A method for measuring signal polarization parameters of a scalar conformal array

Abstract

The application discloses a kind of signal polarization parameter measurement methods of scalar conformal array, belong to array signal processing technical field.The application includes: step one: considering the shielding effect of carrier and polarization sensitivity comprehensively, according to local directional diagram of array element, establish conformal array model;Step two: establish conformal array received signal model;Step three: utilize the polarization sensitive characteristics of signal of the array element of different direction in conformal array and select part of array element to construct observation equation;Step four: estimate the polarization parameter of signal based on least square method.The method avoids the influence of cross-polarization coupling degree of two orthogonal polarization channels in conventional polarization measurement on polarization measurement, also avoids isolation, calibration and switching etc.Link, with small cost, obtains higher practical value.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, and more specifically, relates to a method for measuring the signal polarization parameters of a scalar conformal array. Background Technology

[0002] In real-world battlefield environments, array radars often face strong interference from the enemy. How to effectively suppress this interference, especially main lobe interference, has always been a key concern for researchers. To suppress main lobe interference, most existing methods focus on the spatial domain. Classical spatial methods for combating main lobe interference include covariance matrix reconstruction, sum-difference main lobe interference cancellation (MLC), blind source separation, and sparse recovery. However, when the angle between the main lobe interference direction and the beam pointing direction is small, the performance of these methods is significantly reduced. Therefore, relying solely on spatial information to combat interference is insufficient.

[0003] As a dimension independent of the spatial and temporal domains, the polarization domain presents a significant challenge: how to effectively utilize polarization information and filter out main lobe interference. However, acquiring interference polarization information is a prerequisite and foundation for countering interference in the polarization domain, making the accurate measurement of the interference signal's polarization parameters a primary concern. Existing polarization measurement methods often rely on orthogonal cross-dipoles. However, during radar beam scanning in space, cross-polarization coupling occurs between the two polarization channels, and this coupling increases with the beam scanning range. Therefore, the accuracy of polarization measurements using this method is often limited by the degree of cross-polarization coupling. Furthermore, polarization measurements using two orthogonal polarization channels often require a series of steps, including channel isolation, calibration, and switching, which places high demands on equipment complexity and production costs. Based on this, some methods utilize the spatial polarization characteristics of the antenna and design signal processing algorithms by rotating a single dipole to measure signal polarization parameters using a single polarization channel (see: Luo Jia, Wang Xuesong, Li Yongzhen, Xiao Shunping, Dai Huanyao. A new method for estimating the polarization state of incoming signals [J]. Journal of National University of Defense Technology, 2008(05):56-61.). However, when the beamwidth of a single dipole antenna is narrow and the rate of change of spatial polarization is small, its spatial polarization characteristics exhibit severe ill-conditioning, leading to poor robustness of this method under ill-conditioning conditions and resulting in large polarization measurement errors.

[0004] Conformal arrays have become a hot research topic in array radar due to their numerous advantages, such as a wider spatial scanning range, higher platform space utilization, and lower aerodynamic drag. Benefiting from the spatial pointing differences among the elements of a conformal array, it naturally possesses polarization sensitivity to a given signal, making it highly valuable to effectively utilize this characteristic to measure the signal's polarization parameters. Existing methods for estimating polarization parameters of conformal arrays include super-resolution methods (MUSIC, MVDR) and sparse recovery methods (OMP, SBL), among others. However, it should be noted that the estimation of polarization parameters in these methods often heavily relies on the signal covariance matrix and involves high-dimensional matrix eigenvalue decomposition and matrix inversion, resulting in high computational complexity. Furthermore, errors introduced by mesh generation also play a role. Summary of the Invention

[0005] In view of this, the present invention provides a method for measuring the signal polarization parameters of a scalar conformal array, which reduces the computational complexity of array signal processing.

[0006] The technical solution adopted in this invention is as follows:

[0007] A method for measuring the signal polarization parameters of a scalar conformal array, the method comprising the following steps:

[0008] Step 1: Based on the local radiation pattern of the array elements, establish a conformal array model. Each array element position in the conformal array model contains only one array element, and the array elements are placed in different directions.

[0009] Step 2: Establish a conformal array signal reception model;

[0010] Step 3: Select some array elements to construct the observation equations;

[0011] Step 4: Estimate the polarization parameters of the signal based on the least squares method.

[0012] Furthermore, in step 1, taking into account both carrier shielding effect and polarization sensitivity, the conformal array model is established based on the local radiation pattern of the array elements as follows:

[0013] Local radiation pattern of array elements It can be represented as Specifically there are

[0014]

[0015]

[0016] Where, θ n and Let represent the elevation and azimuth angles of the signal in the local coordinate system of the nth array element, respectively. and Let and represent the basis vectors of direction and direction in the local spherical coordinate system, respectively. and These represent the magnitudes of the components in the corresponding directions.

[0017] It is worth noting that the conversion between the global coordinate system and the local coordinate system can be performed using the Euler rotation operation. The magnitude of the Euler rotation angle is related to the orientation of the array element. The element orientation pattern of the nth array element in the global Cartesian coordinate system is obtained as follows:

[0018]

[0019] Where, θ and g represents the elevation and azimuth angles of the signal in the global coordinate system. n,x g n,y and g n,z These represent the element pattern components in the x, y, and z directions of the global Cartesian coordinate system, respectively. Let x, y, and z represent the basis vectors in the global Cartesian coordinate system, respectively. Then, the element pattern matrix formed by all elements can be represented as:

[0020]

[0021] Where N represents the number of array elements.

[0022] It should be noted that the orientation of the array elements in a conformal array is often different, so the polarization response of different array elements to the same spatial signal is different, which is reflected in... They are all different.

[0023] Furthermore, in step 2, a conformal array received signal model is established. Without loss of generality, for a signal with K unknown polarization parameters, the received signal can be specifically expressed as:

[0024]

[0025] Here, diag(·) represents converting a vector into a diagonal matrix. Let θ be the polarization spatial steering vector of the k-th signal. k and γ represents the elevation and azimuth angles of the k-th signal in the global coordinate system. k and η k The polarization phase descriptor of the k-th signal, or simply the polarization parameter, γ k η represents the polarization angle. k Indicates polarization phase difference, For the specific form of the k-th signal, N s Let N be the number of snapshots, and N be the Gaussian white noise matrix. Let k be the spatial steering vector of the k-th signal. Let p(γ) be the polarization projection matrix of the k-th signal. k ,η k Let be the polarization Jones vector of the k-th signal, containing polarization parameters. For simplicity, let... Right now It is an intermediate parameter that is only related to angle information.

[0026] Furthermore, in step 3, the observation equation is constructed by selecting a subset of array elements to construct an observation equation based on the polarization sensitivity of the array elements with different orientations placed in the conformal array:

[0027] First, to reduce some of the computational complexity, a portion of the unobstructed array elements are selected to re-obstruct the received signal matrix. Specifically, it can be expressed as:

[0028]

[0029] in, Indicates the number of array elements selected. The received signal corresponds to the Gaussian white noise matrix of the selected array elements. The symbolic parameters in the expression are the same as those of the received signal X, and the superscript "~" is only used to distinguish the selected part.

[0030] Secondly, since the local radiation patterns of the array elements and the array model are known, for K spatial regions of interest... The signal yields the observation equation as follows:

[0031]

[0032] To simplify the expression, let p k =p(γ) k ,η k ),

[0033] Further, in step 4, the polarization parameters of the signal are estimated based on the least squares method, specifically as follows:

[0034]

[0035] in, From the polarization Jones vector estimation results of K signals, we can then obtain the estimated values ​​of the polarization parameters of the K signals:

[0036]

[0037]

[0038] in, and These represent the polarization Jones vectors of the estimated k-th signal, respectively. The first and second rows of values, abs(·) represents the absolute value operation, and angle(·) represents the phase angle operation.

[0039] The technical solution provided by this invention brings at least the following beneficial effects:

[0040] This invention establishes a conformal array model and a received signal model based on the local radiation pattern of the array elements. It constructs an observation equation using the polarization sensitivity of spatial signals to array elements with different orientations placed in the conformal array, and obtains estimated values ​​of signal polarization parameters based on the least squares method. Compared with existing methods, this method does not require two orthogonal polarization channels, avoiding the influence of cross-polarization coupling on polarization measurements, and also reducing the requirements for equipment complexity and production costs. Furthermore, based on the advantage of the relatively wider spatial scanning range of the conformal array, this invention avoids polarization measurement errors caused by the ill-conditioned spatial polarization characteristics of a single dipole antenna. It is simple to operate, and even with a high signal-to-noise ratio, measurements can be performed using only a single snapshot, exhibiting strong robustness. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying 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.

[0042] Figure 1 A flowchart illustrating a method for measuring the signal polarization parameters of a scalar conformal array, provided in an embodiment of the present invention;

[0043] Figure 2 A schematic diagram of a hemispherical scalar conformal array;

[0044] Figure 3 and Figure 4 The present invention provides RMSE performance curves for measuring different polarization parameters using the method of the present invention.

[0045] Figure 5 The curve showing the variation of RMSE with signal-to-noise ratio in polarization measurement using the method of this invention;

[0046] Figure 6 The curve showing the change of RMSE with the number of snapshots in the polarization measurement method of this invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0048] like Figure 1 As shown, the present invention provides a method for measuring the signal polarization parameters of a scalar conformal array, comprising the following steps:

[0049] Step 1: Taking into account both carrier shielding effect and polarization sensitivity, establish a conformal array model based on the local radiation patterns of the array elements. (Element local radiation patterns) It can be represented as Specifically there are

[0050]

[0051]

[0052] in, This represents the elevation and azimuth angles of the signal at the nth array element in the local coordinate system.

[0053] It is worth noting that the conversion between the global coordinate system and the local coordinate system can be performed using the Euler rotation operation. The magnitude of the Euler rotation angle is related to the orientation of the array element. The resulting element pattern of the nth array element in the global Cartesian coordinate system is:

[0054]

[0055] in, This represents the elevation and azimuth angles of the signal in the global coordinate system. The element pattern matrix formed by all array elements can then be represented as:

[0056]

[0057] It should be noted that the orientation of the array elements in a conformal array is often different, so the polarization response of different array elements to the same spatial signal is different, which is reflected in... They are all different.

[0058] Common conformal array structures include conical conformal arrays, cylindrical conformal arrays, and spherical conformal arrays. This specific embodiment uses... Figure 2 Taking the hemispherical scalar conformal array shown as an example, a conformal array model is established.

[0059] like Figure 2As shown, the radius of the hemispherical conformal array is R, the vertex of the hemisphere is located on the positive Z-axis of the global Cartesian coordinate system, and the center of the sphere coincides with the origin O. Array elements are placed on the hemisphere along concentric rings, with the largest ring having a radius of R. The largest ring is located in the XOY plane, and the arc length between adjacent rings is l1 = 0.5λ, where λ is the signal wavelength. The spacing between adjacent array elements on the same ring is l2 = 0.5λ. Since the local radiation pattern of the array elements is polarization sensitive, to better perceive the polarization information of the signal, adjacent array elements are placed along the tangent of the ring (denoted by "o") and along the parallel of the ring (denoted by "x"). Assume the conformal array has N array elements, and the coordinates of the nth element in the global Cartesian coordinate system are d. n =[x n ,y n ,z n ] T .

[0060] Step 2: Establish a conformal array signal receiving model. Without loss of generality, for a signal with K unknown polarization parameters, its normalized incident direction vector is: The spatial steering vector of the k-th signal can be expressed as:

[0061]

[0062] The polarization projection matrix of the k-th signal can be expressed as:

[0063]

[0064] The polarization characteristics of the k-th signal can be characterized by the Jones vector, i.e.

[0065] Specifically, the signal received by the hemispherical conformal array can be represented as

[0066]

[0067] To simplify the expression, let This represents the polarization spatial steering vector of the k-th signal. N represents the specific form of the k-th signal. s denoted by , where N represents the number of snapshots and N represents the Gaussian white noise matrix.

[0068] Step 3: Utilizing the polarization sensitivity of array elements with different orientations in a conformal array to the signal, select a portion of the unobstructed array elements to construct the observation equation. First, to reduce some computational complexity, a portion of the array elements can be selected to re-observe the received signal matrix. Specifically, it can be expressed as:

[0069]

[0070] in, This indicates the number of array elements selected.

[0071] Secondly, since the local radiation patterns of the array elements and the array model are known, for K spatial regions of interest... The signal can be used to construct the observation equation as follows:

[0072]

[0073] To simplify the expression, let p k =p(γ) k ,η k ),

[0074] Step 4: Estimate the polarization parameters of the signal based on the least squares method, specifically:

[0075]

[0076] in, The above equation represents the polarization Jones vector estimation results for K signals. Since the orientation and position of each element in the conformal array are different, the above equation... The fact that the list must be full rank indicates that least squares must have a solution. Therefore, the estimated polarization parameters of the K signals can be obtained, specifically:

[0077]

[0078]

[0079] Where angle(·) represents the phase angle operation. and These represent the estimated polarization parameters of the k-th signal.

[0080] In the simulation, the polarization measurement of a signal is used as an example to verify the method of the present invention. The signal carrier frequency is 200MHz. Without loss of generality, Figure 3 and Figure 4 The following parameters are given: Signal-to-noise ratio (SNR) = 20 dB, number of snapshots N, and the results of 500 Monte Carlo experiments with Q = 200. s When the polarization coefficient is 2600, the root mean square error (RMSE) performance curves of the method of the present invention for different polarization parameters are shown. The RMSE is defined as follows:

[0081]

[0082] Figure 5 The following parameters are given: the true polarization parameters of the signal (γ,η) = (56°, 193°), and the number of snapshots N, for Q = 500 Monte Carlo experiments.s When = 2600, the curve of RMSE change with signal-to-noise ratio (SNR) in polarization measurement using the method of the present invention; Figure 6 The following data are presented: under Q = 500 Monte Carlo experiments, the true polarization parameters (γ, η) = (56°, 193°), the signal-to-noise ratio (SNR) = 20 dB, and the RMSE of polarization measurement using the method of this invention varies with the number of snapshots N. s The variation curve is shown. Simulation results show that the method of this invention exhibits small measurement errors for almost any polarization parameter, demonstrating its robustness. Furthermore, the higher the signal-to-noise ratio and the greater the number of snapshots, the better the polarization measurement performance of the method of this invention.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0084] The above descriptions are merely some embodiments of the present invention. For those skilled in the art, various modifications and improvements can be made without departing from the inventive concept of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A method for measuring the signal polarization parameters of a scalar conformal array, characterized in that, The method includes the following steps: Step 1: Based on the local radiation pattern of the array elements, establish a conformal array model. Each array element position in the conformal array model contains only one array element, and the array elements are placed in different directions. Step 2: Establish a conformal array signal reception model; Step 3: Select some array elements to construct the observation equations; Step 4: Estimate the polarization parameters of the signal based on the least squares method; Its characteristic is that a portion of the unobstructed array elements are selected to construct the observation equation, specifically: Step 301: Based on the currently selected array elements, re-obtain the received signal matrix. for: in, This represents the polarization spatial steering vector of the k-th signal under the currently selected array elements. and This represents the elevation and azimuth angles of the k-th signal in the global coordinate system. and The polarization phase descriptor of the k-th signal, or simply the polarization parameter, Indicates the polarization angle. Indicates polarization phase difference, For the specific form of the k-th signal, For the number of snapshots, The Gaussian white noise matrix corresponding to the selected array elements, where K represents the number of signals with unknown polarization parameters to be estimated. This means converting a vector into a diagonal matrix. This represents the spatial steering vector of the k-th signal within the currently selected array elements. Let be the global element radiation pattern matrix of the k-th signal under the currently selected partial array elements. Let be the polarization projection matrix of the k-th signal. Let be the polarization Jones vector of the k-th signal. Indicates the number of array elements selected, intermediate parameter ; Step 302, based on K spatial regions of interest The signal yields the observation equation as follows: Define intermediate parameters , Then the observation equation Transformed into: Let intermediate parameters ,but .

2. The method as described in claim 1, characterized in that, In step 1, the local radiation pattern of the array element is specifically as follows: in, This represents the local radiation pattern of the nth array element. and Let represent the elevation and azimuth angles of the signal in the local coordinate system of the nth array element, respectively. and Let and represent the basis vectors of the pitch direction and the direction of in the local spherical coordinate system, respectively. and These represent the magnitudes of the components in the corresponding directions, and their calculation method is as follows: Based on Euler rotation processing, the element radiation pattern of each array element in the global Cartesian coordinate system is obtained: in, and This represents the elevation and azimuth angles of the signal in the global coordinate system. , and These represent the element pattern components in the x, y, and z directions in the global Cartesian coordinate system, respectively. , , These represent the basis vectors in the x, y, and z directions of the global Cartesian coordinate system, respectively. The global element radiation pattern matrix is ​​obtained based on the element radiation patterns of all elements in the global Cartesian coordinate system: Where N represents the number of array elements.

3. The method as described in claim 2, characterized in that, In step 2, the conformal array receiving signal model is specifically as follows: in, Represents the received signal matrix. This represents the polarization spatial steering vector of the k-th signal. The Gaussian white noise matrix is... Let k be the spatial steering vector of the k-th signal. Let be the global element pattern matrix of the k-th signal; Define intermediate parameters Then the received signal matrix Represented as: .

4. The method as described in claim 3, characterized in that, In step 4, the polarization parameters of the signal are estimated using the least squares method as follows: in, From the polarization Jones vector estimation results of K signals, we can then obtain the estimated values ​​of the polarization phase descriptors of the K signals: in, and These represent the polarization Jones vectors of the estimated k-th signal, respectively. The first row of values ​​and the second row of values, This indicates the absolute value operation. This indicates the phase angle operation.

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