A method for fast estimation of direction of arrival of mixed polarized signal with enhanced separation

Abstract

This invention relates to a fast method for estimating the direction of arrival (DOA) of mixed polarization signals with enhanced separation, comprising the following steps: multi-polarization array arrangement; multi-polarization array output modeling; fast estimation of the DOA of partially polarized signals; elimination of low-precision DOA of fully polarized signals; initialization of the oblique projection matrix; and estimation of the DOA of fully polarized signals based on oblique projection iteration. The advantages of this invention are: firstly, the method eliminates the influence of leakage from fully polarized signals and improves the accuracy of the oblique projection matrix through iterative calculation, thereby enhancing the separation between fully polarized and partially polarized signals; secondly, the method fully utilizes the characteristics of mixed polarization signals, resulting in high DOA estimation accuracy; and finally, the method does not require spatial domain search, thus exhibiting fast algorithm execution speed.

Description

Technical Field

[0001] This invention relates to a fast method for estimating the direction of arrival (DOA) of a hybrid polarized signal with enhanced separation, belonging to the field of array signal processing technology. Background Technology

[0002] Array signal processing significantly enhances signal analysis capabilities by incorporating spatial observation data into time-domain observation data. For electromagnetic signals, spatial observation data is obtained through signal reception and sampling using an array of antennas. Array signal processing is widely used in military and civilian fields, such as electromagnetic signal reconnaissance and spectrum monitoring. Electromagnetic signals possess polarization information. To fully utilize this polarization information and enhance the ability to analyze signal polarization, multi-polarization arrays—arrays composed of antennas with various polarizations—are introduced. Signal polarization can be categorized as fully polarized and partially polarized; the former corresponds to a fixed signal polarization, while the latter indicates that the signal polarization characteristics change over time. Fully polarized signals are relatively common, but with factors such as the utilization of signal polarization dimensions, variable polarization signals are becoming increasingly prevalent. For example, polarization-agile signals are frequently used to increase communication security and channel capacity. Therefore, for applications such as signal reconnaissance and spectrum monitoring, it is essential to consider scenarios where fully polarized and partially polarized signals coexist. We call such scenarios hybrid polarization scenarios.

[0003] Signal direction of arrival (DOA) estimation is a crucial parameter for reconnaissance and surveillance missions. Currently, only a few papers address DOA estimation under mixed polarization conditions, such as Reference 1 (J.He, L.Li, T.Shu, Direction finding of mixed fully and partially polarized sources using linear COLDarrays, Signal Processing, 2021, vol.178, no.107815.) and Reference 2 (K.Ho, K.Tan, A.Nehorai, Estimating directions of arrival of completely and incompletely polarized signals with electromagnetic vector sensors, IEEE trans. on Signal Processing, 1999, vol.47, no.10, pp.2845-2852.). Reference 1 first uses the root-MUSIC algorithm to estimate the DOA of partially polarized signals, then uses oblique projection to eliminate partially polarized signals, and finally estimates the DOA of the remaining fully polarized signals. However, on the one hand, leakage from fully polarized signals can occur when estimating partially polarized signals; on the other hand, the finite number of snapshots leads to errors in the oblique projection matrix, preventing the complete elimination of fully polarized signals. These two factors result in insufficient separation between partially and fully polarized signals, affecting the accuracy of direction-of-arrival (DOA) estimation. Reference 2 is a slightly modified version of a DOA estimation method for fully polarized signals based on the ESPRIT algorithm, using only the similarity of eigenvalues ​​to determine whether a signal belongs to a partially polarized component. Therefore, Reference 2 does not fully utilize the characteristics of mixed polarization signals. Summary of the Invention

[0004] To overcome the shortcomings of existing research, this invention provides a fast method for estimating the direction of arrival of hybrid polarized signals with enhanced separation.

[0005] The specific steps of a fast method for estimating the direction of arrival (DOA) of a hybrid polarization signal with enhanced separation are as follows:

[0006] Step 1: Multi-polarization array arrangement: Place two subarrays on one axis of a three-dimensional Cartesian coordinate system. Each subarray is an M-element uniform linear array, and the element spacing of each subarray is the same, denoted as d. One subarray consists of z-polarized electric dipole antennas, and the other subarray consists of z-polarized magnetic dipole antennas. The two subarrays may or may not overlap.

[0007] Step 2: Multi-polarization array output modeling: Assume K far-field narrowband uncorrelated signals arrive from directions θ1, θ2, ..., θ K An incident signal is projected onto the array, containing K1 fully polarized signals and K2 partially polarized signals, where K = K1 + K2. The array output is sampled, and the total array output of the nth snapshot is obtained. It can be represented as in Let represent the set of complex numbers, (·) T Indicates the transpose operation, x p [n] represents the output of the subarray composed of the p-th polarization antenna in the nth snapshot, where p = 1, 2, N represents the total number of sampling snapshots.

[0008] Step 3: Fast estimation of direction of arrival for partially polarized signals: First, calculate the array covariance matrix. in(·) H This represents the complex conjugate transpose operation. Then, for R... y Perform eigenvalue decomposition, and construct a matrix U by taking the 2M-K1-2*K2 eigenvectors corresponding to the 2M-K1-2*K2 smallest eigenvalues. Let U n =[U 1:M,: U M+1:2M,: ], where U 1:M,: with U M+1:2M,: Let U be a matrix consisting of the first M rows and the last M rows of U. n Treating it as a noisy subspace, the root-MUSIC algorithm is executed, outputting K direction-of-arrival estimates. The K directions of arrival (DOA) estimates correspond to K1 fully polarized signals and K2 partially polarized signals, and the DOA estimates of the K2 partially polarized signals are high-precision estimates.

[0009] Step 4: Low-precision fully polarized signal direction of arrival elimination: Calculation in I2 denotes the Kronecker product, and I2 denotes the 2nd order identity matrix. As the guide vector, λ is the signal wavelength. Find... The K1 maximum values ​​are selected, and the corresponding K1 direction-of-arrival (DOA) estimates are removed. The remaining K2 DOA estimates are high-precision DOA estimates for partially polarized signals, which are represented as follows: Where ||·||2 represents the 2-norm of the matrix.

[0010] Step 5: Initialize the oblique projection matrix: First, calculate the smoothing covariance matrix. and array manifold and R x Projected to The orthogonal complement space is obtained in To The orthogonal complement projection matrix of the column space. Then, for R... x Perform singular value decomposition, and take the K1 right singular vectors corresponding to the K1 smallest singular values ​​to form matrix V. Finally, initialize the oblique projection matrix T to... in Let V be the orthogonal complement projection matrix onto the column space of matrix V.

[0011] Step Six: Direction of Arrival Estimation of Fully Polarized Signal Based on Oblique Projection Iteration: In the q-th iteration, firstly, the projection covariance matrix R is calculated. t =(I M -T (q) )R x (I M -T (q) ) H , among which, T (q) Let I represent the oblique projection matrix of the q-th iteration. M Let R represent the M-order identity matrix. t Perform eigenvalue decomposition, and select M-K1 eigenvectors corresponding to the M-K1 smallest eigenvalues ​​to form a matrix U′. Then, treat U′ as a noise subspace, execute the root-MUSIC algorithm, and output K1 directions of arrival estimates. Finally, calculate in, To The orthogonal complement projection matrix of the column space. Then, in the (q+1)th iteration, T is... (q) Replace with T (q+1) Everything else remains unchanged. Specifically, during the first iteration, T... (1) =T. After iterative convergence, the K1 directions of arrival estimates for the corresponding fully polarized signal can be obtained.

[0012] Furthermore, in step one, when the aperture size is sufficient, the two subarrays do not overlap; when there is a limitation on the aperture size, the two subarrays partially or completely overlap.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0014] 1. The direction-of-arrival estimation method under mixed polarization conditions proposed in this invention eliminates the influence of leakage of fully polarized signals and improves the accuracy of the oblique projection matrix by using iterative calculation, thereby enhancing the separation between fully polarized signals and partially polarized signals.

[0015] 2. The direction-of-arrival estimation method under mixed polarization conditions proposed in this invention makes full use of the characteristics of mixed polarization signals, thus enabling it to have high direction-of-arrival estimation accuracy.

[0016] 3. The method proposed in this invention does not require spatial domain search, thus it has the advantage of fast algorithm execution speed. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the overall process of the method of this invention;

[0019] Figure 2 It is a multi-polarization array consisting of an electric dipole antenna and a magnetic dipole antenna;

[0020] Figure 3 It is a non-overlapping multipolar array consisting of an electric dipole antenna and a magnetic dipole antenna;

[0021] Figure 4 This is a comparison chart of the accuracy of the method of this invention and other methods in estimating the direction of arrival of a fully polarized signal at a signal-to-noise ratio of -5dB;

[0022] Figure 5 This is a comparison chart of the accuracy of the method of this invention and other methods in estimating the direction of arrival of partially polarized signals at a signal-to-noise ratio of -5dB;

[0023] Figure 6 This is a comparison of the accuracy of the method of this invention with other methods for estimating the direction of arrival of fully polarized signals at a signal-to-noise ratio of 10 dB;

[0024] Figure 7 This is a comparison chart of the accuracy of the method of this invention and other methods in estimating the direction of arrival of partially polarized signals at a signal-to-noise ratio of 10 dB. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] like Figure 1 As shown, the present invention includes the following:

[0027] Step 1: Multi-polarization array arrangement: Place two subarrays on one axis of a three-dimensional Cartesian coordinate system. Each subarray is an M-element uniform linear array, and the element spacing of each subarray is the same, denoted as d. One subarray consists of z-polarized electric dipole antennas, and the other subarray consists of z-polarized magnetic dipole antennas. The two subarrays may or may not overlap.

[0028] An electric dipole antenna can receive the electric field component of an electromagnetic signal, while a magnetic dipole antenna can receive the magnetic field component of an electromagnetic signal.

[0029] like Figure 2 The image shows an overlapping multipolar array, such as... Figure 3 The diagram shows a non-overlapping multipolar array.

[0030] Step 2: Multi-polarization array output modeling: Assume K far-field narrowband uncorrelated signals arrive from directions θ1, θ2, ..., θ K An incident signal is projected onto the array, containing K1 fully polarized signals and K2 partially polarized signals, where K = K1 + K2. The array output is sampled, and the total array output of the nth snapshot is obtained. It can be represented as in Let represent the set of complex numbers, (·) T Indicates the transpose operation, x p [n] represents the output of the subarray composed of the p-th polarization antenna in the nth snapshot, where p = 1, 2, N represents the total number of sampling snapshots.

[0031] The rank of the 2x2 covariance matrix formed by the horizontal and vertical polarization components of a fully polarized signal is 1, while the rank of the 2x2 covariance matrix corresponding to a partially polarized signal is 2. The degree of polarization of a signal can be represented by the polarizability parameter ρ, where 0 ≤ ρ ≤ 1. When ρ = 1, it corresponds to a fully polarized signal; otherwise, it corresponds to a partially polarized signal. ρ equals the power of the constant polarization component of the signal divided by the total power of the signal.

[0032] Step 3: Fast estimation of direction of arrival for partially polarized signals: First, calculate the array covariance matrix. in(·) H This represents the complex conjugate transpose operation. Then, for R... y Perform eigenvalue decomposition, and construct a matrix U by taking the 2M-K1-2*K2 eigenvectors corresponding to the 2M-K1-2*K2 smallest eigenvalues. Let U n =[U 1:M,: U M+1:2M,: ], where U 1:M,: with UM+1:2M,: Let U be a matrix consisting of the first M rows and the last M rows of U. n Treating it as a noisy subspace, the root-MUSIC algorithm is executed, outputting K direction-of-arrival estimates. The K directions of arrival (DOA) estimates correspond to K1 fully polarized signals and K2 partially polarized signals, and the DOA estimates of the K2 partially polarized signals are high-precision estimates.

[0033] The direction-of-arrival (DOA) estimates of the K2 partially polarized signals here have high estimation accuracy, but there are also K1 fully polarized signals whose DOA estimates have leaked in, and their estimation accuracy is low. Therefore, further elimination work is required.

[0034] Step 4: Removal of low-precision fully polarized signal direction of arrival: Calculation in I2 denotes the Kronecker product, and I2 denotes the 2nd order identity matrix. As the guide vector, λ is the signal wavelength. Find... The K1 maximum values ​​are selected, and the corresponding K1 direction-of-arrival (DOA) estimates are removed. The remaining K2 DOA estimates are high-precision DOA estimates for partially polarized signals, which are expressed as follows: Where ||·||2 represents the 2-norm of the matrix.

[0035] Step 5, Initialization of the oblique projection matrix: First, calculate the smoothing covariance matrix. and array manifold and R x Projected to The orthogonal complement space is obtained in To The orthogonal complement projection matrix of the column space. Then, for R′ x Perform singular value decomposition, and construct matrix V from the K1 right singular vectors corresponding to the K1 smallest singular values. Finally, initialize the oblique projection matrix T to... in Let V be the orthogonal complement projection matrix onto the column space of matrix V.

[0036] The oblique projection matrix is ​​used to remove some polarization signals from the received data. However, due to the limited number of snapshots, the oblique projection matrix obtained in this step has a large error. Therefore, a next step is needed to improve its accuracy.

[0037] Step 6: Direction of Arrival Estimation of Fully Polarized Signal Based on Oblique Projection Iteration: In the q-th iteration, firstly, the projection covariance matrix R is calculated. t =(IM -T (q) )R x (I M -T (q) ) H , among which, T (q) Let I represent the oblique projection matrix of the q-th iteration. M Let R represent the M-order identity matrix. t Perform eigenvalue decomposition, and select M-K1 eigenvectors corresponding to the M-K1 smallest eigenvalues ​​to form a matrix U′. Then, treat U′ as a noise subspace, execute the root-MUSIC algorithm, and output K1 directions of arrival estimates. Finally, calculate in, To The orthogonal complement projection matrix of the column space. Then, in the (q+1)th iteration, T is... (q) Replace with T (q+1) Everything else remains unchanged. Specifically, during the first iteration, T... (1) =T. After iterative convergence, the K1 directions of arrival estimates for the corresponding fully polarized signal can be obtained.

[0038] Preferably, in step one, when the aperture size is sufficient, the two subarrays do not overlap; when there is a limitation on the aperture size, the two subarrays partially or completely overlap.

[0039] The effectiveness of this invention is verified below using simulation examples. The root mean square error of the object's orientation is evaluated and compared with the methods in References 1 and 2. All statistical results are based on 500 Monte Carlo experiments.

[0040] Simulation Example 1: Array Formation Figure 2 The array is configured with 12 array elements (M), 2 total signal sources (K), 1 fully polarized signal source (K1), 1 partially polarized signal source (K2), a polarization degree (ρ) of 0.5, a snapshot number (N) of 100, and a signal-to-noise ratio (SNR) of -5 dB. The direction of arrival (ROA) of the fully polarized signal is 0 degrees, while the ROA of the partially polarized signal varies from -10 degrees to 10 degrees.

[0041] Simulation results are as follows Figure 4 , 5 The figures show the direction-of-arrival (DOA) estimation accuracy for fully polarized and partially polarized signals, respectively. As can be seen from the figures, when the angular interval between the two signals is small, the estimation accuracy of the proposed method is generally better than that of the comparison algorithm, meaning that the proposed method has better signal separation.

[0042] Simulation Example 2: Increase the signal-to-noise ratio to 10dB, while keeping other conditions unchanged.

[0043] Simulation results are as follows Figure 6 ,7 The figures show the direction-of-arrival (DOA) estimation accuracy for fully polarized and partially polarized signals, respectively. As can be seen from the figures, at higher signal-to-noise ratios, the estimation accuracy of the method described in this invention is still generally better than that of the comparison algorithm.

[0044] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A fast method for estimating the direction of arrival (DOA) of a hybrid polarization signal with enhanced separation, characterized in that: Includes the following steps: Step 1: Multi-polarization array arrangement: Place two sub-arrays on one of the coordinate axes of a three-dimensional Cartesian coordinate system. Each sub-array is... A uniform linear array with equal element spacing in each subarray is represented as follows: One subarray consists of z-polarized electric dipole antennas, and the other subarray consists of z-polarized magnetic dipole antennas. Step 2: Multi-polarization array output modeling: Assumptions A far-field narrowband uncorrelated signal from the direction of arrival Incident on the array, containing A fully polarized signal and Partial polarization signal, The array output is sampled, the first... Total output of the array of snapshots Represented as ,in Represents the set of complex numbers. This indicates the transpose operation. Indicates the first The first snapshot was taken by the first The output of a subarray composed of polarized antennas, , This represents the total number of sampling snapshots; Step 3: Fast estimation of direction of arrival for partially polarized signals: Calculation of array covariance matrix ,in Represents the complex conjugate transpose operation, for Perform feature decomposition and take the corresponding The minimum eigenvalues The matrix is ​​composed of eigenvectors. ,make ,in, and They are respectively The former Actions and After A matrix composed of rows, Treat it as a noisy subspace, execute the root-MUSIC algorithm, and output... One direction of arrival estimate , Each direction of arrival estimation corresponds to A fully polarized signal and Partially polarized signals, and The direction of arrival estimates of the partially polarized signals are high-precision estimates; Step 4: Low-precision fully polarized signal direction of arrival elimination: Calculation , ,in Indicates the Kronecker product. Represents a 2x2 identity matrix. As the guide vector, , , For the signal wavelength, find In Find the maximum value and remove the corresponding value. One direction of arrival estimate, the remaining ones Each direction-of-arrival (DOA) estimate is a high-precision DOA estimate for partially polarized signals, expressed as: ,in, Represents the 2-norm of a matrix; Step 5: Initialize the oblique projection matrix: Calculate the smoothing covariance matrix and array manifold and will Projected to The orthogonal complement space is obtained ,in To The orthogonal complement projection matrix of the column space, for Perform singular value decomposition and take the corresponding The minimum singular value A matrix is ​​formed by right singular vectors. Oblique projection matrix Initialize to ,in , To the matrix The orthogonal complement projection matrix of the column space; Step Six: Direction of Arrival Estimation of Fully Polarized Signal Based on Oblique Projection Iteration: In the first step... In this iteration, the projection covariance matrix is ​​calculated first. ,in, Indicates the first The oblique projection matrix of the next iteration express An identity matrix of order 1, for Perform feature decomposition and take the corresponding The minimum eigenvalues The matrix is ​​composed of eigenvectors. , and then Treat it as a noisy subspace, execute the root-MUSIC algorithm, and output... One direction of arrival estimate ,calculate ,in, To The orthogonal complement projection matrix of the column space, then in the... During the next iteration, Replace with Everything else remains unchanged, except that during the first iteration... After iterative convergence, the corresponding fully polarized signal can be obtained. One estimated direction of arrival.

2. The method for fast estimation of direction of arrival of hybrid polarized signals with enhanced separation as described in claim 1, characterized in that: In step one, when the aperture size is sufficient, the two subarrays do not overlap; When there are limitations on the aperture size, the two subarrays may partially or completely overlap.

Images