Irregular conformal array radiation source direction finding and polarization beam forming method

Abstract

The invention relates to the field of array signal processing, and discloses an irregular conformal array radiation source direction finding and polarization beam forming method, which comprises the following steps of: establishing a parameterized array steering vector model capable of separating a direction parameter from a polarization parameter; on the basis of the model and a generalized eigendecomposition theory, four-dimensional MUSIC spectrum search is subjected to dimensionality reduction to be two-dimensional, a signal direction is efficiently estimated by searching a peak value of a two-dimensional spectrum function, a polarization parameter is solved by using an eigenvector corresponding to a maximum generalized eigenvalue, and joint estimation and automatic matching of the parameter are realized; parametrically reconstructing an interference noise covariance matrix which does not contain target signal components by using the estimated interference parameters and noise power; and calculating an optimal beam forming weight vector based on the reconstructed covariance matrix and the target steering vector to realize enhancement of a target signal and depth suppression of interference. The method is clear in process, and the direction finding precision and the output signal to interference plus noise ratio of the irregular array in the complex electromagnetic environment can be remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of array signal processing, in particular to a non-regular conformal array radiation source direction finding and polarization beam synthesis method. BACKGROUND

[0002] Conformal array antennas have been widely used in radar, communication, electronic countermeasures and other fields due to their low radar scattering cross section, wide scanning space and reduced aerodynamic resistance. In practical engineering, in order to adapt to the complex shape of the carrier, the array often needs to be designed in a non-regular layout, and the array elements often have different spatial orientations, i.e. non-regular conformal array. This irregularity brings flexibility in array layout, but also brings severe challenges to array signal processing.

[0003] The most important technical problem comes from the inconsistency of the orientation of the array elements. For a non-regular conformal array, the polarization sensitive direction of each antenna element is different. When an electromagnetic wave with a specific polarization state is incident, the response of each array element to it is different, which leads to the fact that the steering vector of the array is not only related to the direction of arrival (DOA) of the signal, but also closely coupled with the polarization state parameters (such as polarization auxiliary angle and polarization phase difference) of the signal itself.

[0004] This parameter coupling makes the traditional direction finding algorithm (such as the MUSIC algorithm) face failure. If such algorithms are to be directly applied, a joint search must be performed in the entire high-dimensional space containing the direction and polarization parameters. For example, a joint search of two-dimensional direction angle and two-dimensional polarization angle will constitute a four-dimensional spectral function search problem. This high-dimensional search brings a huge computational burden, making it difficult to achieve real-time processing in engineering. More troublesome is that even if the high-dimensional search is completed and the spectral peak is found, it is difficult to automatically and correctly correspond the estimated direction parameters and polarization parameters to each signal source, which requires an additional complex matching step, increasing the uncertainty of the algorithm.

[0005] In terms of beam synthesis, existing adaptive beam forming techniques also have inherent performance bottlenecks. Traditional methods usually directly use the sample covariance matrix containing all signal components to calculate the optimal weight vector. However, in practical applications, due to limited snapshots, array errors or inaccurate target steering vector estimation, this method will misjudge the real target signal as an undesirable signal component and suppress it, resulting in a decrease in the gain of the target signal, i.e. the so-called "signal self-cancellation" phenomenon. In addition, when the number of received snapshots is insufficient, the estimation accuracy of the sample covariance matrix will be severely deteriorated, which will lead to a significant decline in the performance of adaptive beam synthesis, and the formation of precise nulls to suppress strong interference. These defects jointly restrict the performance and engineering application of non-regular conformal arrays in complex electromagnetic environments. SUMMARY

[0006] The technical problem to be solved by the present application is that the existing signal processing method has a polarization mismatch problem when applied to a non-regular conformal array with randomly inconsistent element orientations, resulting in low radiation source direction finding accuracy and poor anti-interference beam synthesis performance.

[0007] To solve the above technical problems, the present application is implemented by the following technical solutions:

[0008] The present application provides a non-regular conformal array radiation source direction finding and polarization beam synthesis method in the first aspect, comprising the following steps:

[0009] Constructing a signal model of the non-regular conformal array to obtain an array steering vector separating the signal direction parameters and polarization parameters;

[0010] Based on the array steering vector and the signal data received by the non-regular conformal array, a two-dimensional spectrum peak search is performed by constructing a reduced dimension MUSIC spectrum function to jointly estimate the direction parameters and polarization parameters of the target signal and interference signal;

[0011] Based on the estimated direction parameters and polarization parameters, the steering vector of the target signal and the interference noise covariance matrix are reconstructed, and the optimal beam synthesis weight vector is calculated.

[0012] In one embodiment, to separate the direction parameters and polarization parameters, the construction process of the array steering vector is as follows: first, according to the spatial orientation parameters of each element and the signal wave direction parameters, the response functions of each element to the horizontal and vertical polarization components of the incoming wave signal are determined, and the phase delay factor determined by the position of each element is combined to construct the array steering vector a h (θ,φ) for the horizontal polarization component of the signal and a v (θ,φ) for the vertical polarization component of the signal, respectively;

[0013] Then, the two steering vectors are combined into an array space-polarization manifold matrix b(θ,φ)=[a h (θ,φ),a v (θ,φ)] related only to the direction parameters (θ,φ);

[0014] Finally, the matrix is multiplied by a polarization vector h(γ,η) related only to the polarization parameters (γ,η) to obtain the final array steering vector a(θ,φ,γ,η)=b(θ,φ)h(γ,η).

[0015] In one embodiment, the present application utilizes the above steering vector structure and proposes a reduced-dimension parameter estimation algorithm. The core of the algorithm is that it converts the four-dimensional spectrum peak search problem due to parameter coupling in the traditional method into a computationally feasible two-dimensional search problem. Specifically, the traditional MUSIC spectrum function is:

[0016]

[0017] where U n is the noise subspace. The present application defines two 2x2 matrices Z(θ, φ) = b H and At this time, the spectrum function P becomes a generalized Rayleigh quotient with respect to the polarization vector h. For any given direction (θ, φ), the maximum value of the Rayleigh quotient is equal to the maximum generalized eigenvalue of the matrix pair (Z(θ, φ), W(θ, φ)). Therefore, the present application constructs a reduced-dimension MUSIC spectrum function:

[0018] F(θ, φ) = λ max {Z(θ, φ), W(θ, φ)};

[0019] By performing spectrum peak search on the two-dimensional spectrum function F(θ, φ), the direction parameters can be estimated, thereby avoiding the exhaustive search of the polarization parameters (γ, η) and greatly reducing the computational complexity. After obtaining the estimated value of the direction parameters , the corresponding polarization vector can be directly determined by the generalized eigenvector corresponding to the maximum generalized eigenvalue, and then the polarization parameters are solved, realizing the accurate estimation and automatic matching of the parameters.

[0020] In one embodiment, to improve the anti-interference performance of beam synthesis, the present application uses a parameterized method to reconstruct the interference noise covariance matrix. This process constructs a covariance matrix containing only interference and noise information by accurately estimating the noise power and the power of each interference signal, and combining the estimated interference steering vectors:

[0021]

[0022] where is the estimated power of the kth interference signal, is the noise estimated power, is the reconstructed steering vector of the kth interference signal. Using the reconstructed matrix to calculate the optimal beam synthesis weight vector can effectively avoid the signal self-cancellation problem that may be caused by the sample covariance matrix containing target signal components in the traditional method, thereby obtaining a higher output signal-to-interference-and-noise ratio.

[0023] The second aspect of the present application provides an electronic device, comprising a processor and a memory, wherein the memory stores a computer program, and the processor implements the method for direction finding and polarization beam synthesis of irregular conformal array radiation source according to the first aspect of the present application when running the computer program.

[0024] The third aspect of the present application provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the method for direction finding and polarization beam synthesis of irregular conformal array radiation source according to the first aspect of the present application.

[0025] The present application provides a method for direction finding and polarization beam synthesis of irregular conformal array radiation source. The method has the following advantages:

[0026] 1. The present application constructs an array steering vector model decoupling the direction parameter and the polarization parameter, and combines the generalized eigenvalue decomposition to reduce the four-dimensional spectrum peak search problem in the traditional method to a two-dimensional spectrum peak search, thereby significantly reducing the operation complexity of signal parameter estimation. This makes the high-resolution joint direction finding and polarization parameter estimation method have engineering practicability, and is particularly suitable for real-time electronic reconnaissance systems with high processing speed requirements.

[0027] 2. The present application accurately models the independent spatial orientation of each array element in the irregular conformal array, fully utilizes the polarization diversity characteristics of the array, and realizes the joint accurate estimation of the signal direction and polarization parameters. This method fundamentally solves the polarization mismatch problem caused by the traditional method ignoring the inconsistency of the array element orientation, thereby greatly improving the direction finding and parameter estimation accuracy under the complex array platform.

[0028] 3. The present application reconstructs the interference noise covariance matrix by using the parameterization method, and calculates the optimal beam synthesis weight vector based on the reconstructed matrix. By accurately removing the target signal component in the covariance matrix, this method effectively avoids the signal self-cancellation problem that the target signal is canceled by its own energy in the interference suppression process, can form a deep null to suppress interference while maximizing the protection of the target signal, and thus obtains a higher output signal-to-noise ratio. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 FIG. 1 is a flowchart of the method for direction finding and polarization beam synthesis of irregular conformal array radiation source according to an embodiment of the present application;

[0030] Figure 2 FIG. 2 is a structural schematic diagram of the electronic device according to the present application;

[0031] Figure 3 FIG. 3 is a directional diagram of the half-wave dipole antenna element placed along the z-positive half-axis according to an embodiment of the present application;

[0032] Figure 4 is the reduced dimension MUSIC spatial spectrum obtained in Embodiment 1 of the present application;

[0033] Figure 5 is a performance comparison curve of output signal-to-interference-and-noise ratio changing with input signal-to-noise ratio of different algorithms when the target signal is elliptical polarization in Embodiment 2 of the present application;

[0034] Figure 6 is a performance comparison curve of different algorithms when the target signal is linear polarization.

[0035] Wherein, 10, signal modeling module; 20, parameter estimation module; 30, beam synthesis module. DETAILED DESCRIPTION

[0036] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions of the present application will be described in detail below. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0037] In modern electronic reconnaissance platforms such as unmanned aerial vehicles and missiles, conformal array antennas are widely used because they can conform to the surface of the carrier. However, the curved surface of these platforms is usually irregular, resulting in inconsistent orientations of each antenna element in the array, forming an irregular conformal array with polarization diversity characteristics. If the traditional signal processing method is used, the randomness of the element orientation will cause serious polarization mismatch problems, reducing the direction finding accuracy and anti-interference ability of the system to the radiation source.

[0038] Embodiments of the present application aim to solve the above technical problems, and provide an effective method that can fully utilize the polarization diversity characteristics of irregular conformal arrays, realize joint accurate estimation of the direction parameters and polarization parameters of target signals and interference signals, and form an optimal polarization matching beam to suppress interference. The specific implementation process and technical details of the method proposed by the present application will be described in detail below.

[0039] Referring to the accompanying Figure 1 and the accompanying Figure 2 , the accompanying Figure 1 is a flowchart of a method for direction finding and polarization beam synthesis of an irregular conformal array radiation source according to an embodiment of the present application, and the accompanying Figure 2 is a structural schematic diagram of an electronic device for implementing the method. The method for direction finding and polarization beam synthesis of an irregular conformal array radiation source provided by the present application can include the following steps:

[0040] S100, constructing a signal model of the irregular conformal array, which decouples the direction parameters and polarization parameters of the incident signals at the level of array steering vectors.

[0041] S200, based on the signal model constructed in S100 and the signal data received by the array, using a dimension reduction parameter estimation algorithm, jointly estimating the direction parameters and polarization parameters of all incident signals.

[0042] S300, based on the accurate parameters estimated in S200, reconstructing the interference noise covariance matrix not containing the target signal component, and calculating the optimal beam synthesis weight vector for maximizing the output signal-to-interference-and-noise ratio.

[0043] The method of the embodiment of the application can be executed by an electronic device, as shown in the accompanying drawings. Figure 2 The device can include a signal modeling module 10, a parameter estimation module 20, and a beam synthesis module 30. These modules can be realized by a processor executing program instructions in a memory.

[0044] In a specific execution process, the signal modeling module 10 first executes step S100. The core task of this module is to establish a mathematical description for the conformal array with irregular physical structure. It converts the physical position, spatial orientation, and other information of each antenna element in the array into array steering vectors that can reflect the response characteristics of the array to different direction and polarization signals.

[0045] The steering vector a constructed in this step has a special separated structure a(θ,φ,γ,η)=b(θ,φ)h(γ,η), where the matrix b only carries information related to the signal incident direction (defined by the pitch angle θ and the azimuth angle φ) and the array physical structure, and the vector h independently carries the polarization characteristics of the signal itself (defined by the polarization auxiliary angle γ and the polarization phase difference η). This structural decoupling is a prerequisite for subsequent efficient parameter estimation.

[0046] Subsequently, the parameter estimation module 20 receives the original signal data collected by the array antenna, and uses the steering vector model provided by the signal modeling module 10 to execute step S200. This step aims to accurately back-solve all parameters of all signal sources including the target and the interference from the mixed received signals. In the face of the four unknown parameters contained in the steering vector, instead of using a four-dimensional joint search with a huge amount of calculation, this module uses the separated structure of the steering vector and cleverly converts the four-dimensional search problem into a two-dimensional spectrum function search only for the direction parameters (θ,φ) through the mathematical tool of generalized eigenvalue decomposition. After the direction parameters are determined, the polarization parameters corresponding to each signal can be obtained directly through the closed-form solution. The output of this module is a series of accurately estimated and automatically paired signal parameter groups

[0047] Finally, the beamforming module 30 receives the refined parameter set output by the parameter estimation module 20 and performs step S300. The final goal of this step is to generate a digital beamforming weight vector w, which is used to weight and sum the array received signals so as to form a gain in the direction of the target signal and a null in the directions of all the interference signals. To achieve the optimal interference suppression effect, this module first reconstructs a parameterized interference noise covariance matrix R only containing the statistical characteristics of the interference and noise by using the estimated interference signal parameters and noise level Based on this reconstructed matrix and the steering vector of the target signal, this module calculates the optimal weight vector w according to the minimum variance distortionless response criterion. The application of this weight vector enables the system to finally output a signal with the maximum signal-to-interference-and-noise ratio.

[0048] To construct a signal model that can accurately describe the characteristics of a non-regular conformal array, it is necessary to first establish a space-polarization response model of a single arbitrarily oriented antenna element in a global coordinate system. In the embodiment of the present application, a half-wave dipole antenna is used as the basic unit of the array.

[0049] Referring to the accompanying drawings Figure 3 , Figure 3 is a diagram of the directional pattern of a half-wave dipole antenna element placed along the z-positive half-axis according to an embodiment of the present application. For a half-wave dipole antenna element placed along the z-positive half-axis of a global coordinate system as a reference, the directional pattern function can be expressed as:

[0050]

[0051] where θ is the signal elevation angle measured from the z-positive half-axis, φ is the signal azimuth angle measured from the x-positive half-axis, e θ and e φ are two mutually orthogonal unit polarization vectors pointing in the θ-direction and the φ-direction, respectively, in the global coordinate system.

[0052] In a non-regular conformal array, the orientations of the antenna elements are different. Therefore, a local coordinate system (x', y', z') is established for each antenna element, where the main axis direction of the antenna element defines the z'-positive half-axis direction of the local coordinate system. In this local coordinate system, the directional pattern function of the antenna element has the same standard form as formula (1):

[0053]

[0054] where θ' is the signal elevation angle measured from the z'-positive half-axis, φ' is the signal azimuth angle measured from the x'-positive half-axis, e θ′ and e φ′ are unit polarization vectors in the local coordinate system.

[0055] The spatial orientation of the element in the global coordinate system can be uniquely determined by two rotation angles (ξ, ε). Here, ξ is the angle between the element principal axis (i.e., z'-axis) and the global coordinate system z-axis, and ε is the angle between the projection of the element principal axis on the global coordinate system xoy plane and the x-positive half-axis. The rotation matrix T(ξ, ε) from the local coordinate system to the global coordinate system is thus determined as:

[0056]

[0057] To obtain the response model of the element in the global coordinate system, the directional pattern function of the element in the local coordinate system needs to be projected onto the two orthogonal unit polarization vectors e θ and e φ in the global coordinate system, and expressed as follows:

[0058]

[0059] where p θ (θ', φ') and p φ (θ', φ') are the polarization component functions of the response of the element in the global coordinate system in the θ and φ directions, respectively. In the global coordinate system, each unit vector can be expressed as:

[0060]

[0061] By performing an inner product operation on equation (2), the expressions of the two polarization component functions can be obtained, where the inner product operation is denoted by the symbol:

[0062]

[0063] To obtain the final response model that is only related to the parameters of the global coordinate system, the local coordinate system directional parameters (θ', φ') in the above expressions need to be replaced by the global coordinate system directional parameters (θ, φ) and the element orientation parameters (ξ, ε). The conversion relationship between them is as follows:

[0064]

[0065] Substituting the conversion relationship in equation (11) into equations (9) and (10), and simplifying, the spatial-polarization response model of an arbitrary conformal state element in the global coordinate system can be obtained, which is completely defined by global parameters:

[0066] e(ξ, ε, θ, φ) = p θ (ξ, ε, θ, φ) e θ + p φ (ξ, ε, θ, φ) e φ (12)

[0067] Among them, the two core polarization component functions p θ (ξ,ε,θ,φ) and p φ The final expression for (ξ,ε,θ,φ) is:

[0068]

[0069] This completes the mathematical modeling of the response of a single array element with arbitrary orientation, laying the foundation for constructing the signal model of the entire irregular conformal array.

[0070] After establishing the response model of a single array element, it is necessary to further construct the signal model of the entire irregular conformal array. This process integrates the responses of all array elements and considers the phase difference generated by the signal propagation in space, ultimately forming a mathematical expression that can describe the characteristics of the received signal of the entire array.

[0071] First, the electric field vector e of any incident signal s All of them can be decomposed into mutually orthogonal horizontal polarization components and vertical polarization components on their equiphase surfaces, as follows:

[0072] e s =s h (t)e h +s v (t)e v (15)

[0073] Among them, s h (t) and s v (t) represent the complex envelopes of the horizontal and vertical polarization signals, respectively, e h and e v These are the unit vectors for horizontal and vertical polarization, respectively.

[0074] Based on this decomposition, the array's response to the entire signal can also be decomposed into independent responses to the two polarization components. The array's response to the entire signal can then be further decomposed into independent responses to the two polarization components. Horizontal polarization response function of each array element (Given by formula (14)) Multiplying this by the phase delay factor determined by the position of the array element, and stacking the results of this term for all L array elements vertically, the steering vector a of the array for the horizontal polarization component of the signal can be constructed. h (θ,φ):

[0075]

[0076] in, Here, L is the element index, L is the total number of elements, k = 2π / λ is the angular wavenumber, and λ is the signal wavelength. It is the first Position vector of an array element, r = [sinθcosφ, sinθsinφ, cosθ] T is the unit propagation vector of the signal.

[0077] Similarly, the vertical polarization response function of each array element (given by equation (13)) is multiplied by the corresponding phase delay factor to construct the array steering vector a v (θ,φ) for the vertical polarization component of the signal:

[0078]

[0079] To realize the separation of the signal direction parameter and the polarization parameter, the present application combines the above two steering vectors into an Lx2 array space-polarization manifold matrix b(θ,φ), which is only related to the direction parameter (θ,φ) of the signal and the physical structure of the array:

[0080]

[0081] At the same time, the polarization state of the incident signal is independently described by a 2x1 polarization vector h(γ,η):

[0082]

[0083] Where γ is the polarization auxiliary angle of the signal, and η is the polarization phase difference of the signal.

[0084] Finally, the complete steering vector a(θ,φ,γ,η) of the irregular conformal array for an incident signal with parameters (θ,φ,γ,η) can be expressed as the product of the manifold matrix and the polarization vector:

[0085]

[0086] This structure decomposes the complex steering vector into the direction-dependent part and the polarization-dependent part, laying the foundation for subsequent dimension reduction processing.

[0087] Based on this steering vector model, it is assumed that there are K+1 far-field narrowband signals in space, one of which is the target signal, and the remaining K are interference signals. At time t, the Lx1-dimensional received signal vector x(t) of the array can be modeled as a linear superposition of all signals and additive noise:

[0088]

[0089] Where a k = a(θ k ,φ k ,γ k ,η k) is the steering vector of the kth signal, s1(t) represents the complex envelope of the target signal, {s k (t),k=2,…,K+1} represent the complex envelope of each interference signal, n(t) is an additive Gaussian white noise vector with zero mean and variance

[0090] After completing the signal modeling of the irregular conformal array, the embodiment of the application adopts a dimension reduction parameter estimation algorithm to realize efficient and accurate joint estimation of the direction parameters and polarization parameters of all incident signals. The specific construction process of the dimension reduction MUSIC spectrum function in the algorithm will be described in detail below.

[0091] First, the received signal vector x(t n ) collected by the array at N time points is processed to calculate the sample covariance matrix

[0092]

[0093] Subsequently, the sample covariance matrix is subjected to eigenvalue decomposition, and the eigenvalues are arranged in descending order. According to the total number of sources K+1 estimated or known in advance, the L eigenvalues are divided into two groups: the first K+1 larger eigenvalues {λ1,…,λ K+1} and the last L-(K+1) smaller eigenvalues {λ K+2 ,…,θ L}. The eigenvectors corresponding to the larger eigenvalues span the signal and interference subspace , while the eigenvectors corresponding to the smaller eigenvalues span the noise subspace

[0094] Based on the orthogonality principle of the signal subspace and the noise subspace, a four-dimensional MUSIC spectrum function can be constructed, which has the following form:

[0095]

[0096] By performing four-dimensional spectral peak search on this function, theoretically, the parameters of all signals can be found. However, the huge amount of calculation brought by four-dimensional search makes it difficult to apply in practical engineering.

[0097] To solve this problem, the application utilizes the steering vector separation structure a(θ,φ,γ,η)=b(θ,φ)h(γ,η) established in formula (20). Substituting this structure into formula (23), the four-dimensional spectrum function can be rewritten as:

[0098]

[0099] ​In this expression, the part only related to the direction parameters (θ, φ) can be clearly separated. From the numerator, a 2x2 matrix Z(θ, φ) can be defined:

[0100] Z(θ, φ) = b H (θ, φ) b(θ, φ) (25)

[0101] Similarly, from the denominator, another 2x2 matrix W(θ, φ) can be defined:

[0102]

[0103] With these two matrices, the spectral function in formula (24) can be further simplified into a generalized Rayleigh quotient form with respect to the polarization vector h(γ, η):

[0104]

[0105] For any given direction (θ, φ), the value of formula (27) is only related to the polarization vector h. The maximum value of this generalized Rayleigh quotient is equal to the maximum generalized eigenvalue of the matrix pair (Z(θ, φ), W(θ, φ)). This property inspires a dimension reduction method, i.e., constructing a spectral function only dependent on the direction parameters, whose function value at each direction is equal to the maximum value of the spectral peak that can be achieved by the polarization parameters in the corresponding direction. Therefore, the present application proposes a reduced-dimension MUSIC spectral function F(θ, φ), which is defined as:

[0106] F(θ, φ) = λ max {Z(θ, φ), W(θ, φ)} (28)

[0107] where λ max {·, ·} represents the operation of solving the generalized eigenvalue problem and taking the maximum generalized eigenvalue. In this way, the original four-dimensional search problem is successfully converted into a computationally feasible search problem for the two-dimensional spectral function F(θ, φ), greatly improving the efficiency of the algorithm.

[0108] After constructing the reduced-dimension MUSIC spectral function F(θ, φ) as shown in formula (28), the present embodiment solves the specific parameters of all incident signals by processing this function. This process consists of two steps: first, estimate the direction parameters by two-dimensional spectral peak search, and then solve the polarization parameters in the estimated direction using generalized eigenvalue decomposition, thereby realizing the joint estimation and automatic matching of all parameters.

[0109] Specifically, first, the entire spatial perspective range to be detected is grid-divided to form a series of discrete direction grid points. Subsequently, at each grid point (θ i ,φ j) at this point, calculate the reduced-dimension MUSIC spectral value F(θ i ,φ j ) at this point. Compare the spectral values of all grid points, find the K+1 largest spectral peaks in the formed two-dimensional spectrum. The direction grid points corresponding to these spectral peaks are the estimated values of the direction parameters of all K+1 incident signals (including targets and interference), denoted as

[0110] After obtaining the direction parameter estimate value of each signal , the generalized eigenvalue decomposition can be used to estimate the polarization parameters of each source. Substitute the direction parameter estimate value of the kth source into equations (25) and (26) to obtain matrices and Perform generalized eigenvalue decomposition on the matrix pair , and the generalized eigenvector corresponding to the largest generalized eigenvalue is the estimate value of the polarization vector of this source, denoted as:

[0111]

[0112] where α max {·,·} represents the operation of solving the generalized eigenvalue problem and taking the generalized eigenvector corresponding to the largest generalized eigenvalue. This step uses the same calculation process as the direction parameter estimation, without additional complex operations, thus realizing automatic pairing of direction parameters and polarization vectors.

[0113] After obtaining the normalized polarization vector estimate value , let and represent the first and second elements of this two-dimensional vector, respectively. By calculating the amplitude angle of the ratio of these two elements and the inverse tangent of the absolute value of the ratio, the estimate value of the polarization phase difference and the estimate value of the polarization auxiliary angle of this signal can be obtained, denoted as:

[0114]

[0115] where ∠(·) represents the principal value operation of taking the argument of a complex number, |·| represents the modulus operation of a complex number, and arctan(·) represents the inverse tangent operation. Thus, the joint accurate estimation of the direction parameters and polarization parameters of all incident signals is completed.

[0116] After estimating the direction and polarization parameters of all incident signals, this embodiment further performs optimal polarization beam synthesis to enhance the target signal and suppress the interference signal. The first step of this process is to reconstruct an interference noise covariance matrix that is pure and does not contain target signal components using a parameterized method.

[0117] First, the parameter set of all sources estimated in the last stage Substitute into the steering vector model defined by equation (20), the steering vectors of the target signal and all interference signals can be reconstructed, denoted as:

[0118]

[0119] where, is the reconstructed steering vector of the target signal, is the reconstructed steering vector of each interference signal.

[0120] Next, the power of noise is estimated. Using the smaller eigenvalues {λ K+2 ,…,λ L} corresponding to the noise subspace obtained in the eigenvalue decomposition step, the estimate of the noise power can be obtained by calculating the average of these eigenvalues, and its expression is:

[0121]

[0122] Then, the power of each interference signal needs to be accurately estimated. To this end, first, the noise component is removed from the sample covariance matrix (see equation (22)), and a covariance matrix containing only signal and interference components is obtained

[0123]

[0124] where I is an LxL identity matrix. Then, for each interference signal (k = 2, …, K + 1), its power can be estimated using a Capon-like spectrum estimator, and the specific calculation method is as follows:

[0125]

[0126] This method uses the reconstructed interference steering vector and the pure signal interference covariance matrix to obtain an accurate estimate of the power of each interference source.

[0127] Finally, the estimated power of each interference signal is used as a weight to weight the outer product of the corresponding interference signal steering vector and then add the estimated noise power to reconstruct the final interference noise covariance matrix

[0128]

[0129] The reconstructed matrix precisely describes the interference and noise environment faced by the array, and crucially, it contains no information about the target signal at all, laying the foundation for the subsequent computation of the optimal beamforming weight vector that avoids signal self-cancellation.

[0130] After the precise parametric reconstruction of the interference and noise covariance matrix R is completed, the final step of the present invention is to utilize this matrix and the estimated target signal steering vector to compute the weight vector for optimal beamforming.

[0131] To ensure the accuracy of the interference and noise covariance matrix, the powers of the individual interference signals ( where k = 2,..., K + 1) need to be accurately estimated. One specific implementation is as follows: first, construct a diagonal matrix Q K+1 from all the large eigenvalues {λ1,..., λ s+i} corresponding to the signal subspace obtained in the aforementioned eigen-decomposition, with the diagonal elements being the eigenvalues:

[0132] Q s+i = diag [λ1,..., λ K+1 ] (37)

[0133] Subsequently, subtract the diagonal matrix composed of the noise power estimates from this diagonal matrix, and utilize the signal subspace U s+i obtained in the aforementioned eigen-decomposition to reconstruct the signal and interference covariance matrix excluding the effects of noise, denoted as

[0134]

[0135] Finally, substitute this reconstructed signal and interference covariance matrix into the Capon spectrum estimator formula, and the accurate estimates of the powers of the individual interference signals can be obtained:

[0136]

[0137] Substitute the estimates of the individual interference powers obtained using this method into formula (36), and the high-precision interference and noise covariance matrix

[0138] Based on this high-precision reconstructed interference and noise covariance matrix and the target signal steering vector , the optimal beamforming weight vector w is computed according to the minimum variance distortionless response (MVDR) criterion as follows:

[0139]

[0140] The weight vector w is normalized by the denominator, which can ensure that the response gain of the beam in the direction of the target signal is 1, and at the same time, the total output power from all other directions (i.e. interference and noise) is minimized. The weight vector is multiplied by the conjugate transpose of the array received signal vector x(t), that is, y(t) = w H x(t), that is, the final output signal can be obtained. In the output signal, the target signal component is maximally preserved, and all interference signals are effectively suppressed, thereby realizing the maximization of the output signal-to-interference-and-noise ratio.

[0141] In order to further verify the technical effects and advantages of the method proposed in the application, two specific simulation examples will be described in detail below.

[0142] Example 1: Performance verification of parameter estimation algorithm

[0143] This example aims to verify the effectiveness and accuracy of the dimension reduction MUSIC search method proposed in the application in joint estimation of signal direction parameters and polarization parameters.

[0144] In a simulation scenario, a linear irregular conformal array composed of L = 10 half-wave dipole antennas is set, and the spacing between the array elements is set to one half of the system operating wavelength. In order to simulate irregularity, the elevation rotation angle of each dipole antenna in the array is randomly generated on a uniform distribution U(-45°, 45°). The azimuth rotation angle of each dipole antenna in the array is randomly generated on a uniform distribution U(-60°, 60°). The azimuth rotation angle of each dipole antenna in the array is randomly generated on a uniform distribution U(-60°, 60°).

[0145] It is assumed that there are three mutually independent far-field narrowband signals in the spatial environment, and the real parameters of each are set as shown in Table 1. The system center frequency is set to 10 GHz, the receiver sampling frequency is 25.6 kHz, and the number of snapshots for calculating the covariance matrix is N = 200.

[0146] Table 1 Parameter setting table of spatial signals in scenario 1

[0147] Signal k Pitch angle θ k ]] Azimuth angle φ k ]] Polarization auxiliary angle γ k ]]> Polarization phase difference η k ]]> Signal to noise ratio 1 20° 40° 10° 30° 40 dB 2 90° -60° 45° 90° 40 dB 3 120° 20° 60° 0° 40 dB

[0148] The parameter estimation algorithm proposed in the application is used to process the array received signal. Referring to the attached Figure 4 , Figure 4 is the dimension reduction MUSIC spatial spectrum obtained in Example 1 of the application. From the figure, three sharp spectral peaks can be clearly observed, and the spectral peak positions correspond to the direction parameters of the three signals in Table 1 (θ k ,φ k ) are highly consistent, which proves that the method of the application can effectively and accurately estimate the direction of the incident signal.

[0149] After estimating the direction parameters, the estimated values of the polarization parameters of each signal are further solved by the method of the present application, and compared with the true values, the results are shown in Table 2.

[0150] Table 2 Comparison of estimated values and actual values of polarization parameters of spatial signals in scenario 1

[0151]

[0152] From the data in Table 2, it can be seen that the estimated values of the polarization auxiliary angle γ k and the polarization phase difference η k of the three signals are very close to the actual values, with very small errors. This result shows that the method of the present application can not only accurately estimate the polarization parameters, but also realize the automatic and correct pairing of the direction parameters and the polarization parameters. This embodiment fully verifies the excellent performance of the proposed parameter estimation algorithm.

[0153] Example 2: Verification of polarization beam synthesis performance

[0154] This embodiment aims to verify the performance of the beam synthesis method proposed by the present application in suppressing strong interference and improving the output signal-to-interference-and-noise ratio, and to compare it with various existing methods.

[0155] In the simulation scenario, a linear irregular conformal array similar to that in Example 1 is used, where L = 10, the element spacing is half a wavelength, and the elevation rotation angle is randomly generated on a uniform distribution U(-45°, 45°), and the azimuth rotation angle is set to

[0156] A target signal and two strong interference signals are set in space, which are all far-field narrowband signals, and their specific parameters are shown in Table 3. The input signal-to-noise ratio (SNR) of the target signal varies in the range of -20 dB to 40 dB, while the signal-to-noise ratio (INR) of the two interference signals is fixed at 40 dB. The system parameters (center frequency, sampling rate, number of snapshots) are consistent with those in Example 1.

[0157] Table 3 Parameter setting table of spatial signals in scenario 2

[0158]

[0159]

[0160] The method of the application (labeled Prop) is compared with seven existing methods in performance, which include: sample covariance inverse method (SMI), diagonal loading SMI method (LSMI), eigen space decomposition method (ESD), worst case performance optimization method (WCPO), and three interference noise covariance matrix reconstruction methods based on different theories (INCM-INT, INCM-RMT, INCM-GVA). At the same time, the theoretically optimal performance (OPT) is taken as a benchmark.

[0161] In order to comprehensively evaluate the performance of the algorithm, tests are carried out under the conditions that the target signal is elliptical polarization and linear polarization respectively.

[0162] Referring to the accompanying drawings Figure 5 , Figure 5 is a performance comparison curve of the output signal-to-interference-and-noise ratio (SINR) of different algorithms with respect to the input signal-to-noise ratio (SNR) when the target signal is elliptical polarization, i.e. (γ1, η1) = (40°, 90°). As can be seen from the figure, the performance curve of the method of the application (Prop) is very close to the theoretically optimal (OPT) curve in the entire SNR range, and is significantly superior to all the other seven comparison methods.

[0163] Referring to the accompanying drawings Figure 6 , Figure 6 is a performance comparison curve of each algorithm when the target signal is linear polarization, i.e. (γ1, η1) = (20°, 0°). Similarly, the performance of the method of the application is still close to the optimal, and is significantly ahead of the other comparison methods.

[0164] The above two comparison results show that the interference noise covariance matrix construction method and beam synthesis method based on parameter reconstruction proposed in the application can effectively utilize the accurate parameters of the signal to achieve deep suppression of strong interference, and can obtain an output signal-to-interference-and-noise ratio close to the theoretical optimal value, stable and superior performance, regardless of the polarization form of the target signal.

[0165] In summary, the embodiments of the application fully prove that the radiation source direction finding and polarized beam synthesis method proposed can effectively solve the polarization mismatch problem in the irregular conformal array, realize accurate estimation of the signal parameters and effective suppression of the interference, and has significant technical advantages and practical value.

[0166] Although embodiments of the application have been shown and described, it will be understood by those having ordinary skill in the art that various changes, modifications, replacements and variations of these embodiments can be made without departing from the principles and spirit of the application, and the scope of the application is defined by the appended claims and their equivalents.

Claims

1. A method for direction finding and polarized beam synthesis of a non-regular conformal array of radiating sources, characterized in that, The method comprises the following steps: constructing a signal model of the irregular conformal array to obtain array steering vectors separating signal direction parameters from polarization parameters; based on the array steering vectors and signal data received by the irregular conformal array, performing two-dimensional spectral peak searching by constructing a reduced-dimension MUSIC spectral function to jointly estimate direction parameters and polarization parameters of target signals and interference signals; based on the estimated direction parameters and polarization parameters, reconstructing steering vectors of target signals and interference noise covariance matrices and calculating optimal beam synthesis weight vectors.

2. The irregular conformal array source direction finding and polarized beam synthesis method of claim 1, wherein, The step of constructing a signal model of the irregular conformal array to obtain array steering vectors separating signal direction parameters from polarization parameters specifically comprises: respectively constructing steering vectors of the irregular conformal array for signal horizontal polarization components and steering vectors of the irregular conformal array for signal vertical polarization components; combining the steering vectors of the horizontal polarization components and the steering vectors of the vertical polarization components to form an array space-polarization manifold matrix only related to the direction parameters; multiplying the array space-polarization manifold matrix by polarization vectors only related to the polarization parameters to obtain the array steering vectors separating signal direction parameters from polarization parameters.

3. The non-uniform conformal array source direction finding and polarized beam synthesis method of claim 2, wherein, The steering vectors of the horizontal polarization components and the steering vectors of the vertical polarization components are constructed by combining response functions of horizontal and vertical polarization components of each array element to a wave signal and phase delay factors determined by positions of the array elements; The response functions are determined according to spatial orientation parameters of each array element in a global coordinate system and signal wave direction parameters.

4. The method of claim 1, wherein, The step of performing two-dimensional spectral peak searching by constructing a reduced-dimension MUSIC spectral function specifically comprises: calculating a sample covariance matrix of signal data received by the irregular conformal array and performing eigenvalue decomposition to obtain a signal subspace and a noise subspace; based on the noise subspace and the array space-polarization manifold matrix, constructing two 2*2 matrices only related to the direction parameters; by solving a generalized eigenvalue problem of the two 2*2 matrices, taking a maximum generalized eigenvalue as a value of the reduced-dimension MUSIC spectral function, and searching a spectral peak of the function to obtain an estimated value of the direction parameters.

5. The method of claim 4, wherein, The step of jointly estimating direction parameters and polarization parameters of target signals and interference signals further comprises: substituting the estimated direction parameters of each signal into the two 2*2 matrices; solving a generalized eigenvalue problem at this time and taking a generalized eigenvector corresponding to a maximum generalized eigenvalue as an estimated value of the polarization vector to calculate the polarization parameters.

6. The non-uniform conformal array source direction finding and polarized beam synthesis method of claim 1, wherein, The step of reconstructing an interference noise covariance matrix specifically comprises: estimating noise power and estimating power of each interference signal by using a signal subspace and estimated steering vectors of each interference signal; weighting outer products of the steering vectors of each interference signal by using the power of each interference signal as a weight value, summing up the weighted outer products, and adding a noise covariance matrix composed of the noise power to obtain the reconstructed interference noise covariance matrix.

7. The non-uniform conformal array source direction finding and polarized beam synthesis method of claim 6, wherein, The step of estimating power of each interference signal specifically comprises: constructing a signal and interference covariance matrix by using the signal subspace and its corresponding eigenvalues and the estimated noise power; substituting the estimated steering vectors of the interference signals into a Capon spectrum estimation formula based on the signal and interference covariance matrix to calculate the estimated values of the interference signal powers.

8. The method of claim 6, wherein, The step of calculating the optimal beamforming weight vector comprises: inverting the reconstructed interference noise covariance matrix and multiplying the result by the reconstructed target signal steering vector to obtain an intermediate weight vector; scaling the intermediate weight vector by a normalization factor to ensure that the response to the target signal is not distorted, thereby obtaining the final beamforming weight vector.

9. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor, when executing the computer program, implements the method of any one of claims 1-7.

10. A storage medium having stored thereon a computer program, characterized in that The computer program, when executed by the processor, implements the method of any one of claims 1-7.

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