CN113283055A - Multi-signal separation and direction finding combined processing method based on parallel factor model - Google Patents

Multi-signal separation and direction finding combined processing method based on parallel factor model Download PDF

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CN113283055A
CN113283055A CN202110441319.8A CN202110441319A CN113283055A CN 113283055 A CN113283055 A CN 113283055A CN 202110441319 A CN202110441319 A CN 202110441319A CN 113283055 A CN113283055 A CN 113283055A
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阙中元
张小飞
李宝宝
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a multi-signal separation and direction finding combined processing method based on a parallel factor model, which utilizes a uniform area array to collect mixed electromagnetic signals containing multiple signals as receiving sampling signals; preprocessing a received sampling signal, and performing angle estimation by utilizing a subspace rotation algorithm to obtain a primary angle estimation value; constructing an initial estimated guide matrix according to the obtained initial angle estimation value; re-modeling the received sampled signal into a PARAFAC model; taking the constructed guide matrix as an initial value of PARAFAC decomposition, fitting a PARAFAC model by utilizing a TALS algorithm until a convergence condition is met, and acquiring an information source matrix and a guide matrix; extracting a separation signal from the estimated source matrix; and estimating the arrival angle corresponding to the separation signal from the estimated steering matrix. The method has low calculation complexity, and can effectively separate the source signals and estimate the corresponding angle parameters.

Description

Multi-signal separation and direction finding combined processing method based on parallel factor model
Technical Field
The invention belongs to the technical field of array signal processing, and particularly relates to a parallel factor model-based multi-signal separation and direction finding combined processing method applied to a uniform area array.
Background
The multi-signal separation and direction finding are key problems in radio frequency spectrum monitoring, electronic reconnaissance and wireless communication, and the main realization method is to receive electromagnetic signals propagated in space by using an array antenna, estimate the arrival directions of different signals by a digital signal processing means and extract the signals from a mixed signal.
At present, beamforming and subspace estimation technologies are mainly adopted for multi-signal separation and direction finding, and a relatively wide algorithm with subspace rotation methods such as ESPRIT, PM and the like is used, and parameter estimation is performed by using signal subspace rotation invariance of signal vectors, but the two algorithms can only estimate angles, cannot separate source signals, and have limited angle estimation performance. The beamforming method can separate signals in a certain direction, but the angular resolution of the method is low.
Tensor decomposition is an emerging technology in signal processing and data analysis, and has been widely applied in the fields of biomedicine, wireless communication, machine learning and the like, wherein parallel factor (PARAFAC) decomposition is one of the most commonly used tensor decomposition methods. When the parallel factor model is applied to array signal processing, source separation and direction finding can be realized by utilizing Trilinear Alternating Least Squares (TALS), and better performance can be obtained. However, the standard PARAFAC decomposition method has the problems of low convergence rate and high calculation complexity.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a multi-signal separation and direction finding combined processing method based on a parallel factor model, which can improve the performance of signal separation and angle estimation under a uniform area array and simultaneously reduce the calculation complexity of standard PARAFAC decomposition.
The technical scheme is as follows: the invention relates to a multi-signal separation and direction finding combined processing method based on a parallel factor model, which comprises the following steps of:
(1) collecting a mixed electromagnetic signal containing multiple signals by using a uniform area array as a receiving sampling signal;
(2) preprocessing a received sampling signal, and performing angle estimation by utilizing a subspace rotation algorithm to obtain a primary angle estimation value;
(3) constructing a steering matrix of initial estimation;
(4) re-modeling the received sampled signal in step (1) into a PARAFAC model;
(5) using the guide matrix as an initial value of PARAFAC decomposition, fitting a PARAFAC model by using a TALS algorithm until a convergence condition is met, and acquiring an information source matrix and a guide matrix;
(6) extracting a separation signal from the source matrix estimated in the step (5);
(7) and (5) estimating the arrival angle corresponding to the separation signal from the steering matrix estimated in the step (5).
Further, the step (2) comprises the steps of:
(21) estimating covariance matrix using received sampled signals
Figure BDA0003035158140000021
(22) Using covariance matrices
Figure BDA0003035158140000022
Block submatrix computation propagation operator
Figure BDA0003035158140000023
Constructing a signal subspace matrix E by the least square estimation of the method;
(23) computing a rotation matrix using a blocking sub-matrix of the signal sub-space matrix E
Figure BDA0003035158140000024
(24) Rotating matrix
Figure BDA0003035158140000025
Performing feature decomposition to obtain its feature value, and calculating angular frequency according to the feature value
Figure BDA0003035158140000026
Wherein K is the number of signals;
(25) reconstruction messageObtaining new signal subspace matrix E 'from the signal subspace matrix E', repeating the steps (23) and (24), and calculating another angular frequency
Figure BDA0003035158140000027
(26) According to the formula uk＝sinθkcosφkAnd vk＝sinθksinφkCalculating the pitch angle of the signal
Figure BDA0003035158140000028
And azimuth angle
Figure BDA0003035158140000029
Further, the initial estimation steering matrices in step (3) are respectively:
Ax＝[ax(u1),ax(u2),...,ax(uK)]
Ay＝[ay(v1),ay(v2),...,ay(vK)]
wherein, ax(uk) And ay(vk) The steering vectors on the x-axis and y-axis, respectively.
Further, the step (4) is realized as follows:
reusing third order tensor of received sampling signal according to parallel factor model
Figure BDA00030351581400000210
Representing, three data matrices are obtained by segmentation and stitching along three different dimensions:
Figure BDA00030351581400000211
Figure BDA00030351581400000212
and
Figure BDA00030351581400000213
wherein N and M each independently representThe number of array elements of the uniform array along the x axis and the y axis, and L represents the number of time domain sampling points.
Further, the step (5) includes the steps of:
(51) initialization with initial steering matrix
Figure BDA0003035158140000031
And
Figure BDA0003035158140000032
(52) computing
Figure BDA0003035158140000033
The least-squares estimation of (a) is,
Figure BDA0003035158140000034
wherein the symbol |, indicates a Khatri-Rao product, is indicated by the upper scale
Figure BDA0003035158140000035
Represents a pseudo-inverse;
(53) computing
Figure BDA0003035158140000036
The least-squares estimation of (a) is,
Figure BDA0003035158140000037
(54) computing
Figure BDA0003035158140000038
The least-squares estimation of (a) is,
Figure BDA0003035158140000039
(55) judging whether a set convergence condition is reached, and stopping the algorithm if the set convergence condition is reached; otherwise, the step (52) is returned to continue to calculate new estimated value.
Further, the step (7) includes the steps of:
(71) will be provided with
Figure BDA00030351581400000310
And
Figure BDA00030351581400000311
normalizing the column vectors to make the first term equal to 1;
(72) by axkAnd aykTo represent
Figure BDA00030351581400000312
And
Figure BDA00030351581400000313
the k-th column vector of (2), calculate rx＝-angle(axk)，ry＝-angle(ayk) Angle () represents the calculated phase angle;
(73) calculating a least squares estimate of the angular frequency from the phase versus angular frequency relationship:
Figure BDA00030351581400000314
Figure BDA00030351581400000315
wherein,
Bx＝[0,2πdx/λ,...,2π(N-1)dx/λ]T
By＝[0,2πdy/λ,...,2π(M-1)dy/λ]T
wherein d isx＝dyD is array element distance, and lambda is wavelength;
(74) according to the formula uk＝sinθkcosφkAnd vk＝sinθksinφkCalculating the pitch angle of the signal
Figure BDA00030351581400000316
And azimuth angle
Figure BDA00030351581400000317
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: 1. according to the multi-signal separation and direction finding combined processing method, a parallel factor analysis model is applied to the field of array signal processing, the direction finding precision in a uniform area array is superior to that of traditional algorithms such as PM and ESPRIT, angle pairing is not needed, and separation signals can be obtained during angle finding;
2. the method of the invention utilizes PM algorithm to carry out initial estimation of the angle, so that the TALS algorithm reaches the convergence stagnation point more quickly, and the calculated amount of the standard TALS algorithm adopting random initialization is reduced.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a uniform area array structure involved in the method of the present invention;
FIG. 3 is a schematic diagram of the waveform of the isolated signal obtained by the processing method of the present invention when the signal-to-noise ratio is 10 dB;
FIG. 4 is a scatter plot of the angle estimates obtained by the processing method of the present invention at a signal-to-noise ratio of 10 dB;
FIG. 5 is a graph comparing the convergence rate of the method of the present invention and the standard PARAFAC algorithm for the same array structure and the same fast beat number;
FIG. 6 is a graph comparing the angular estimation performance of the method of the present invention with the PM, ESPRIT, and PARAFAC methods for the same array structure and the same fast beat count;
FIG. 7 is a graph comparing the signal separation performance of the two methods of the present invention and standard PARAFAC at different signal-to-noise ratios;
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a multi-signal separation and direction finding combined processing method based on a parallel factor model, which specifically comprises the following steps as shown in figure 1:
step 1: and collecting a mixed electromagnetic signal containing multiple signals by using a uniform area array to serve as a receiving sampling signal.
FIG. 2 shows a method of the present inventionSchematic diagram of the related uniform area array structure. The planar array has N × M array elements, which are uniformly distributed, and the distance between adjacent array elements is d ═ dx＝dyD is less than or equal to lambda/2 (lambda is wavelength). Suppose that K incoherent far-field signals are incident on the uniform area array in the space, and the arrival direction is (theta)k,φk) K is 1,2, …, K, where θkAnd phikRepresenting the pitch and azimuth angles, respectively, of the k-th signal. The array received sample signal can be written as:
Figure BDA0003035158140000041
wherein,
Figure BDA0003035158140000042
a data matrix containing noise; l represents the number of time-domain sampling points;
Figure BDA0003035158140000043
is an information source matrix; n is a Gaussian white noise matrix;
Figure BDA0003035158140000044
for an array manifold matrix, it can be expressed that:
Figure BDA0003035158140000051
wherein, the symbol
Figure BDA0003035158140000052
Represents the Kronecker product, uk＝sinθkcosφk，vk＝sinθksinφk；ax(uk) And ay(vk) The steering vectors on the x-axis and y-axis, respectively, can be expressed as:
ax(uk)＝[1,exp(-j2πdxuk/λ),...,exp(-j2π(N-1)dxuk/λ)]T (3)
ay(vk)＝[1,exp(-j2πdyvk/λ),...,exp(-j2π(M-1)dyvk/λ)]T (4)
equation (2) can be further expressed as:
A＝[Ay⊙Ax] (5)
wherein, l represents a Khatri-Rao product, Ax＝[ax(u1),ax(u2),...,ax(uK)]，Ay＝[ay(v1),ay(v2),...,ay(vK)]。
Step 2: and (3) preprocessing the received sampling signal obtained in the step (1), and performing angle estimation by utilizing a subspace rotation algorithm to obtain a primary angle estimation value.
After a received data matrix is obtained, the PM algorithm is utilized to carry out initial angle estimation, and the method comprises the following steps:
(1) using a matrix of received sampled signals
Figure BDA0003035158140000053
Estimating a covariance matrix
Figure BDA0003035158140000054
(2) The covariance matrix
Figure BDA0003035158140000055
According to
Figure BDA0003035158140000056
Is divided into blocks, wherein
Figure BDA0003035158140000057
Is that
Figure BDA0003035158140000058
The first K column vectors of (a) make up a sub-matrix,
Figure BDA0003035158140000059
is left overA submatrix composed of column vectors;
(3) according to the formula
Figure BDA00030351581400000510
Computing least squares solutions for propagation operators
Figure BDA00030351581400000511
(4) Definition matrix
Figure BDA00030351581400000512
Wherein IKIs a K × K identity matrix, constructing a matrix Ex＝E1:N(M-1),1:KAnd Ey＝EN+1:MN,1:K，ExA sub-matrix composed of the 1 st to N (M-1) th rows of the matrix E, EyA sub-matrix formed by the N +1 th row to the MN th row of the matrix E;
(5) calculating a matrix according to a formula
Figure BDA00030351581400000513
(6) To pair
Figure BDA00030351581400000514
Decomposing the characteristic value to obtain the characteristic value
Figure BDA00030351581400000515
Calculating the angular frequency:
Figure BDA00030351581400000516
where λ is the signal wavelength and angle (-) represents the calculated phase angle;
(7) reconstructing the matrix E to obtain a matrix E', and constructing the matrix Ex'＝E'1:M(N-1),1:KAnd Ey'＝E'M+1:MN,1:K，Ex'submatrix composed of 1 st to M (N-1) th rows of a matrix E', Ey'is a sub-matrix composed of the M +1 th to the MN th rows of the matrix E';
(8) calculating a matrix according to a formula
Figure BDA0003035158140000061
(9) To pair
Figure BDA0003035158140000062
Decomposing the characteristic value to obtain the characteristic value
Figure BDA0003035158140000063
Another angular frequency is calculated:
Figure BDA0003035158140000064
(10) according to a formula
Figure BDA0003035158140000065
Figure BDA0003035158140000066
Wherein
Figure BDA0003035158140000067
Is an estimate of the pitch angle of the k-th signal,
Figure BDA0003035158140000068
is an estimate of the k-th signal azimuth.
And step 3: and (3) constructing an initial estimated steering matrix according to the initial angle estimation value obtained in the step (2).
After obtaining the initial angle estimation value calculated by the PM algorithm, a steering vector may be constructed according to formula (3) and formula (4), and then an initial estimation steering matrix is formed:
Ax＝[ax(u1),ax(u2),...,ax(uK)]
Ay＝[ay(v1),ay(v2),...,ay(vK)]
wherein, ax(uk) And ay(vk) The steering vectors on the x-axis and y-axis, respectively.
And 4, step 4: the received sampled signal in step 1 is re-modeled as a PARAFAC model.
According to the parallel factor (PARAFAC) model, the array received signal can be represented in the form of a trilinear model:
Figure BDA0003035158140000069
wherein A isx(n,k)，Ay(m, k), S (l, k) are each an x-axis direction matrix AxThe (n, k) -th element of (a), y-axis direction matrix AyAnd the (l, k) th element, x, of the source matrix Sn,l,mIs third order tensor
Figure BDA00030351581400000610
The (n, l, m) th element of (a).
Will be provided with
Figure BDA00030351581400000611
Three data matrixes are obtained by cutting and splicing along three different dimensions
Figure BDA00030351581400000612
Figure BDA00030351581400000613
And
Figure BDA00030351581400000614
wherein N and M respectively represent the array element number of the uniform area array used in the step 1 along the x axis and the y axis, and L represents the time domain sampling point number.
And 5: and (4) taking the guide matrix constructed in the step (3) as an initial value of PARAFAC decomposition, and fitting a PARAFAC model by utilizing a TALS algorithm until a convergence condition is met.
(1) Initialization of initial steering matrix obtained by PM initial estimation
Figure BDA0003035158140000071
And
Figure BDA0003035158140000072
(2) computing
Figure BDA0003035158140000073
The least-squares estimation of (a) is,
Figure BDA0003035158140000074
(3) computing
Figure BDA0003035158140000075
The least-squares estimation of (a) is,
Figure BDA0003035158140000076
(4) computing
Figure BDA0003035158140000077
The least-squares estimation of (a) is,
Figure BDA0003035158140000078
(5) calculating the convergence rate of the sum of the squares of the residual errors, and stopping the algorithm when the convergence rate is smaller than a set smaller value; otherwise, returning to the step (2) to continue to calculate a new estimated value.
Step 6: a separate signal is extracted from the source matrix estimated in step 5.
After the TALS algorithm is completed, the finally obtained information source matrix
Figure BDA0003035158140000079
Extracting by line to obtain K separated signal vectors { sk|1≤k≤K}。
And 7: and estimating the arrival angle corresponding to the separation signal from the steering matrix estimated in the step 5.
(1) Mixing the final product obtained in step 5
Figure BDA00030351581400000710
And
Figure BDA00030351581400000711
normalizing the column vectors to make the first term equal to 1;
(2) by axkAnd aykTo represent
Figure BDA00030351581400000712
And
Figure BDA00030351581400000713
the k-th column vector of (2), calculate rx＝-angle(axk)，ry＝-angle(ayk) Angle (·) represents the calculated phase angle;
(3) calculating a least squares estimate of the angular frequency from the phase to angular frequency relationship
Figure BDA00030351581400000714
Figure BDA00030351581400000715
Wherein B isx＝[0,2πdx/λ,...,2π(N-1)dx/λ]T，By＝[0,2πdy/λ,...,2π(M-1)dy/λ]T，dx＝dyD is the array element spacing;
(4) calculating the final angle estimation value according to a formula
Figure BDA00030351581400000716
Figure BDA00030351581400000717
Where the symbol | represents the modulus of the computed complex number.
Taking an 8 × 8 uniform area array as an example, suppose there are three different types of typical modulation signals in space, which are single carrier frequency signals s1(t)＝cos(2π×5×106t), chirp signal s2(t)＝cos(π×1012t2+2π×2×106t), amplitude modulated signal s3(t)＝cos(2π×3×105t)sin(2π×5×106t) angles of arrival are respectively (theta)1,φ1)＝(10°,15°)，(θ2,φ2) Equal to (20 °,25 °) and (θ3,φ3) At (30 °,35 °) a sampling frequency of 100 MHz.
Fig. 3 is a schematic diagram of a waveform of a separated signal obtained by the processing method of the present invention when the signal-to-noise ratio is 10dB, fig. 4 is a scatter diagram of an angle estimation obtained by the processing method of the present invention when the signal-to-noise ratio is 10dB, and the number L of time-domain sampling points is 800. As can be seen from fig. 3 and 4, the method of the present invention can effectively separate the source signals and estimate the corresponding angle parameters.
Fig. 5 is a comparison graph of the computational complexity of the method and the standard parafacc algorithm under the condition of the same array structure and the same number of sampling points, where the number of time-domain sampling points L is 800, and the number of simulation statistics is 1000. As can be seen from fig. 5, the computational complexity of the method of the present invention is lower than that of the standard PARAFAC decomposition method, and the convergence rate is increased by more than ten times in the present embodiment.
Fig. 6a and fig. 6b are comparison graphs of the angle estimation performance of the method of the present invention and four methods of PM, ESPRIT, and standard parafacc under the same array structure and the same fast beat number, where the number of time-domain sampling points L is 800, and the number of simulation statistics is 1000. RMSE represents the root mean square error of an angle. As can be seen from the graph, the angle estimation performance of the method is superior to that of the 2D-PM and 2D-ESPRIT algorithms, and the estimation performance of the method is close to that of the standard PARAFAC algorithm.
Fig. 7 is a comparison graph of the signal separation performance of the method of the present invention and the standard parafacc method under different signal-to-noise ratios, where the number L of time-domain samples is 800, and the number of simulation statistics is 1000. ρ represents an average similarity coefficient between the separated signal and the original signal. The figure shows that the signal separation performance of the method is close to the estimation performance of the standard PARAFAC algorithm, and the separation performance is improved along with the improvement of the signal-to-noise ratio.
Although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions should be considered to be within the scope of the present invention without departing from the principles of the invention.

Claims (6)

1. A multi-signal separation and direction finding combined processing method based on a parallel factor model is characterized by comprising the following steps:
(1) collecting a mixed electromagnetic signal containing multiple signals by using a uniform area array as a receiving sampling signal;
(2) preprocessing a received sampling signal, and performing angle estimation by utilizing a subspace rotation algorithm to obtain a primary angle estimation value;
(3) constructing a steering matrix of initial estimation;
(4) re-modeling the received sampled signal in step (1) into a PARAFAC model;
(5) using the guide matrix as an initial value of PARAFAC decomposition, fitting a PARAFAC model by using a TALS algorithm until a convergence condition is met, and acquiring an information source matrix and a guide matrix;
(6) extracting a separation signal from the source matrix estimated in the step (5);
(7) and (5) estimating the arrival angle corresponding to the separation signal from the steering matrix estimated in the step (5).
2. The parallel factor model-based multi-signal separation and direction-finding joint processing method according to claim 1, wherein the step (2) comprises the steps of:
(21) estimating covariance matrix using received sampled signals
Figure FDA0003035158130000011
(22) Using covariance matrices
Figure FDA0003035158130000012
Block submatrix computation propagation operator
Figure FDA0003035158130000013
Is estimated by least squaresA signal making subspace matrix E;
(23) computing a rotation matrix using a blocking sub-matrix of the signal sub-space matrix E
Figure FDA0003035158130000014
(24) Rotating matrix
Figure FDA0003035158130000015
Performing feature decomposition to obtain its feature value, and calculating angular frequency according to the feature value
Figure FDA0003035158130000016
K is 1,2, …, K; wherein K is the number of signals;
(25) reconstructing the signal subspace matrix E to obtain a new signal subspace matrix E', repeating the steps (23) and (24), and calculating another angular frequency
Figure FDA0003035158130000017
k＝1,2,…,K；
(26) According to the formula uk＝sinθkcosφkAnd vk＝sinθksinφkCalculating the pitch angle of the signal
Figure FDA0003035158130000018
And azimuth angle
Figure FDA0003035158130000019
3. The method of claim 1, wherein the initial estimation steering matrices in step (3) are respectively:
Ax＝[ax(u1),ax(u2),...,ax(uK)]
Ay＝[ay(v1),ay(v2),...,ay(vK)]
wherein, ax(uk) And ay(vk) The steering vectors on the x-axis and y-axis, respectively.
4. The parallel factor model-based multi-signal separation and direction-finding joint processing method according to claim 1, wherein the step (4) is implemented as follows:
reusing third order tensor of received sampling signal according to parallel factor model
Figure FDA0003035158130000021
Representing, three data matrices are obtained by segmentation and stitching along three different dimensions:
Figure FDA0003035158130000022
and
Figure FDA0003035158130000023
wherein N and M respectively represent the array element number of the uniform area array along the x axis and the y axis, and L represents the time domain sampling point number.
5. The parallel factor model-based multi-signal separation and direction-finding joint processing method according to claim 1, wherein the step (5) comprises the steps of:
(51) initialization with initial steering matrix
Figure FDA0003035158130000024
And
Figure FDA0003035158130000025
(52) computing
Figure FDA0003035158130000026
The least-squares estimation of (a) is,
Figure FDA0003035158130000027
wherein the symbol |, indicates a Khatri-Rao product, is indicated by the upper scale
Figure FDA0003035158130000028
Represents a pseudo-inverse;
(53) computing
Figure FDA0003035158130000029
The least-squares estimation of (a) is,
Figure FDA00030351581300000210
(54) computing
Figure FDA00030351581300000211
The least-squares estimation of (a) is,
Figure FDA00030351581300000212
(55) judging whether a set convergence condition is reached, and stopping the algorithm if the set convergence condition is reached; otherwise, the step (52) is returned to continue to calculate new estimated value.
6. The parallel factor model-based multi-signal separation and direction-finding joint processing method according to claim 1, wherein the step (7) comprises the steps of:
(71) will be provided with
Figure FDA00030351581300000213
And
Figure FDA00030351581300000214
normalizing the column vectors to make the first term equal to 1;
(72) by axkAnd aykTo represent
Figure FDA00030351581300000215
And
Figure FDA00030351581300000216
the k-th column vector of (2), calculate rx＝-angle(axk)，ry＝-angle(ayk) Angle () represents the calculated phase angle;
(73) calculating a least squares estimate of the angular frequency from the phase versus angular frequency relationship:
Figure FDA00030351581300000217
Figure FDA00030351581300000218
wherein,
Bx＝[0,2πdx/λ,...,2π(N-1)dx/λ]T
By＝[0,2πdy/λ,...,2π(M-1)dy/λ]T
wherein d isx＝dyD is array element distance, and lambda is wavelength;
(74) according to the formula uk＝sinθkcosφkAnd vk＝sinθksinφkCalculating the pitch angle of the signal
Figure FDA0003035158130000031
And azimuth angle
Figure FDA0003035158130000032
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