristics of a sparse dictionary set, successfully estimates the incoming wave direction of the coherent source, can be used for solving the parameter estimation problems in a complex noise environment, a low signal-to-noise ratio and a small snapshot sampling number direction-finding environment, and has the advantages of low calculation complexity, high estimation speed and high estimation accuracy.
1. A coherent signal parameter estimation method based on a uniform circular array in an impact noise environment is characterized by comprising the following steps:
step one, performing snapshot sampling on space D information source signals;
the antenna array is a circular array with the radius r on the xy plane, M isotropic array elements are uniformly distributed on the circumference, and the circle center of the circular array antenna is a reference point; d far-field narrowband signals are distributed in azimuth angle { theta } 1 ,θ 2 ,…,θ D Incident on a uniform circular array where azimuth angle θ d ∈[0,360°](d=1, 2, …, D) means that the projection of the origin-to-source line on the xy plane is at an angle to the x-axis that is counter-clockwise and the source is coplanar with the array, i.e. the angle between the z-axis and the origin-to-source line is specified to be 90 °; the array receives the kth snapshot sample data as X (k) =a (θ) S (k) +n (k), where X (k) = [ X ] 1 (k),x 2 (k),…,x M (k)] T A (θ) = [ a (θ 1 ) a(θ 2 ) … a(θ D )]Is a signal steering vector matrix, where θ= (θ) 1 ,θ 2 ,…,θ D ) Is the angle vector, θ d Is the incoming wave direction of the D-th source, d=1, 2, …, D, S (k) = [ S ] 1 (k),s 2 (k),…,s D (k)] T For receiving a received signal vector of an antenna reference point, N (k) = [ N ] 1 (k),n 2 (k),…,n M (k)] T For the impact noise vector which is independently and uniformly distributed and meets the S alpha S distribution, determining the impact degree of noise by the characteristic index alpha; the d-th steering vector a (θ d )＝[exp(jk 0 rcos(θ d -γ 0 )),exp(jk 0 rcos(θ d -γ 1 )),…,exp(jk 0 rcos(θ d -γM-1))] T D=1, 2, …, D, where k 0 Represents wave number, k 0 =2pi/λ, λ is the wavelength of the incident signal, γ m =2πm/M, m=0, 1,2, …, M-1, representing the angle between the M-th element of the array and the x-axis;
step two, performing impact removal pretreatment on snapshot sampling data;
taking single snapshot sampling data as a unit, constructing the upper limit max { |x of the amplitude of the kth snapshot sampling data 1 (k)|,|x 2 (k)|,…,|x M (k) -max is a maximum function; to be used for
Normalizing the received data for a standard, wherein the value of q is determined according to the characteristic index alpha of the impact noise S alpha S distribution;
step three, performing mode excitation transformation on the array output data;
step four, constructing a sparse reconstruction dictionary set;
consider that under the condition of K-time snapshot sampling, the output signal data matrix is
Define covariance matrix of output signal +.>
For covariance matrix->
Performing eigenvalue decomposition, wherein D eigenvectors corresponding to large eigenvaluesThe amounts are v respectively 1 ,v 2 ,…,v D By E S ＝span{v 1 ,v 2 ,…v D Construction of Signal subspace E S The method comprises the steps of carrying out a first treatment on the surface of the Dividing the possible range (0, 360 DEG) of the source at equal intervals, phi= (phi) 1 ,φ 2 ,…,φ P ) Wherein the value of P is determined by the dividing precision, P is far greater than the far-field narrowband signal number D, and a signal guide vector sparse dictionary set B (phi) = [ B (phi) 1 ) b(φ 2 ) … b(φ P )]，b(φ p ) For sparse dictionary set atoms, p=1, 2, …, P, where b (φ p )＝exp(jlφ p ) L= -h, …,0, …, h; signal subspace E S Initial residual r defined as sparse reconstruction 0 Setting t as the iteration times of sparse reconstruction, t=1, 2, … and D, setting t=1 for initial values, setting an index set U, and setting the initial index set as an empty set;
step five, sparse reconstruction is carried out to obtain a coherent information source azimuth angle;
respectively calculating residual errors r in the t-th iteration process t-1 At each signal steering vector sparse dictionary set atom b (phi) p ) (p=1, 2, …, P) recording the atom corresponding to the maximum projection coefficient
Adding the index set U into the index set; reconstructing an original signal using an index set U, an approximation solution s of the original signal t ＝U + r t-1 ＝(U T U) -1 U T r t-1 And updates the residual to +.>
Step six, judging whether the maximum iteration times are reached, if so, executing a step seven; if not, let t=t+1, return to step five;
and seventhly, obtaining a sparse reconstruction result, obtaining information source azimuth angle information by using the index set U, and outputting a coherent information source direction of arrival estimation result.
Claims (1)
1. A coherent signal parameter estimation method based on a uniform circular array in an impact noise environment is characterized by comprising the following steps:
step one, performing snapshot sampling on space D information source signals;
the antenna array is a circular array with the radius r on the xy plane, M isotropic array elements are uniformly distributed on the circumference, and the circle center of the circular array antenna is a reference point; d source signals are transmitted in azimuth angle { θ } 1 ,θ 2 ,…,θ D Incident on a uniform circular array where azimuth angle θ d ∈[0,360°]D=1, 2, …, D, which means that the projection of the line from the center reference point of the circular array antenna to the source on the xy plane forms an angle with the x axis in the counterclockwise direction, and the source is coplanar with the array, that is, the angle between the line from the center reference point of the circular array antenna to the source and the z axis is 90 °; the array receives the kth snapshot sample data as X (k) =a (θ) S (k) +n (k), where X (k) = [ X ] 1 (k),x 2 (k),…,x M (k)] T A (θ) = [ a (θ 1 ) a(θ 2 )…a(θ D )]Is a signal steering vector matrix, where θ= (θ) 1 ,θ 2 ,…,θ D ) Is the angle vector, θ d Is azimuth, where d=1, 2, …, D, S (k) = [ S ] 1 (k),s 2 (k),…,s D (k)] T For receiving a received signal vector of an antenna reference point, N (k) = [ N ] 1 (k),n 2 (k),…,n M (k)] T For the impact noise vector which is independently and uniformly distributed and meets the S alpha S distribution, determining the impact degree of noise by the characteristic index alpha; the d-th steering vector a (θ d )＝[exp(jk 0 rcos(θ d -γ 0 )),exp(jk 0 rcos(θ d -γ 1 )),…,exp(jk 0 rcos(θ d -γ M-1 ))] T D=1, 2, …, D, where k 0 Represents wave number, k 0 =2pi/λ, λ is the wavelength of the incident signal, γ m 2 pi M/M, where m=0, 1,2, …, M-1, represents the angle of the M-th element of the array with the x-axis;
step two, performing impact removal pretreatment on snapshot sampling data;
in single snapshot sampling numberAccording to the unit, constructing the upper limit max { |x of the amplitude of the sampling data of the kth snapshot 1 (k)|,|x 2 (k)|,…,|x M (k) -max is a maximum function; to be used for
Normalizing the received data for a standard, wherein the value of q is determined according to the characteristic index alpha of the impact noise S alpha S distribution;
thirdly, performing mode excitation conversion on the array output data subjected to the de-impact pretreatment;
step four, constructing a sparse reconstruction dictionary set in the following manner;
consider that under the condition of K-time snapshot sampling, the output signal data matrix is
Define covariance matrix of output signal +.>
For covariance matrix->
Performing feature value decomposition, wherein D features corresponding to large feature valuesVectors are v respectively 1 ,v 2 ,…,v D By E S ＝span{v 1 ,v 2 ,…v D Construction of Signal subspace E S The method comprises the steps of carrying out a first treatment on the surface of the Dividing the possible range (0, 360 DEG) of the source at equal intervals, phi= (phi) 1 ,φ 2 ,…,φ P ) Wherein the value of P is determined by the dividing precision, P is larger than the signal number D of the signal source, and a signal guiding vector sparse dictionary set B (phi) = [ B (phi) 1 ) b(φ 2 )…b(φ P )]，b(φ p ) Wherein p=1, 2, …, P is a sparse dictionary set atom, where b (φ p )＝exp(jlφ p ) L= -h, …,0, …, h; signal subspace E S Initial residual r defined as sparse reconstruction 0 Setting t as the iteration times of sparse reconstruction, wherein t=1, 2, … and D, setting t=1 for initial values, setting an index set U, and setting the initial index set as an empty set;
step five, sparse reconstruction is carried out to obtain a coherent information source azimuth angle;
respectively calculating residual errors r in the t-th iteration process t-1 At each signal steering vector sparse dictionary set atom b (phi) p ) Projection values of p=1, 2, …, P, recording atoms corresponding to maximum projection coefficients
Adding the index set U into the index set; reconstructing an original signal using an index set U, an approximation solution s of the original signal t ＝U + r t-1 ＝(U T U) -1 U T r t-1 And updates the residual to +.>
Step six, judging whether the maximum iteration times are reached, if so, executing a step seven; if not, let t=t+1, return to step five;
and seventhly, obtaining a sparse reconstruction result, obtaining information source azimuth angle information by using the index set U, and outputting a coherent information source direction of arrival estimation result.
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