Broadband direction finding method based on electromagnetic vector array
By employing a broadband direction finding method based on electromagnetic vector arrays and utilizing frequency domain processing and eigenvalue decomposition algorithms, the complexity and resource requirements of electromagnetic vector arrays in broadband applications are solved, achieving multi-signal separation and broadband signal detection, which is suitable for miniaturized devices.
Patent Information
- Application Number
- CN202511110161.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-08
- Publication Date
- 2025-11-21
AI Technical Summary
Existing electromagnetic vector arrays suffer from high algorithm complexity, high processing resource requirements, and difficulty in miniaturization in broadband applications. Furthermore, existing algorithms are difficult to promote in miniaturized broadband direction finding equipment.
A broadband direction finding method based on electromagnetic vector array is adopted. By establishing a receiving model, digitizing the signal, performing short-time Fourier transform, extracting eigenvalues of the covariance matrix, and solving the direction of arrival using a vector cross product algorithm or MVDR algorithm, frequency domain processing and multi-signal separation are achieved.
It enables multi-signal separation and broadband signal detection of signals at different frequencies, reduces computational load, and is suitable for miniaturized devices.
Smart Images
Figure CN120995048A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of array signal processing, specifically relating to a broadband direction finding method based on an electromagnetic vector array. Background Technology
[0002] Electromagnetic vector arrays are an emerging branch of array signal processing and are increasingly being applied in fields such as communications. Compared with conventional scalar arrays, electromagnetic vector arrays have greater degrees of freedom, higher parameter estimation accuracy, stronger anti-interference capabilities, and the ability to extract more signal parameters.
[0003] In recent years, research on direction finding algorithms for electromagnetic vector arrays has become increasingly active both domestically and internationally, but the following problems still exist in engineering implementation.
[0004] 1. Limited consideration is given to wideband application scenarios.
[0005] 2. The algorithm has high complexity and requires high processing resources. If the spectral estimation algorithm of scalar arrays is directly extended to electromagnetic vector arrays, it is necessary to jointly search for spectral peaks in the polarization domain and the spatial domain, or to pair the spatial angle and polarization parameters.
[0006] 3. It is difficult to promote electromagnetic vector arrays in miniaturized broadband direction finding equipment. Summary of the Invention
[0007] In view of the current situation of the prior art, the present invention overcomes the above-mentioned defects and provides a broadband direction finding method based on electromagnetic vector array.
[0008] This invention employs the following technical solution: a broadband direction finding method based on an electromagnetic vector array, comprising the following steps:
[0009] Step 1: Establish an electromagnetic vector array receiver model;
[0010] Step 2: Digitize each received signal, frame the time-domain snapshot sequence, and then convert it into frequency-domain data through short-time Fourier transform;
[0011] Step 3: Based on the data obtained in Step 2, search for the K channels with the most concentrated spectral energy to form the filtered data;
[0012] Step 4: Based on the data obtained in Step 3, calculate the covariance matrix of each channel and extract eigenvalues to obtain the steering vector of the signal;
[0013] Step 5: Solve for the direction of arrival using the vector cross product algorithm or search for the direction of arrival using the MVDR algorithm. As a preferred technical solution, Step 1 is specifically implemented as follows:
[0014] Assuming that under far-field conditions, K electromagnetic wave signals with different carriers are incident on the electromagnetic vector array and satisfy a stationary random process, the array output model expression is shown in equation (1):
[0015] X = A·S + N(1);
[0016] In equation (1), X∈CM is called the output signal vector of the electromagnetic vector array, which physically represents the measured values of the M array elements, denoted as X=[x1 x2 … x M ] T A∈CM,K is called the electromagnetic vector array steering vector matrix (A is also called the array manifold matrix); S∈CK is called the input signal vector, which physically represents the complex envelope of K incident signals; N∈C M , is called the electromagnetic vector array noise vector, and its physical meaning is M zero-mean Gaussian independent white noises.
[0017] As the preferred technical solution above, step two is specifically implemented as follows:
[0018] The received signal is resampled and digitally down-converted to become digital baseband data. After digitization, the signal rate is represented by fs, ensuring that all K signals are within the fs digital bandwidth. The received signal is converted into a time-discrete sequence, and a finite number of snapshots are taken from each array element to form a frame of data, denoted by y. m It means that y m ∈C 1,N1 The data structure of the signal becomes Equation (2), which is an M×N1-dimensional matrix;
[0019]
[0020] For each frame of data y m Perform a short-time Fourier transform, with the number of Fourier points set to L; obtain M×L dimensional spectral data [z(1)z(2)…z(L)]' where z(l)∈C M Each row of the spectral data contains L points, representing N·f within the fs bandwidth. s The spectrum within a time period, with a channel spacing of f between adjacent points. s / L.
[0021] As the preferred technical solution above, step three is implemented as follows:
[0022] The search process for the K channels with the highest spectral energy concentration is represented by Formula 3:
[0023]
[0024] When ||z(l)|| is higher than this threshold, obtain the sequence number of the corresponding channel;
[0025] Select the spectral data corresponding to the sequence number and form an M×K dimensional spectral dataset, written as... in,
[0026] As the preferred technical solution above, step four is specifically implemented as follows:
[0027] Based on the data obtained in step three, calculate the covariance matrix for each channel;
[0028] The average of the N2 frames of data is shown in equation (4);
[0029]
[0030] Given that R(k) is nonsingular and a positive definite Hermitain matrix, R(k)∈CM,M; after eigenvalue decomposition, it can be written as equation (5):
[0031]
[0032] In equation (5), λ(k) i Represents the eigenvalue, u(k) i This represents the eigenvector; the eigenvector corresponding to the largest eigenvalue is taken and labeled as u(k). max Then normalize it to obtain the steering vector a(k) of the Kth signal, as shown in equation (6);
[0033]
[0034] As the preferred technical solution above, step five, "solving the direction of arrival using the vector cross product algorithm," is specifically implemented as follows:
[0035] For co-located electromagnetic vector arrays, the analytical solution can be directly obtained using the vector cross product algorithm. Taking a three-dimensional co-located electric field vector array as an example, the guiding vector of this type of sensor is written as a(k)=[d1 d2 d3] T This type of array performs direction finding on electromagnetic signals within a hemispherical space; the analytical expression is given directly, and the azimuth measurement formula is shown in equation (7);
[0036]
[0037] The formula for measuring pitch angle is shown in equation (8);
[0038]
[0039] As the preferred technical solution above, step five, "searching for the direction of arrival using the MVDR algorithm," is specifically implemented as follows:
[0040] For unconventional electromagnetic vector arrays, where it is difficult to derive analytical solutions, a search solution is performed based on the principle of minimum mean square distortion-free response; the search function is shown in equation (9).
[0041]
[0042] In equation (9), This represents the steering vector corresponding to each direction under each channel; it is obtained by traversing... When f(k,φ) j ,θ j When ) is at its maximum, the corresponding (φ) j ,θ j ( ) refers to the azimuth and elevation angles of the incident light.
[0043] The broadband direction finding method based on electromagnetic vector array disclosed in this invention has the following advantages:
[0044] 1. Convert the time-domain snapshot signal to the frequency domain for processing. For signals incident at different frequencies, use their frequency domain energy distribution characteristics to achieve multi-signal separation.
[0045] 2. Parallel processing of multiple frequency channels enables broadband signal detection.
[0046] 3. Perform eigenvalue decomposition on each frequency channel to obtain the steering vector, and use the vector cross product algorithm or MVDR algorithm to solve for the direction of arrival. Compared with the spectral estimation algorithm, the computational load is smaller. Attached Figure Description
[0047] Figure 1 This is a flowchart illustrating the implementation of the present invention.
[0048] Figure 2 This is a schematic diagram of the three-dimensional co-located electric field vector array of the present invention.
[0049] Figure 3 This is a spectrum diagram of the four incoherent signals presented in this invention.
[0050] Figure 4 The figure shows the simulation results of direction finding for four incoherent signals according to the present invention. Detailed Implementation
[0051] This invention discloses a broadband direction finding method based on an electromagnetic vector array. The following description, in conjunction with a preferred embodiment (Embodiment 1), is shown in the accompanying drawings. Figures 1 to 4 The specific embodiments of the present invention will be further described below.
[0052] Example 1.
[0053] Preferably, the broadband direction finding method based on electromagnetic vector array includes the following steps:
[0054] Step 1: Establish an electromagnetic vector array receiver model;
[0055] Step 2: Digitize each received signal, frame the time-domain snapshot sequence, and then convert it into frequency-domain data through short-time Fourier transform;
[0056] Step 3: Based on the data obtained in Step 2, search for the K channels with the most concentrated spectral energy to form the filtered data;
[0057] Step 4: Based on the data obtained in Step 3, calculate the covariance matrix of each channel and extract eigenvalues to obtain the steering vector of the signal;
[0058] Step 5: Use the vector cross product algorithm to solve for the direction of arrival (DOA) or use the MVDR algorithm to search for the DOA.
[0059] Step one is specifically implemented as follows:
[0060] Assuming that under far-field conditions, K electromagnetic wave signals with different carriers are incident on the electromagnetic vector array and satisfy a stationary random process, the array output model expression is shown in equation (1):
[0061] X = A·S + N (2);
[0062] In equation (1), X∈CM is called the output signal vector of the electromagnetic vector array, which physically represents the measured values of the M array elements. It can also be written as X=[x1 x2 … x M ] T A∈CM,K is called the electromagnetic vector array steering vector matrix (A is also called the array manifold matrix); S∈CK is called the input signal vector, which physically represents the complex envelope of K incident signals; N∈C M , is called the electromagnetic vector array noise vector, and its physical meaning is M zero-mean Gaussian independent white noises.
[0063] Step two is specifically implemented as follows:
[0064] The received signal is resampled and digitally down-converted to become digital baseband data. After digitization, the signal rate is represented by fs, ensuring that all K signals are within the fs digital bandwidth. The received signal is converted into a discrete-time sequence, and each array element takes a finite number of snapshots (N1 snapshots) to form a frame of data, denoted by y. m It means (y) m ∈C 1,N1 The data structure of the signal becomes Equation (2), which is an M×N1-dimensional matrix.
[0065]
[0066] For each frame of data ym Perform a short-time Fourier transform, with the number of Fourier points set to L. This yields M×L dimensional spectral data [z(1)z(2)…z(L)]. Where z(l)∈C M Each row of the spectral data contains L points, representing N·f within the fs bandwidth. s The spectrum within a time period, with a channel spacing of f between adjacent points. s / L.
[0067] Step three is specifically implemented as follows:
[0068] The search for the indices of the K channels with the highest spectral energy can be represented by Formula 3:
[0069]
[0070] Optionally, if the number of incident signals is unknown, Equation (3) can be omitted for filtering. In this case, a reasonable threshold should be set, and when ||z(l)|| is higher than the threshold, the corresponding channel number should be obtained.
[0071] Select the spectral data corresponding to the sequence number and form an M×K dimensional spectral dataset, written as... in,
[0072] Step four is specifically implemented as follows:
[0073] Based on the data obtained in step three, calculate the covariance matrix for each channel.
[0074] Optionally, the N2 frames of data can be averaged (equivalent to time averaging. If time averaging is not performed, the value of N2 is 1), as shown in equation (4).
[0075]
[0076] Given that R(k) is nonsingular and a positive definite Hermitain matrix (R(k)∈CM,M), it can be written as equation (5) through eigenvalue decomposition:
[0077]
[0078] In equation (5), λ(k) i Represents the eigenvalue, u(k) i This represents the eigenvector. The eigenvector corresponding to the largest eigenvalue is taken and labeled as u(k). max Then, normalize the vector to obtain the steering vector a(k) of the Kth signal, as shown in equation (6).
[0079]
[0080] Step five, “using the vector cross product algorithm to solve for the direction of arrival,” is specifically implemented in the following steps.
[0081] For co-located electromagnetic vector arrays, the analytical solution can be directly obtained using the vector cross product algorithm. Taking a three-dimensional co-located electric field vector array as an example, the guiding vector of this type of sensor can be written as a(k) = [d1 d2 d3]. T This type of array can perform direction finding of electromagnetic signals within a hemispherical space. The analytical expression is given directly; the azimuth measurement formula is shown in equation (7).
[0082]
[0083] The formula for measuring pitch angle is shown in equation (8).
[0084]
[0085] Step five, “using the MVDR algorithm to search for the direction of arrival,” is specifically implemented in the following steps.
[0086] For unconventional electromagnetic vector arrays, where it is difficult to derive analytical solutions, a search can be performed based on the principle of Minimum Variance Distortionless Response (MVDR). The search function is shown in equation (9).
[0087]
[0088] In equation (9), This represents the steering vector corresponding to each direction under each channel (which can be obtained through simulation or actual measurement). It is obtained by traversing... When f(k,φ) j ,θ j When ) is at its maximum, the corresponding (φ) j ,θ j ( ) refers to the azimuth and elevation angles of the incident light.
[0089] The working principle of the broadband direction finding method based on electromagnetic vector array disclosed in this embodiment is explained below.
[0090] Specifically, the broadband direction finding method based on electromagnetic vector arrays includes the following steps:
[0091] Step 1: Establish an electromagnetic vector array receiver model.
[0092] Assuming that under far-field conditions, K electromagnetic wave signals with different carriers are incident on the electromagnetic vector array and satisfy a stationary random process, the array output model expression is shown in equation (1):
[0093] X = A·S + N(3);
[0094] In equation (1), X∈CM is called the output signal vector of the electromagnetic vector array, which physically represents the measured values of the M array elements. It can also be written as X=[x1 x2 … x M ] T A∈CM,K is called the electromagnetic vector array steering vector matrix (A is also called the array manifold matrix); S∈CK is called the input signal vector, which physically represents the complex envelope of K incident signals; N∈C M , is called the electromagnetic vector array noise vector, and its physical meaning is M zero-mean Gaussian independent white noises.
[0095] Step 2: Digitize each received signal, frame the time-domain snapshot sequence, and then convert it into frequency-domain data through short-time Fourier transform.
[0096] The received signal is resampled and digitally down-converted to become digital baseband data. After digitization, the signal rate is represented by fs, ensuring that all K signals are within the fs digital bandwidth. The received signal is converted into a discrete-time sequence, and each array element takes a finite number of snapshots (N1 snapshots) to form a frame of data, denoted by y. m It means (y) m ∈C 1,N1 The data structure of the signal becomes Equation (2), which is an M×N1-dimensional matrix.
[0097]
[0098] For each frame of data y m Perform a short-time Fourier transform, with the number of Fourier points set to L. This yields M×L dimensional spectral data [z(1) z(2) … z(L)]. Where z(l)∈C M Each row of the spectral data contains L points, representing N·f within the fs bandwidth. s The spectrum within a time period, with a channel spacing of f between adjacent points. s / L.
[0099] Step 3: Based on the data obtained in Step 2, search for the K channels with the most concentrated spectral energy to form the filtered data.
[0100] The search for the indices of the K channels with the highest spectral energy can be represented by Formula 3:
[0101]
[0102] Optionally, if the number of incident signals is unknown, Equation (3) can be omitted for filtering. In this case, a reasonable threshold should be set, and when ||z(l)|| is higher than the threshold, the corresponding channel number should be obtained.
[0103] Select the spectral data corresponding to the sequence number and form an M×K dimensional spectral dataset, written as... in,
[0104] Step 4: Based on the data obtained in Step 3, calculate the covariance matrix of each channel and extract eigenvalues to obtain the steering vector of the signal.
[0105] Based on the data obtained in step three, calculate the covariance matrix for each channel.
[0106] Optionally, the N2 frames of data can be averaged (equivalent to time averaging. If time averaging is not performed, the value of N2 is 1), as shown in equation (4).
[0107]
[0108] Given that R(k) is nonsingular and a positive definite Hermitain matrix (R(k)∈CM,M), it can be written as equation (5) through eigenvalue decomposition:
[0109]
[0110] In equation (5), λ(k) i Represents the eigenvalue, u(k) i This represents the eigenvector. The eigenvector corresponding to the largest eigenvalue is taken and labeled as u(k). max Then, normalize the vector to obtain the steering vector a(k) of the Kth signal, as shown in equation (6).
[0111]
[0112] Step 5: Use the vector cross product algorithm to solve for the direction of arrival (DOA) or use the MVDR algorithm to search for the DOA.
[0113] For co-located electromagnetic vector arrays, the analytical solution can be directly obtained using the vector cross product algorithm. Taking a three-dimensional co-located electric field vector array as an example, the guiding vector of this type of sensor can be written as a(k) = [d1 d2 d3]. T This type of array can perform direction finding of electromagnetic signals within a hemispherical space. The analytical expression is given directly; the azimuth measurement formula is shown in equation (7).
[0114]
[0115] The formula for measuring pitch angle is shown in equation (8).
[0116]
[0117] For unconventional electromagnetic vector arrays, where it is difficult to derive analytical solutions, a search can be performed based on the principle of Minimum Variance Distortionless Response (MVDR). The search function is shown in equation (9).
[0118]
[0119] In equation (9), This represents the steering vector corresponding to each direction under each channel (which can be obtained through simulation or actual measurement). It is obtained by traversing... When f(k,φ) j ,θ j When ) is at its maximum, the corresponding (φ) j ,θ j ( ) refers to the azimuth and elevation angles of the incident light.
[0120] The following describes the simulation method, results, and analysis of the broadband direction finding method based on electromagnetic vector array disclosed in this embodiment.
[0121] Selected array such as Figure 2 The diagram shows a three-dimensional co-located electric field vector array (with 3 array elements, measuring the electric fields along the X, Y, and Z axes). Four incoherent signals are incident on the array, all QPSK modulated; the symbol rate is 0.04 fs; the normalized carrier frequency f0 / fs = [0.1; 0.2; 0.3; 0.4]; the azimuth angle φ = [-55°; -10°; 15°; 60°]; the elevation angle θ = [45°; 85°; 90°; 100°]; the polarization tilt angle α = [45°; 15°; 15°; 1°]; and the polarization ellipticity angle β = [45°; 30°; 25°; 20°]. The number of snapshots N1 = 1000, the time averaging parameter N2 = 1 (no time averaging performed), the signal-to-noise ratio = 20 dB, and the number of simulations = 50. Figure 3 The spectrum results of the received signals from the three array elements are given. It can be seen that the four signals are sparsely distributed in the frequency domain. Using frequency domain processing algorithms, the signals can be directly sorted.
[0122] Figure 4 Simulation results for direction finding are presented. The root mean square (RMS) direction finding accuracy for signal 1 is 1.81°, for signal 2 it is 1.92°, for signal 3 it is 2.28°, and for signal 4 it is 2.84°. For a three-dimensional co-located electric field vector array, the smaller the polarization ellipticity angle of the incident signal, the worse the direction finding accuracy. Simulation results confirm this correlation.
[0123] It is worth mentioning that the specific steps and other technical features of the frequency domain processing algorithm involved in this patent application should be regarded as prior art. The specific structure, working principle, and possible control methods and spatial arrangement methods of these technical features can be conventionally selected in the field and should not be regarded as the inventive point of this patent. This patent will not be further elaborated in detail.
[0124] For those skilled in the art, 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. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.
Claims
1. A broadband direction finding method based on an electromagnetic vector array, characterized in that, Includes the following steps: Step 1: Establish an electromagnetic vector array receiver model; Step 2: Digitize each received signal, frame the time-domain snapshot sequence, and then convert it into frequency-domain data through short-time Fourier transform; Step 3: Based on the data obtained in Step 2, search for the K channels with the most concentrated spectral energy to form the filtered data; Step 4: Based on the data obtained in Step 3, calculate the covariance matrix of each channel and extract eigenvalues to obtain the steering vector of the signal; Step 5: Use the vector cross product algorithm to solve for the direction of arrival (DOA) or use the MVDR algorithm to search for the DOA.
2. The broadband direction finding method based on electromagnetic vector array according to claim 1, characterized in that, Step one is implemented in the following steps: Assuming that under far-field conditions, K electromagnetic wave signals with different carriers are incident on the electromagnetic vector array and satisfy a stationary random process, the array output model expression is shown in equation (1): X = A·S + N(1); In equation (1), X∈CM is called the output signal vector of the electromagnetic vector array, which physically represents the measured values of the M array elements, denoted as X=[x1 x2 … x M ] T A∈CM,K is called the electromagnetic vector array steering vector matrix (A is also called the array manifold matrix); S∈CK is called the input signal vector, which physically represents the complex envelope of K incident signals; N∈C M , is called the electromagnetic vector array noise vector, and its physical meaning is M zero-mean Gaussian independent white noises.
3. The broadband direction finding method based on electromagnetic vector array according to claim 2, characterized in that, Step two is implemented in the following steps: The received signal is resampled and digitally down-converted to become digital baseband data. After digitization, the signal rate is represented by fs, ensuring that all K signals are within the fs digital bandwidth. The received signal is converted into a time-discrete sequence, and a finite number of snapshots are taken from each array element to form a frame of data, denoted by y. m It means that y m ∈C 1,N1 The data structure of the signal becomes Equation (2), which is an M×N1-dimensional matrix; For each frame of data y m Perform a short-time Fourier transform, with the number of Fourier points set to L; obtain M×L dimensional spectral data [z(1) z(2) … z(L)]' where z(l)∈C M Each row of the spectral data contains L points, representing N·f within the fs bandwidth. s The spectrum within a time period, with a channel spacing of f between adjacent points. s / L.
4. The broadband direction finding method based on electromagnetic vector array according to claim 3, characterized in that, Step three is implemented in the following steps: The search process for the K channels with the highest spectral energy concentration is represented by Formula 3: When ||z(l)|| is higher than this threshold, obtain the sequence number of the corresponding channel; Select the spectral data corresponding to the sequence number and form an M×K dimensional spectral dataset, written as... in, 5. The broadband direction finding method based on electromagnetic vector array according to claim 4, characterized in that, Step four is implemented in the following steps: Based on the data obtained in step three, calculate the covariance matrix for each channel; The average of the N2 frames of data is shown in equation (4); Given that R(k) is nonsingular and a positive definite Hermitain matrix, R(k)∈CM,M; after eigenvalue decomposition, it can be written as equation (5): In equation (5), λ(k) i Represents the eigenvalue, u(k) i Represents the eigenvector; Take the eigenvector corresponding to the largest eigenvalue and label it u(k). max Then normalize it to obtain the steering vector a(k) of the Kth signal, as shown in equation (6); 6. The broadband direction finding method based on electromagnetic vector array according to claim 5, characterized in that, Step five, "using the vector cross product algorithm to solve for the direction of arrival," is specifically implemented as follows: For co-located electromagnetic vector arrays, the analytical solution can be directly obtained using the vector cross product algorithm. Taking a three-dimensional co-located electric field vector array as an example, the guiding vector of this type of sensor is written as a(k)=[d1 d2 d3] T This type of array performs direction finding on electromagnetic signals within a hemispherical space; the analytical expression is given directly, and the azimuth measurement formula is shown in equation (7); The formula for measuring pitch angle is shown in equation (8); 7. The broadband direction finding method based on electromagnetic vector array according to claim 5, characterized in that, Step five, "Searching for the direction of arrival using the MVDR algorithm," is specifically implemented as follows: For unconventional electromagnetic vector arrays, where it is difficult to derive analytical solutions, a search solution is performed based on the principle of minimum mean square distortion-free response; the search function is shown in equation (9). In equation (9), This represents the steering vector corresponding to each direction under each channel; it is obtained by traversing... When f(k,φ) j ,θ j When ) is at its maximum, the corresponding (φ) j ,θ j ( ) refers to the azimuth and elevation angles of the incident light.