CN112748407A - Airspace-polarization domain combined spectrum estimation method based on polarization sensitive area array - Google Patents

Airspace-polarization domain combined spectrum estimation method based on polarization sensitive area array Download PDF

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CN112748407A
CN112748407A CN202011481220.2A CN202011481220A CN112748407A CN 112748407 A CN112748407 A CN 112748407A CN 202011481220 A CN202011481220 A CN 202011481220A CN 112748407 A CN112748407 A CN 112748407A
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陈志坤
刘淳熙
彭冬亮
郭云飞
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Hangzhou Dianzi University
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Abstract

The invention discloses an airspace-polarization domain combined spectrum estimation method based on a polarization sensitive area array. Most of the existing polarization sensitive arrays are linear arrays, only one-dimensional space angles can be detected, and the polarization state is limited on a large circular track with a Poincare spherical surface eta of 90 degrees, so that the practical value is low. The invention is as follows: firstly, a two-dimensional polarized area array receiving signal model is established. The invention researches a novel high-efficiency low-complexity improvement method by using the thought of the MUSIC algorithm. Aiming at the parameter estimation problem of an incoherent signal source, in order to reduce the calculation amount and complexity of an algorithm and in consideration of the characteristic that the norm of a polarization vector is constant, a Lagrange multiplier method is adopted for dimension reduction operation, the four-dimensional parameter estimation problem is successfully converted into two-dimensional spectral peak search of an azimuth angle and a pitch angle, and then a polarization amplitude and a polarization phase difference are estimated.

Description

Airspace-polarization domain combined spectrum estimation method based on polarization sensitive area array
Technical Field
The invention belongs to the technical field of array signal processing, and particularly relates to an airspace-polarization domain combined spectrum estimation algorithm based on a polarization area array.
Background
As a branch of the array signal processing field, the polarization sensitive array is widely used in many fields such as radar and communication. The polarization sensitive array can simultaneously obtain DOA and polarization information of an incident signal through the spatial distribution and phase difference of the array elements. The polarization sensitive array outputs vector information instead of scalar information, and compared with a common array, the polarization sensitive array has stronger anti-interference capability, more stable detection capability, higher resolution capability and polarization multiple access capability.
The complete space electromagnetic wave signal is a six-dimensional complex vector signal, and different from the traditional scalar array which only acquires one-dimensional information in the electromagnetic wave signal, the electromagnetic vector sensor can acquire the six-dimensional or at least higher one-dimensional information of the space electromagnetic wave signal, so that the polarization information of the space electromagnetic wave signal can be sensed.
The polarization sensitive array parameter estimation comprises two aspects of DOA (direction of arrival) estimation and polarization parameter estimation, and the DOA and the polarization parameter of a signal can be obtained simultaneously through combined processing in a polarization domain and a space domain. Meanwhile, due to the introduction of polarization information, the dimension of array signal processing is changed from a pure spatial domain to a polarization domain-spatial domain combined processing, the dimension is obviously increased, and the complexity of the algorithm is correspondingly improved, so that the research on the polarization domain-spatial domain combined dimension reduction parameter estimation algorithm is necessary.
Most of existing polarization sensitive array receiving signal models are linear arrays, only one-dimensional space angles can be detected, and the polarization state is limited on a large circular track with a Poincare spherical surface eta of 90 degrees, so that the practical value is low. A receiving signal model of a polarization sensitive area array is provided (established on a four-dimensional space), the model is reduced to two dimensions by adopting a dimensionality reduction MUSIC algorithm to search a spectral peak, a space azimuth angle and a pitch angle are calculated in advance, a polarization amplitude angle and a polarization phase difference are estimated, and the practical value is greatly improved.
Disclosure of Invention
The invention aims to provide a space domain-polarization domain combined spectrum estimation method based on a polarization area array.
The method comprises the following specific steps:
generating an envelope s (t) of a linear frequency modulation signal according to a preset information source number, a fast beat number, a carrier frequency, a modulation frequency and a sampling rate;
setting the azimuth angle theta and the pitch angle of the information source
Figure BDA0002837643770000021
Four electromagnetic signal parameters of a polarization amplitude eta and a polarization phase difference gamma;
setting array-related parameters, including: number of horizontal array elements NxNumber of vertical array elements NyAnd array element spacing d.
Step two, generating a traditional array steering vector matrix, wherein the method comprises the following steps:
projecting the array element space information in the y-axis direction to the x-axis direction, wherein the projection matrix is
Figure BDA0002837643770000022
(symbol)
Figure BDA0002837643770000023
The Kronecker product, ones () representing a matrix is a function that generates a full 1 matrix, dxRepresenting the x-axis array element spacing dx＝[0:Nx-1]×d；
Projecting the array element space information in the x-axis direction to the y-axis direction, wherein the projection matrix is
Figure BDA0002837643770000024
dyRepresenting the spacing d of the array elements of the y-axisy＝[0:Ny-1]×d；
Combining the x-axis projection matrix, the y-axis projection matrix and the components of the signals in the coordinate axis direction to form a traditional array steering vector matrix as shown in the formula (1):
Figure BDA0002837643770000025
wherein j represents the imaginary part of the complex number, and λ is the wavelength of the incoming wave signal.
Step three, in an actual scene, the array elements can only measure electric field and magnetic field vectors in the x direction and the y direction, and the electric field and the magnetic field vectors are measured according to the spaceThe electromagnetic signal polarization domain-space domain combined representation is realized, and the polarization receiving vector contains all polarization information of the signal
Figure BDA0002837643770000026
And partial spatial information
Figure BDA0002837643770000027
The space domain guide vector comprises space domain information of signals and aperture information of an array, so that a signal polarization receiving vector received by an array element is represented by the following formula (2):
Figure BDA0002837643770000028
in the formula
Figure BDA0002837643770000029
Represents a polarization component, where γ is a polarization phase difference; eta is the polarization amplitude angle.
And (3) constructing a beam scanning vector of the polarization sensitive array by using the signal polarization receiving vector, wherein the beam scanning vector is shown in formula (3):
Figure BDA00028376437700000210
step four, calling a randn () function and setting a proper signal-to-noise ratio parameter (SNR) to add noise N (t), wherein the data received by the polarization sensitive array is in the following form:
Figure BDA0002837643770000031
in the formula
Figure BDA0002837643770000032
Beam scan vector, s, representing the k-th signalk(t) represents the envelope of the kth signal, a is the array prevalence matrix, a ═ a1 a2 ··· ak ··· aK]Wherein
Figure BDA0002837643770000033
S (t) represents the envelope of all signals;
step five, calculating a covariance matrix of the received signals, and performing eigenvalue decomposition on the covariance matrix to obtain 2M eigenvalues, wherein M is the number of array elements; taking the eigenvectors corresponding to 2M-K (K is the number of signals) eigenvalues as a noise subspace Un。
Covariance matrix of received signal:
Figure BDA0002837643770000034
where x (t) represents a received signal at time t, symbol H represents a conjugate transpose operation, and E represents a desire to obtain a matrix.
The characteristic values satisfy the following relationship
λ1≥λ2≥···λK＞λK+1＝···＝λ2M (6)
Step six, setting B to be omegaHUnUn HΩ, wherein
Figure BDA0002837643770000035
B is a 2 x 2 matrix, two characteristic values exist, all pitch angles and all azimuth angles are traversed, and all characteristic values lambda of the matrix B are solvedB；
Step seven, according to the eigenvalue lambda of the matrix BBConstructing spectral functions
Figure BDA0002837643770000036
Peaks of the spectral function, i.e. pitch angle theta and azimuth angle of the corresponding signal
Figure BDA0002837643770000037
An estimate of (d).
Figure BDA0002837643770000038
And step eight, setting a eigenvector corresponding to the minimum eigenvalue of the matrix B as w, and solving the estimated values of the polarization phase difference gamma and the polarization amplitude eta according to an equation (8).
Figure BDA0002837643770000041
Furthermore, dimension reduction processing is performed on the spectrum function formula in the seventh step, which is more efficient and simpler than the conventional general line number, and the expression of the conventional spectrum function is as follows:
Figure BDA0002837643770000042
in the formula
Figure BDA0002837643770000043
Representing conventional array steering vectors
Figure BDA0002837643770000044
And signal polarization vector spKronecker product of. It can be known that the conventional spectral peak search requires traversal through four dimensions. Both the calculated amount and the actual operation angle are difficult to realize, so that the Lagrange multiplier method is introduced to reduce the calculated amount to two dimensions, and the maximum value of the spectral function can be obtained only by searching the pitch angle and the phase angle.
The invention has the beneficial effects that:
1. the invention provides a joint representation of a polarization domain-space domain and models a received signal of a polarization area array.
2. The invention researches a novel high-efficiency and low-complexity improvement method by using the thought of the MUSIC algorithm. Aiming at the parameter estimation problem of an incoherent signal source, in order to reduce the calculation amount and complexity of the algorithm and in consideration of the characteristic that the norm of a polarization vector is constant, the Lagrange multiplier method is adopted for dimension reduction operation, the four-dimensional parameter estimation problem is successfully converted into two-dimensional spectral peak search of an azimuth angle and a pitch angle, the polarization amplitude and the polarization phase difference are estimated, and the effectiveness of the algorithm is proved by true simulation verification.
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FIG. 1 is an overall flow chart of the present invention;
FIG. 2 is a flow chart of the polar-array received signal model derivation section (i.e., steps two through five) of the present invention;
FIG. 3 is a flow chart of a dimension reduction algorithm in the present invention;
FIG. 4 is a diagram of the simulation effect of the spectrum function after dimension reduction in the present invention;
FIG. 5 is a two-dimensional spatial angle simulation effect diagram of the present invention;
FIG. 6 is a diagram illustrating the simulation effect of polarization parameters according to the present invention;
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, a spatial domain-polarization domain combined spectrum estimation algorithm based on a polarization area array specifically includes the following steps:
generating an envelope s (t) of a linear frequency modulation signal according to a preset information source number, a fast beat number, a carrier frequency, a modulation frequency and a sampling rate;
setting the azimuth angle theta and the pitch angle of the information source
Figure BDA0002837643770000045
Four electromagnetic signal parameters of a polarization amplitude eta and a polarization phase difference gamma;
setting array-related parameters, including: number of horizontal array elements NxNumber of vertical array elements NyAnd array element spacing d.
FIG. 2 is a flow chart of the polar-array received signal model derivation section (i.e., steps two through five) of the present invention;
step two, generating a traditional array steering vector matrix, wherein the method comprises the following steps:
projecting the array element space information in the y-axis direction to the x-axis direction, wherein the projection matrix is
Figure BDA0002837643770000051
(symbol)
Figure BDA0002837643770000052
Representing a matrixThe Kronecker product, ones () is a function that generates a full 1 matrix, dxRepresenting the x-axis array element spacing dx＝[0:Nx-1]×d；
Projecting the array element space information in the x-axis direction to the y-axis direction, wherein the projection matrix is
Figure BDA0002837643770000053
dyRepresenting the spacing d of the array elements of the y-axisy＝[0:Ny-1]×d；
Combining the x-axis projection matrix, the y-axis projection matrix and the components of the signals in the coordinate axis direction to form a traditional array steering vector matrix as shown in the formula (1):
Figure BDA0002837643770000054
wherein j represents the imaginary part of the complex number, and λ is the wavelength of the incoming wave signal.
In an actual scene, array elements can only measure electric field and magnetic field vectors in the x direction and the y direction, and the polarization receiving vectors contain all polarization information of signals according to the joint representation of the space electromagnetic signal polarization domain-space domain
Figure BDA0002837643770000055
And partial spatial information
Figure BDA0002837643770000056
The space domain guide vector comprises space domain information of signals and aperture information of an array, so that a signal polarization receiving vector received by an array element is represented by the following formula (2):
Figure BDA0002837643770000057
in the formula
Figure BDA0002837643770000058
Represents a polarization component, where γ is a polarization phase difference; eta is the polarization amplitude angle.
And (3) constructing a beam scanning vector of the polarization sensitive array by using the signal polarization receiving vector, wherein the beam scanning vector is shown in formula (3):
Figure BDA0002837643770000059
step four, calling a randn () function and setting a proper signal-to-noise ratio parameter (SNR) to add noise N (t), wherein the data received by the polarization sensitive array is in the following form:
Figure BDA0002837643770000061
in the formula
Figure BDA0002837643770000062
Beam scan vector, s, representing the k-th signalk(t) represents the envelope of the kth signal, a is the array prevalence matrix, a ═ a1 a2 ··· ak ··· aK]Wherein
Figure BDA0002837643770000063
S (t) represents the envelope of all signals;
step five, calculating a covariance matrix of the received signals, and performing eigenvalue decomposition on the covariance matrix to obtain 2M eigenvalues, wherein M is the number of array elements; taking the eigenvectors corresponding to 2M-K (K is the number of signals) eigenvalues as a noise subspace Un。
Covariance matrix of received signal:
Figure BDA0002837643770000064
where x (t) represents a received signal at time t, symbol H represents a conjugate transpose operation, and E represents a desire to obtain a matrix.
The characteristic values satisfy the following relationship
λ1≥λ2≥···λK＞λK+1＝···＝λ2M (6)
Step six, setting B to be omegaHUnUn HΩ, wherein
Figure BDA0002837643770000065
B is a 2 x 2 matrix, two characteristic values exist, all pitch angles and all azimuth angles are traversed, and all characteristic values lambda of the matrix B are solvedB；
Step seven, according to the eigenvalue lambda of the matrix BBConstructing spectral functions
Figure BDA0002837643770000066
Peaks of the spectral function, i.e. pitch angle theta and azimuth angle of the corresponding signal
Figure BDA0002837643770000067
An estimate of (d).
Figure BDA0002837643770000068
And step eight, setting a eigenvector corresponding to the minimum eigenvalue of the matrix B as w, and solving the estimated values of the polarization phase difference gamma and the polarization amplitude eta according to an equation (8).
Figure BDA0002837643770000069
FIG. 3 is a flow chart of a dimension reduction algorithm in the present invention;
the invention researches a novel high-efficiency and low-complexity improvement method by using the thought of the MUSIC algorithm. Aiming at the parameter estimation problem of an incoherent signal source, in order to reduce the calculation amount and complexity of the algorithm and in consideration of the characteristic that the norm of a polarization vector is constant, the Lagrange multiplier method is adopted for dimension reduction operation, the four-dimensional parameter estimation problem is successfully converted into two-dimensional spectral peak search of an azimuth angle and a pitch angle, the polarization amplitude and the polarization phase difference are estimated, and the effectiveness of the algorithm is proved by true simulation verification.
The results of simulation analysis performed on the examples of the present invention are as follows:
the pulse signal to be measured is simulated by pulse signals which comprise 2 linear frequency modulation signals (LFM), the center frequencies of the 2 linear frequency modulation signals are respectively 150MHz and 750MHz, the signal bandwidths are respectively 50MHz and 80MHz, and the pulse width is 36.409 mus, and Gaussian white noise is added in the pulse signals to be measured. System sampling frequency Fs＝1800MHz。
Consider that 8 orthogonal polarization antennas form a uniform area array (4 horizontal and 2 vertical), the array element spacing is 0.5 times wavelength, the sampling snapshot number is set to 1000, the noise variance is 1, the signal-to-noise ratio of all signals is 15, and it is assumed that the incident signals are narrowband plane waves of the original factory and the information sources are mutually independent.
The 2 signal pitch angles are respectively 5 degrees and 20 degrees; the azimuth angles are respectively 10 degrees and 50 degrees; the polarization amplitude angles are 60 degrees and 80 degrees respectively; the polarization phase differences were 30 ° and 45 °, respectively.
The arrival angles and polarization parameters of the two signals are different, the combined spectrum presents two spectral peaks (as shown in fig. 4), the spectral peaks are sharp, the two signals can be clearly distinguished, and the polarization angle is estimated as shown in fig. 5. FIG. 6 is a diagram illustrating the simulation effect of polarization parameters according to the present invention.
The estimated dimension of the invention is higher than that of the traditional linear array, while the operation amount is obviously lower than that of the general high latitude estimation algorithm, and the invention has stronger anti-noise and anti-interference performance.

Claims (3)

1. A space domain-polarization domain combined spectrum estimation method based on a polarization sensitive area array is characterized by comprising the following steps:
generating an envelope s (t) of a linear frequency modulation signal according to a preset information source number, a fast beat number, a carrier frequency, a modulation frequency and a sampling rate;
setting the azimuth angle theta and the pitch angle of the information source
Figure FDA0002837643760000011
Four electromagnetic signal parameters of a polarization amplitude eta and a polarization phase difference gamma;
setting array-related parameters, including: number of horizontal array elements NxNumber of vertical array elements NyBetween array elementsA distance d;
step two, generating a traditional array steering vector matrix;
in an actual scene, array elements can only measure electric field and magnetic field vectors in the x direction and the y direction, and the polarization receiving vectors contain all polarization information of signals according to the joint representation of the space electromagnetic signal polarization domain-space domain
Figure FDA0002837643760000012
And partial spatial information
Figure FDA0002837643760000013
Therefore, the polarization receiving vector of the signal received by the array element is as follows (2):
Figure FDA0002837643760000014
in the formula
Figure FDA0002837643760000015
Representing polarization components, wherein gamma is a polarization phase difference and eta is a polarization amplitude;
and (3) constructing a beam scanning vector of the polarization sensitive array by using the signal polarization receiving vector, wherein the beam scanning vector is shown in formula (3):
Figure FDA0002837643760000016
step four, calling a randn () function and setting a proper signal-to-noise ratio parameter (SNR) to add noise N (t), wherein the data received by the polarization sensitive array is in the following form:
Figure FDA0002837643760000017
in the formula
Figure FDA0002837643760000018
Beam scan vector, s, representing the k-th signalk(t) represents the envelope of the kth signal, a is the array prevalence matrix, a ═ a1 a2…ak…aK]Wherein
Figure FDA0002837643760000019
S (t) represents the envelope of all signals;
step five, calculating a covariance matrix of the received signals, and performing eigenvalue decomposition on the covariance matrix to obtain 2M eigenvalues, wherein M is the number of array elements; taking the eigenvectors corresponding to 2M-K eigenvalues as a noise subspace Un；
Step six, setting B to be omegaHUnUn HΩ, wherein
Figure FDA0002837643760000021
B is a 2 x 2 matrix, all pitch angles and all azimuth angles are traversed, and all eigenvalues lambda of the matrix B are solvedB；
Step seven, according to the eigenvalue lambda of the matrix BBConstructing spectral functions
Figure FDA0002837643760000022
Peaks of the spectral function, i.e. pitch angle theta and azimuth angle of the corresponding signal
Figure FDA0002837643760000023
An estimated value of (d);
Figure FDA0002837643760000024
step eight, setting a eigenvector corresponding to the minimum eigenvalue of the matrix B as w, and solving the estimated values of the polarization phase difference gamma and the polarization amplitude eta according to an equation (8);
Figure FDA0002837643760000025
2. the spatial domain-polarization domain combined spectrum estimation method based on the polarization sensitive area array as claimed in claim 1, wherein the second step is to project the array element space information in the y-axis direction to the x-axis direction, and the projection matrix is
Figure FDA0002837643760000026
(symbol)
Figure FDA0002837643760000027
The Kronecker product, ones () representing a matrix is a function that generates a full 1 matrix, dxRepresenting the x-axis array element spacing dx＝[0:Nx-1]×d；
Projecting the array element space information in the x-axis direction to the y-axis direction, wherein the projection matrix is
Figure FDA0002837643760000028
dyRepresenting the spacing d of the array elements of the y-axisy＝[0:Ny-1]×d；
Combining the x-axis projection matrix, the y-axis projection matrix and the components of the signals in the coordinate axis direction to form a traditional array steering vector matrix as shown in the formula (1):
Figure FDA0002837643760000029
wherein j represents the imaginary part of the complex number, and λ is the wavelength of the incoming wave signal.
3. The method according to claim 1 or 2, wherein the covariance matrix of the received signals in the fifth step:
Figure FDA00028376437600000210
where x (t) represents a received signal at time t, symbol H represents a conjugate transpose operation, and E represents an expectation of matrix solution;
the characteristic values satisfy the following relationship
λ1≥λ2≥…λK＞λK+1＝…＝λ2M (6)。
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CN114113808A (en) * 2021-11-22 2022-03-01 杭州电子科技大学 DOA-polarization information joint estimation method based on incomplete electric vector sensor

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US20060158374A1 (en) * 2002-11-22 2006-07-20 Dayan Rahamin Smart antenna system wtih improved localization of polarized sources
CN104898085A (en) * 2015-05-14 2015-09-09 电子科技大学 Dimension-reduction MUSIC algorithm for parameter estimation of polarization sensitive array
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CN114047473A (en) * 2021-10-18 2022-02-15 中国电子科技集团公司第二十九研究所 Arrival angle and polarization angle measuring method based on polarization sensitive annular array
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