Vortex electromagnetic wave azimuth angle high-resolution estimation method

Abstract

The invention discloses a vortex electromagnetic wave azimuth angle high-resolution estimation method. The azimuth estimation precision under a low signal-to-noise ratio condition is remarkably improved through a characteristic value correction strategy. A uniform circular array (UCA) geometric model based on MIMO is established, vortex electromagnetic waves carrying orbital angular momentum are used as information carriers, and a received signal matrix is constructed through modal domain sampling. Aiming at the problem that the performance of a traditional MUSIC algorithm is reduced under the conditions of a coherent signal source and a low signal-to-noise ratio, a method for carrying out weighted correction on a noise subspace characteristic value is innovatively provided, and the construction of a spatial spectrum function is improved by optimizing the utilization rate of the noise characteristic value. Compared with the traditional MUSIC and FFT methods, the method provided by the invention has more excellent target azimuth estimation performance.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a high-resolution estimation method for the azimuth angle of vortex electromagnetic waves. Background Technology

[0002] Based on the propagation characteristics of electromagnetic waves, radar can operate under all-weather, all-time, and long-range conditions, acquiring the electromagnetic wave scattering information of targets in various complex environments, thereby enabling target reconstruction, detection, identification, and tracking. Traditional radar detection methods depend on the antenna observation angle for azimuth resolution. For example, the azimuth resolution of real aperture radar is related to the size of the real aperture, but in practical applications, it is impossible to obtain a large real aperture. Synthetic aperture radar requires the relative motion between the antenna and the target to generate Doppler information for azimuth resolution, but the resolution quality is easily affected by the platform trajectory, thus having certain limitations.

[0003] Electromagnetic waves, as information carriers, are traditionally modulated primarily in the time, frequency, and polarization domains, utilizing the far-field plane wave approximation. Orbital angular momentum (OAM) introduces a new degree of modulation freedom to electromagnetic waves. Electromagnetic waves carrying orbital angular momentum exhibit a helical wavefront characteristic, hence the name vortex electromagnetic waves. The generation, wireless communication, and radar imaging of vortex electromagnetic waves have attracted extensive research from numerous scholars. When the radiation field of vortex electromagnetic waves illuminates a target, the echo signal received by the radar contains information about the target's azimuth. Therefore, when using vortex electromagnetic waves for target azimuth resolution, the radar and target do not need to undergo relative motion to obtain the target azimuth information from the echo signal through signal processing. Some scholars have applied vortex electromagnetic waves to radar imaging, demonstrating their ability to resolve azimuth for radar targets. Subsequently, some scholars applied the MUSIC algorithm to radar imaging, achieving high azimuth resolution for radar targets with a low number of OAM modes. However, when the signal-to-noise ratio is low, the azimuth resolution accuracy is relatively low. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a high-resolution azimuth estimation method for vortex electromagnetic waves, significantly improving azimuth estimation accuracy under low signal-to-noise ratio (SNR) conditions through an eigenvalue correction strategy. A MIMO-based uniform circular array (UCA) geometric model is established, utilizing vortex electromagnetic waves carrying orbital angular momentum as the information carrier, and constructing the received signal matrix through modal domain sampling. Addressing the performance degradation of traditional MUSIC algorithms under coherent signal sources and low SNR conditions, an innovative method for weighted correction of noise subspace eigenvalues ​​is proposed, improving the construction of the spatial spectrum function by optimizing the utilization rate of noise eigenvalues. Compared to traditional MUSIC and FFT methods, this invention's method exhibits superior target azimuth estimation performance.

[0005] The technical solution adopted by this invention to solve its technical problem is as follows: Step 1: Establish a geometric model for estimating the azimuth angle of a vortex electromagnetic wave target based on MIMO; N identical isotropic array elements form a uniform circular array as a transmitting antenna, and the radius of the UCA is... , No. The azimuth angle of each array element is The circumference is located at noodle; Establish a spherical coordinate system with the center point of UCA as the origin, and the distance... The length of the line connecting the origin and the target, and the pitch angle. The line connecting the origin and the target The angle between the positive and negative axes, azimuth angle The line connecting the origin and the target of the UCA starts from... The angle through which the positive half-axis rotates counterclockwise is the target position. ; Step 2: Use a linear frequency modulated (LFM) signal as the transmission signal. The LFM signal fed into all transmitting array elements is: (1) In the formula For time variables, The duration of the pulse. The modulation frequency of a linear frequency modulation signal. The center frequency of the signal. It is a matrix function, that is: (2) In order to generate OAM modal values The vortex electromagnetic waves sequentially add phase shifts to each element of the circular array. Vortex electromagnetic wave target detection involves illuminating the target to be observed with vortex electromagnetic waves that traverse different modes. The signal transmitted by a single array element is: (3) The UCA transmits a pulse signal as follows: (4) Step 3: Any detection point Transmission signal at location Written as: (5) in , , ; c Indicates the speed of electromagnetic wave propagation; Meet the conditions ,therefore (6) when When large enough, equation (6) is effective for... The summation is approximately expressed as an integral: (7) in , For the first The first-order Bessel function of the first kind, The wavenumber of the signal; Step 4: All antennas on the UCA are used to receive the echo scattered by the target. The signal received by each antenna is multiplied by The total echo signal is then expressed as: (8) in , The radar cross-section (RCS) of a target; Assuming coexistence There are 3 targets, each of which is approximately a point target. The position of each target point is denoted as . The corresponding RCS is denoted as The total echo is then expressed as: (9) in ; When the condition is met and When the Bessel function is used, it undergoes the following approximate transformation: (10) After squaring, we get: (11) Ignoring the high-frequency oscillation term, it simplifies to: (12) Phase term of the echo signal After compensation, the echo signal is approximately represented by equation (12) as follows: (13) Assumption yes The sampling rate in the domain, according to Nyquist sampling theory, is used to ensure that the estimates do not alias. , The following conditions must be met: (14) in, for The maximum frequency of the domain, for The maximum angular frequency of the domain, therefore ; consider Real-time echo signals calibrated under each OAM mode, for vortex echo signals in After sampling in the domain and normalizing the echo amplitude, the received signal matrix is ​​constructed as follows: (15) in The guide vector matrix for the receiving matrix. The modified echo signal vector, Indicates the corrected number The source signal of the target, The received Gaussian white noise, and (16) (17) in, The symbol represents the matrix conjugate transpose; Perform covariance calculation on the received signal matrix to obtain the covariance matrix. for: (18) in, Represents the mathematical expectation. , The covariance matrix of the target source signal is represented. The noise power in the environment, for identity matrix; According to smoothing theory, in the modal domain The samples were divided into 3 mixed sub-sample blocks, each sub-sample block containing For each sample, then To achieve full rank in the echo signal covariance matrix, the number of samples in the sub-sample block should satisfy the following condition. This ensures the orthogonality between the signal space and the noise subspace; The covariance matrix of the echo signal after spatial smoothing and decoherence processing is: (19) in, It is the first Subsample blocks The covariance matrix; For covariance matrix Eigenvalue decomposition yields: (20) in, For eigenvalues, The corresponding feature vector; Sort the eigenvalues ​​from largest to smallest to get: ,forward Components ,back Components Then the covariance matrix It can be broken down into: (twenty one) in and These are the signal subspace and the noise subspace, respectively. The azimuth search formula for the MUSIC algorithm is: (twenty two) Considering the denominator of the spatial spectral function The method of weighting the corresponding noise eigenvector using the corrected noise eigenvalues, independent of the noise eigenvalues, is shown in equation (23): (twenty three) in , These are the corrected eigenvalues. This is a correction value; Under the premise that the information theory criterion can correctly estimate the number of information sources, the ratio of the maximum to the minimum value of the noise eigenvalue does not exceed 2, that is: (twenty four) Substituting equation (23) into equation (24) yields equation (25): (25) Then find the minimum value; The improved noise subspace is written as: (26) in, These are the feature vectors of the original noise subspace. The corrected noise characteristic value is then obtained. : (27) The final spatial spectral function is: (28) in, ; A spectral peak search is performed on the new spatial spectral function to obtain the target's azimuth estimation result.

[0006] An electronic device includes a processor and a memory; the memory stores a computer program, and the processor executes the computer program stored in the memory to enable the electronic device to perform the aforementioned high-resolution azimuth estimation method.

[0007] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described high-resolution azimuth estimation method.

[0008] A chip includes a processor for retrieving and running a computer program from a memory, causing a device equipped with the chip to perform the aforementioned high-resolution azimuth estimation method.

[0009] A computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the above-described high-resolution azimuth estimation method.

[0010] The beneficial effects of this invention are as follows: This invention addresses the problem of poor azimuth estimation accuracy under low signal-to-noise ratio (SNR). First, a geometric model for azimuth estimation of vortex electromagnetic waves based on MIMO is established. A linear frequency modulated (LFM) signal is used to transmit vortex electromagnetic waves, which are reflected by the target to obtain an echo signal. Then, spatial smoothing techniques are used to solve the coherence problem of the echo signal, and the covariance matrix is ​​eigenvalued. Based on the spatial spectrum function of the traditional MUSIC algorithm, an eigenvalue correction method is introduced to obtain a new spatial spectrum function. Peak search is then performed on this new spatial spectrum function, enabling accurate azimuth estimation results under low SNR. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention.

[0012] Figure 2 This is the geometric model for estimating the azimuth angle of a vortex electromagnetic wave target based on MIMO used in this invention.

[0013] Figure 3 This is a schematic diagram of the smoothed echo signal.

[0014] Figure 4 These are spectral peak diagrams of azimuth estimation using different methods.

[0015] Figure 5 These are the curves showing the variation of RMSE of azimuth estimation using different methods with the number of UCA array elements.

[0016] Figure 6 These are the curves showing the variation of RMSE with the number of modes for azimuth estimation using different methods.

[0017] Figure 7 These are the RMSE curves of different azimuth estimation methods as a function of signal-to-noise ratio. Detailed Implementation The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] This invention proposes a novel eigenvalue correction strategy based on the MUSIC algorithm. The core of this method lies in applying specific weighting to the noise subspace to obtain a new spatial spectrum function. Specifically, by using the corrected noise eigenvalues ​​to weight the corresponding noise eigenvectors, the utilization rate of the information contained in the noise eigenvalues ​​is significantly improved. This allows the contribution of eigenvectors corresponding to different noise eigenvalues ​​to the spectrum function to be differentiated during the construction of the spatial spectrum function, thereby effectively improving the accuracy of azimuth estimation.

[0019] This invention proposes a high-resolution azimuth estimation method for vortex electromagnetic wave targets based on an improved MUSIC algorithm. The method significantly improves azimuth estimation accuracy under low signal-to-noise ratio (SNR) conditions through an eigenvalue correction strategy. A MIMO-based uniform circular array (UCA) geometric model is established, utilizing vortex electromagnetic waves carrying orbital angular momentum as the information carrier, and constructing the received signal matrix through modal domain sampling. Addressing the performance degradation of traditional MUSIC algorithms under coherent signal sources and low SNR conditions, an innovative method for weighted correction of noise subspace eigenvalues ​​is proposed, improving the construction of the spatial spectrum function by optimizing the utilization rate of noise eigenvalues. The proposed method exhibits superior target azimuth estimation performance compared to traditional MUSIC and FFT methods. The technical solution adopted in this invention includes the following steps: Step 1: Establish a geometric model for MIMO-based vortex electromagnetic wave target azimuth estimation: N identical isotropic array elements form a uniform circular array as the transmitting antenna, and the radius of the UCA is... , No. The azimuth angle of each array element is The circumference is located at Surface. Establish a spherical coordinate system with the center point of UCA as the origin, distance. The length of the line connecting the origin and the target, and the pitch angle. The line connecting the origin and the target The angle between the positive and negative axes, azimuth angle The line connecting the origin and the target of the UCA starts from... The angle through which the positive half-axis rotates counterclockwise is the target position. .

[0020] Step 2: A linear frequency modulated (LFM) signal is a signal whose frequency changes linearly with time. This invention uses an LFM signal as the transmitted signal. The LFM signal fed into all transmitting array elements is: (1) In the formula For time variables, The duration of the pulse. The modulation frequency of a linear frequency modulation signal. The signal center frequency. It is a matrix function, that is: (2) In order to generate OAM modal values The vortex electromagnetic waves sequentially add phase shifts to each element of the circular array. Vortex electromagnetic wave target detection involves illuminating the target with vortex electromagnetic waves of different modes. The signal transmitted by a single array element is: (3) The UCA transmits a pulse signal as follows: (4) Step 3: Then any detection point Transmission signal at location It can be written as: (5) in , , .

[0021] Under normal circumstances, the conditions are met. ,therefore (6) when When large enough, the above formula is true. The summation can be approximated as an integral. (7) in , For the first The first-order Bessel function of the first kind, denoted as the wavenumber of the signal.

[0022] Step 4: All antennas on the UCA are used to receive the echo scattered by the target. The signal received by each antenna will be multiplied by This term, the total echo signal can then be expressed as: (8) in , The radar cross section (RCS) of the target. Assuming coexistence There are 3 targets, each of which can be approximated as a point target, and the position of each target point is denoted as . The corresponding RCS is denoted as Then the total echo can be expressed as: (9) in .

[0023] When the condition is met and When the Bessel function is used, it can be approximated as follows: (10) After squaring, we get: (11) Ignoring the high-frequency oscillation term, it simplifies to: (12) Phase term of the echo signal After compensation, the echo signal can be approximated by the above equation as follows: (13) By observing the exponential term in the echo signal , Within the domain This can be understood as the angular frequency in the time domain. Therefore, exist The estimation in the domain is similar to the estimation of the time-domain angular frequency. Assume... yes The sampling rate in the domain, according to Nyquist sampling theory, is used to ensure that the estimates do not alias. , The following conditions must be met: (14) in, for The maximum frequency of the domain, for The maximum angular frequency of the domain, therefore .

[0024] Echo signals from different OAM modes are not sampled simultaneously, but since the time slots of adjacent OAM modes are known, the sampling can be adjusted by delaying the value of a specific OAM mode. The corresponding time slots are used for calibration to achieve equivalent synchronous sampling performance. Consideration is given to... Real-time echo signals calibrated under each OAM mode, for vortex echo signals in After sampling in the domain and normalizing the echo amplitude, the received signal matrix is ​​constructed as follows: (15) in The guide vector matrix for the receiving matrix. The modified echo signal vector, Indicates the corrected number The source signal of the target, The received Gaussian white noise, and (16) (17) in, The symbol represents the conjugate transpose of a matrix.

[0025] Perform covariance calculation on the received signal matrix to obtain the covariance matrix. for: (18) in, Represents the mathematical expectation. , The covariance matrix of the target source signal is represented. The noise power in the environment, for Identity matrix.

[0026] Similar to DOA estimation, the matrix The columns are independent, but the echo signals from multiple targets are completely coherent, failing to meet the uncorrelation condition of the algorithm proposed in this paper. Clearly, This leads to leakage from the signal subspace to the noise subspace, disrupting the orthogonality between the two subspaces and reducing the algorithm's resolution performance. For traditional DOA estimation, spatial smoothing techniques are used to address the signal coherence problem; however, this technique is only applicable to uniform linear arrays (ULAs), i.e., uniform spatial sampling arrays. For the proposed OAM-based direction-finding model, Uniform linear OAM mode sampling in the domain is similar to the ULA case in traditional DOA estimation. Therefore, spatial smoothing techniques are suitable for solving the signal coherence problem of the proposed model under uniform sampling.

[0027] According to smoothing theory, in the modal domain The samples were divided into 3 mixed sub-sample blocks, each sub-sample block containing A sample, such as Figure 3 As shown, then To achieve full rank in the echo signal covariance matrix, the number of samples in the sub-sample block should satisfy the following condition. This ensures the orthogonality between the signal space and the noise subspace.

[0028] The covariance matrix of the echo signal after spatial smoothing and decoherence processing is: (19) in, It is the first Subsample blocks The covariance matrix.

[0029] For covariance matrix Eigenvalue decomposition yields: (20) in, For eigenvalues, This is the corresponding feature vector.

[0030] Sort the eigenvalues ​​from largest to smallest to get: ,forward Components ,back Components Then the covariance matrix It can be broken down into: (twenty one) in and These are the signal subspace and the noise subspace, respectively.

[0031] It can be seen that the azimuth search formula of the MUSIC algorithm is: (twenty two) The MUSIC algorithm achieves high spatial resolution primarily through its use of a multi-element antenna array for signal reception. By acquiring a sufficient number of observation data samples, the algorithm asymptotically approximates the true value of the array covariance matrix. Theoretically, as the amount of received data increases, the estimation accuracy of the covariance matrix continuously improves, thereby significantly enhancing the algorithm's resolution performance.

[0032] However, when the system operates under low signal-to-noise ratio (SNR) conditions, the estimation of the covariance matrix exhibits significant bias. Particularly when dealing with adjacent signal sources with small spatial angular intervals, this estimation bias leads to severe aliasing of spatial spectral peaks. This significantly reduces the actual resolving power of the MUSIC algorithm, making it difficult to effectively distinguish between adjacent signal sources.

[0033] Considering the denominator of the spatial spectral function Regardless of the noise eigenvalues, this paper proposes a method to weight the corresponding noise eigenvectors using the corrected noise eigenvalues. The eigenvalue correction method is shown in equation (23): (twenty three) in , These are the corrected eigenvalues. This is the correction value.

[0034] The effectiveness of this method stems from the weighted processing of noise eigenvalues ​​and their corresponding eigenvectors, thereby improving the utilization efficiency of the information contained in the noise eigenvalues. When constructing the spatial spectral function, the contribution of eigenvectors corresponding to different noise eigenvalues ​​to the spectral function varies significantly, and this difference can further optimize the resolution performance of the algorithm.

[0035] In signal environments with a limited number of snapshots or a low signal-to-noise ratio, noise eigenvalues ​​often exhibit divergence. Introducing an appropriate correction factor can effectively control the degree of noise eigenvalue divergence. It is worth noting that this correction factor only affects the noise eigenvalues ​​and has no impact on the signal eigenvalues, thus ensuring the accuracy of source estimation and the stability of the algorithm.

[0036] However, correction factor The value of has a critical impact on the algorithm's performance: if If the value is too small, it cannot effectively suppress the divergence of noise eigenvalues; when When the value is zero, the algorithm performance is not improved at all; while if If the value is too large, the difference between the signal and noise feature values ​​will decrease, which will not only fail to improve resolution but may also introduce estimation bias. Therefore, it is important to choose a reasonable correction factor. The value of is crucial to ensuring optimal algorithm performance.

[0037] Under the premise that the information theory criterion can correctly estimate the number of information sources, the ratio of the maximum to the minimum value of the noise eigenvalue does not exceed 2, that is: (twenty four) Substituting equation (23) into equation (24) yields equation (25): (25) Then, the minimum value of the above inequality can be obtained. value.

[0038] The improved noise subspace can be written as: (26) in, These are the feature vectors of the original noise subspace. This represents the corrected noise characteristic value. Furthermore, we can obtain... : (27) The final spatial spectral function is: (28) in, .

[0039] By performing a spectral peak search on the new spatial spectral function, the azimuth estimation result of the target can be obtained.

[0040] Example: This invention proposes a high-resolution azimuth estimation method for vortex electromagnetic wave targets based on an improved MUSIC algorithm. The method significantly improves azimuth estimation accuracy under low signal-to-noise ratio (SNR) conditions through an eigenvalue correction strategy. A MIMO-based uniform circular array (UCA) geometric model is established, utilizing vortex electromagnetic waves carrying orbital angular momentum as the information carrier, and constructing the received signal matrix through modal domain sampling. Addressing the performance degradation of traditional MUSIC algorithms under coherent signal sources and low SNR conditions, an innovative method for weighted correction of noise subspace eigenvalues ​​is proposed, improving the construction of the spatial spectrum function by optimizing the utilization rate of noise eigenvalues. The proposed method exhibits superior target azimuth estimation performance compared to traditional MUSIC and FFT methods. The invention is further illustrated below with reference to accompanying drawings and examples. These examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0041] like Figure 1 As shown, this invention provides a method for high-resolution estimation of target azimuth using vortex electromagnetic waves, comprising the following specific steps: Step 1: Set initialization parameters. For example... Figure 2 The geometric model for azimuth estimation of vortex electromagnetic wave targets based on MIMO is presented in this scheme. The number of elements in the uniform circular MIMO array is selected as [value missing]. The center frequency of the signal used to transmit vortex electromagnetic waves using a linear frequency modulated signal is selected as . Two target azimuth angles were selected as follows: , .

[0042] Step 2: Obtain the echo signal based on the established signal model. UCA transmits vortex electromagnetic waves using a linear frequency modulated signal. As shown in equation (4). The total echo signal received after reflection from the target. As shown in equation (13).

[0043] Step 3: Sample and receive the echo signal, and obtain the covariance matrix. For the echo signal... exist The domain is sampled and received, and the echo amplitude is normalized to construct the received signal matrix. As shown in equation (15). Then, the received signal matrix... Perform covariance calculations to obtain the covariance matrix. As shown in equation (18).

[0044] Step 4: Use spatial smoothing techniques to solve the echo signal coherence problem and perform eigenvalue decomposition of the covariance matrix. A schematic diagram of the spatial smoothing operation is shown below. Figure 3 As shown, after spatial smoothing operation using equation (19), the echo signal coherence problem is solved, and a new echo signal covariance matrix is ​​obtained. The covariance matrix of the echo signal is decomposed using equation (20), and the decomposition result is shown in equation (21).

[0045] Step 5: Based on the spatial spectrum function of the traditional MUSIC algorithm, an eigenvalue correction method is introduced to obtain a new spatial spectrum function. The spatial spectrum function of the traditional MUSIC algorithm is shown in equation (22). Noise eigenvalue correction is performed using equations (23) and (25) to obtain a new noise subspace. Substituting equation (27) into equation (22) yields a new spatial spectrum function, as shown in equation (28).

[0046] Step 6: Perform a spectral peak search for the new spatial spectral function to obtain the azimuth estimate. After obtaining equation (28), it can be used to perform an azimuth matching search on each estimated steering vector at predefined grid points, and the point with the largest peak value is the azimuth estimate.

[0047] Figure 3 This is a schematic diagram of spatial smoothing of the echo signal. The spatial smoothing technique solves the echo signal coherence problem of the proposed model.

[0048] Figure 4 The azimuth estimation results obtained based on the set model and parameters show that the estimation performance of the method of the present invention is superior.

[0049] Figure 5 The experiment of this invention selects the number of OAM modes. The diagram shows the azimuth estimation error curves under different numbers of UCA array elements. It can be seen that the method of this invention has better azimuth estimation performance under the same number of UCA array elements.

[0050] Figure 6 This is the azimuth estimation error curve for the present invention with a signal-to-noise ratio of 15dB and the number of OAM modes. It can be seen that, for the same number of OAM modes, the method of the present invention has better azimuth estimation performance.

[0051] Figure 7The experiment of this invention selects the number of OAM modes. The error curves for azimuth estimation are shown at different signal-to-noise ratios. It can be seen that the method of this invention has better azimuth estimation performance at the same signal-to-noise ratio.

[0052] In summary, when using vortex electromagnetic waves for target azimuth estimation, the traditional MUSIC algorithm suffers from performance degradation under conditions of coherent signal sources and low signal-to-noise ratio. This invention improves the construction of the spatial spectrum function by optimizing the utilization rate of noise eigenvalues, thereby achieving better azimuth estimation accuracy.

Claims

1. A high-resolution estimation method for the azimuth angle of vortex electromagnetic waves, characterized in that, Includes the following steps: Step 1: Establish a geometric model for estimating the azimuth angle of a vortex electromagnetic wave target based on MIMO; N identical isotropic array elements form a uniform circular array as a transmitting antenna, and the radius of the UCA is... , No. The azimuth angle of each array element is The circumference is located at noodle; Establish a spherical coordinate system with the center point of UCA as the origin, and the distance... The length of the line connecting the origin and the target, and the pitch angle. The line connecting the origin and the target The angle between the positive and negative axes, azimuth angle The line connecting the origin and the target of the UCA starts from... The angle through which the positive half-axis rotates counterclockwise is the target position. ; Step 2: Use a linear frequency modulated (LFM) signal as the transmission signal. The LFM signal fed into all transmitting array elements is: (1) In the formula For time variables, The duration of the pulse. The modulation frequency of a linear frequency modulation signal. The center frequency of the signal. It is a matrix function, that is: （2） In order to generate OAM modal values The vortex electromagnetic waves sequentially add phase shifts to each element of the circular array. Vortex electromagnetic wave target detection involves illuminating the target to be observed with vortex electromagnetic waves that traverse different modes. The signal transmitted by a single array element is: (3) The UCA transmits a pulse signal as follows: (4) Step 3: Any detection point Transmission signal at location Written as: （5） in , , ; c Indicates the speed of electromagnetic wave propagation; Meet the conditions ,therefore （6） when When large enough, equation (6) is effective for... The summation is approximately expressed as an integral: （7） in , For the first The first-order Bessel function of the first kind, The wavenumber of the signal; Step 4: All antennas on the UCA are used to receive the echo scattered by the target. The signal received by each antenna is multiplied by The total echo signal is then expressed as: (8) in , The radar cross-section (RCS) of a target; Assuming coexistence There are 3 targets, each of which is approximately a point target. The position of each target point is denoted as . The corresponding RCS is denoted as The total echo is then expressed as: (9) in ; When the condition is met and When the Bessel function is used, it undergoes the following approximate transformation: (10) After squaring, we get: （11） Ignoring the high-frequency oscillation term, it simplifies to: （12） Phase term of the echo signal After compensation, the echo signal is approximately represented by equation (12) as follows: （13） Assumption yes The sampling rate in the domain, according to Nyquist sampling theory, is used to ensure that the estimates do not alias. , The following conditions must be met: (14) in, for The maximum frequency of the domain, for The maximum angular frequency of the domain, therefore ; consider Real-time echo signals calibrated under each OAM mode, for vortex echo signals in After sampling in the domain and normalizing the echo amplitude, the received signal matrix is ​​constructed as follows: （15） in The guide vector matrix for the receiving matrix. The modified echo signal vector, Indicates the corrected number The source signal of the target, The received Gaussian white noise, and （16） （17） in, The symbol represents the matrix conjugate transpose; Perform covariance calculation on the received signal matrix to obtain the covariance matrix. for: （18） in, Represents the mathematical expectation. , The covariance matrix of the target source signal is represented. The noise power in the environment, for identity matrix; According to smoothing theory, in the modal domain The samples were divided into 3 mixed sub-sample blocks, each sub-sample block containing For each sample, then To achieve full rank in the echo signal covariance matrix, the number of samples in the sub-sample block should satisfy the following condition. This ensures the orthogonality between the signal space and the noise subspace; The covariance matrix of the echo signal after spatial smoothing and decoherence processing is: （19） in, It is the first Subsample blocks The covariance matrix; For covariance matrix Eigenvalue decomposition yields: （20） in, For eigenvalues, The corresponding feature vector; Sort the eigenvalues ​​from largest to smallest to get: ,forward Components ,back Components Then the covariance matrix It can be broken down into: （21） in and These are the signal subspace and the noise subspace, respectively. The azimuth search formula for the MUSIC algorithm is: （22） Considering the denominator of the spatial spectral function The method of weighting the corresponding noise eigenvector using the corrected noise eigenvalues, independent of the noise eigenvalues, is shown in equation (23): （23） in , These are the corrected eigenvalues. This is a correction value; Under the premise that the information theory criterion can correctly estimate the number of information sources, the ratio of the maximum to the minimum value of the noise eigenvalue does not exceed 2, that is: （24） Substituting equation (23) into equation (24) yields equation (25): （25） Then find the minimum value; The improved noise subspace is written as: （26） in, These are the feature vectors of the original noise subspace. The corrected noise characteristic value is then obtained. : (27) The final spatial spectral function is: (28) in, ; A spectral peak search is performed on the new spatial spectral function to obtain the target's azimuth estimation result.

2. An electronic device, characterized in that, include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the electronic device to perform the method as described in claim 1.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in claim 1.

4. A chip, characterized in that, include: A processor for retrieving and running a computer program from memory, causing a device on which the chip is mounted to perform the method as described in claim 1.

5. A computer program product, characterized in that, The computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the method as described in claim 1.

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