A three-dimensional imaging method of whirling electromagnetic wave based on uniform symmetrical concentric circular array

Abstract

The application provides a vortex electromagnetic wave three-dimensional imaging method based on a uniform symmetrical concentric circular array, and specifically comprises the following steps: S1, constructing a uniform concentric circular antenna array to obtain distance and azimuth angle information of a radar target in a spherical coordinate system; S2, obtaining azimuth and elevation angle information of the radar target in the spherical coordinate system; S3, constructing a uniform concentric circular antenna array-average linear antenna array hybrid array, and then optimizing the uniform concentric circular antenna array into a uniform symmetrical concentric circular antenna array; adopting a backward projection algorithm, distance and azimuth information [x, y] of the radar target in a rectangular coordinate system is obtained; and S4, performing correlation processing on the obtained two-dimensional imaging result of the radar target to obtain accurate three-dimensional imaging result of the target. The array elements can form a uniform linear array for observing the radar target in space, the array structure of the uniform symmetrical concentric circular array is further optimized by combining the characteristics of the backward projection algorithm, and the antenna complexity and the total number of array elements are effectively reduced.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional imaging technology, and specifically to a vortex electromagnetic wave three-dimensional imaging method based on a uniform symmetrical concentric ring array. Background Technology

[0002] Vortex electromagnetic waves can alter the phase distribution of electromagnetic waves on the same plane in space by carrying different orbital angular momentum. According to classical electrodynamics, different orbital angular momentum are called modal values. Different modes satisfy an orthogonality relationship, that is, an orthogonal Hilbert space is formed in the modal domain. This provides a new degree of freedom for radar target detection, thus enabling the detection of stationary targets and achieving two-dimensional imaging of targets.

[0003] The ability of plane wave electromagnetic waves to image targets on radar mainly depends on the synthetic aperture formed by the relative motion between the radar and the target, or the actual aperture formed by the radar's antenna array. If the target is stationary relative to the radar, two-dimensional imaging of the stationary target needs to be achieved using the actual aperture of the radar antenna array. Multiple-input multiple-output (MIMO) radar is a typical example of this. MIMO radar transmits multiple mutually orthogonal signals through different transmitting elements and multiple receiving units with signal sorting capabilities, forming multiple completely different virtual channels in space. This gives the radar system a much larger number of virtual elements than the physical array elements, effectively reducing the complexity of the radar system's antenna array while achieving the goal of imaging the radar target. To achieve three-dimensional imaging of the target using the actual antenna aperture, the antenna array surface can be designed and the spatial positions of the array elements optimized to form an antenna aperture with orthogonal relationship to the radar target observation. The difference in observation angles of different apertures can then be used to achieve three-dimensional imaging of the stationary target. However, this method has problems with the correlation of scattering points under different observation angles and the optimization of antenna array elements. Moving a linear array in the height dimension can also create multi-view observations of stationary targets. By utilizing the phase difference of the echo signals received in different height dimensions, three-dimensional imaging of stationary targets can be achieved. However, this method suffers from poor real-time performance.

[0004] Real-aperture radar suffers from problems such as high antenna array complexity and poor real-time imaging performance in 3D imaging of stationary targets. Unlike planar electromagnetic waves, vortex electromagnetic waves exhibit spatial phase distribution variations. Fast Fourier Transform (FFT) can be used to process the echo signals from stationary targets, thereby obtaining 2D imaging results. Most high-resolution 3D imaging methods are based on concentric uniform ring arrays and use Fourier Transform to process the echo signals. In fact, under the same concentric uniform ring array conditions, spatial spectrum estimation methods offer superior azimuth and elevation resolution compared to Fourier Transform-based imaging methods. Among these, Multiple Signal Classification (MUSIC) is a classic spatial spectrum estimation algorithm. It can construct a linear array by optimizing the element distribution of the concentric ring array to form a real-aperture observation of the target, and combine it with vortex electromagnetic wave 2D imaging methods to achieve real-time 3D imaging of the target. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a three-dimensional imaging method for vortex electromagnetic waves based on a uniform symmetrical concentric ring array, specifically including the following steps:

[0006] S1 Constructs a uniform concentric circular ring antenna array. For the echo signal received by the uniform concentric circular ring antenna array, a two-dimensional imaging method based on Fourier transform vortex electromagnetic waves is used to obtain the range and azimuth information of the radar target in a spherical coordinate system. ;

[0007] S2. Then, for the echo signal received by the uniform concentric ring antenna array, a fast two-dimensional imaging method based on minimum mode vortex electromagnetic waves with real-valued processing is used to obtain the azimuth and elevation angle information of the radar target in the spherical coordinate system. ;

[0008] S3 constructs a hybrid array of uniform concentric ring antenna array and uniform linear antenna array. This hybrid array is then optimized into a uniform symmetrical concentric ring antenna array. Based on the mode values ​​carried by the vortex electromagnetic waves, phase compensation is performed on the array elements distributed along the negative X-axis in the uniform symmetrical concentric ring antenna array. Finally, a back projection algorithm is used to obtain the range and azimuth information of the radar target in a Cartesian coordinate system. ;

[0009] S4 performs correlation processing on the obtained two-dimensional imaging results of the radar target, reconstructs the three-dimensional imaging results of the target in the rectangular coordinate system using coordinate system transformation relationships, and filters out false scattering points in the reconstructed three-dimensional imaging results according to the resolution in the rectangular coordinate system to obtain accurate three-dimensional imaging results of the target.

[0010] Furthermore, S1 specifically includes:

[0011] S11 Construct a uniform concentric circular ring antenna array. Let the mathematical model for estimating the direction of arrival be expressed as: (1)

[0012] in, The signal data vector received by a uniform concentric circular ring antenna array. For spatial array manifold vectors, It is a spatial signal vector. For a uniform concentric circular ring antenna array noise data vector, Indicated as fast time, express The pitch angle of the point;

[0013] S12 Considering the complexity of the uniform concentric ring antenna array in the observation model, a single-transmitter, multiple-receiver observation model based on the uniform concentric ring antenna array is adopted. The transmitting element is an independent omnidirectional antenna located at the origin of the coordinate system. The receiving unit is a uniform concentric circular ring antenna array, and the center of the array is also located at the origin of the coordinate system. The receiving unit array consists of The array consists of n identical antenna elements, and the nth element is denoted as . The radius of the circular array is b;

[0014] set up Let be any scattering point in space, where, express Point to the center of the circular array Distance between points express The pitch angle of the point, express The azimuth angle of the point is the angle received by the uniform concentric circular ring antenna array. The normalized echo signal of a point is represented as: (2)

[0015] in, The radar cross section of the scattering point. Modal values, Represented as wave number, For a Bessel function of the first kind, In order to transmit signals, This is a noise signal;

[0016] S13 Assume the radar target is... Composed of 5 ideal scattering points, the radar target echo signal is expressed as:

[0017] (3)

[0018] in, , , The first The distance, azimuth, and elevation angles of each scattering point in spherical coordinates. For the first Radar scattering cross section of each scattering point;

[0019] Analyzing the radar target echo signal represented by equation (3), it can be seen that the exponential terms contained in the radar target echo signal are respectively and The radar target range can be seen from the exponential term. With the frequency of the transmitted signal Radar target azimuth angle Modal values ​​of vortex electromagnetic waves They are in a dual relationship, and the radar target range and azimuth information are obtained by using two-dimensional Fourier transform on the radar target echo signal.

[0020] Furthermore, S2 specifically includes:

[0021] S21 treats each scattering point of the radar target as an independent radiation source and uses the MUSIC algorithm to estimate the arrival parameters of the equivalent radiation sources in order to obtain radar target information on the target elevation and azimuth angles.

[0022] According to equation (1), let the vortex electromagnetic wave mode value The range of values ​​is Then equation (2) can be further expressed as:

[0023] (4)

[0024] in, , As the guide vector, For the echo signal vector, the first... The steering vector and echo vector corresponding to each signal are respectively and , This represents the number of sampling points for the echo signal;

[0025] S22 According to the MUSIC algorithm, the covariance matrix of the target signal received by the uniform concentric ring antenna array needs to be obtained; assuming the noise interference is Gaussian white noise, different mode values The covariance matrix of the target signal is expressed as:

[0026] (5)

[0027] in, Let be the covariance matrix of the signal. For noise energy, The identity matrix; typically, the target signal received by a uniform concentric circular ring antenna array is complex, and considering the actual length of the received signal, the covariance matrix is... Represented as:

[0028] (6)

[0029] in, The target signal received by the uniform concentric circular ring antenna array; through the analysis of equation (6), and Considered as the two basic elements storing target spatial information, according to equation (6), the real part and the imaginary part of the covariance matrix of the target signal are respectively expressed as: (7)

[0030] (8)

[0031] As can be seen from equations (7) and (8), the real or imaginary part of the covariance matrix of the echo signal completely contains the spatial information of the target; therefore, processing the real or imaginary part of the covariance matrix alone can obtain the spatial information of the target, and the target azimuth and elevation angle information can be obtained by performing a two-dimensional spatial peak search. The search process is expressed as follows:

[0032] (9)

[0033] (10)

[0034] in, for or The noise subspace eigenvector matrix obtained by eigenvalue decomposition. The guiding vector of the signal subspace;

[0035] S23 When the number of radar target scattering points is unknown, the problem of unknown target scattering points is solved by using the minimum modulus algorithm weighted MUSIC algorithm, a generalized form of the MUSIC algorithm. When using the minimum modulus algorithm weighted MUSIC algorithm, equation (9) is expressed as:

[0036] (11)

[0037] in, , For noise subspace The first line, For noise subspace remove The rest If so, the spatial spectrum estimation formula based on the minimum modulus algorithm weighted MUSIC algorithm is expressed as:

[0038] (12).

[0039] Furthermore, S3 specifically includes:

[0040] S31 Constructs a hybrid array of uniform concentric circular ring antenna array and uniform linear antenna array. Both the uniform concentric circular ring antenna array and the uniform linear antenna array serve as receiving elements. The uniform concentric circular ring antenna array consists of... A uniform linear antenna array consists of M antenna elements uniformly distributed on a ring of diameter b. On the straight line, the transmitting element is an omnidirectional antenna located at the origin of the coordinate system. Analysis of the complexity of the hybrid array of uniform concentric ring antenna array and uniform linear antenna array shows that the total length of the antenna array in the hybrid array is... The total number of antenna array elements in the hybrid array of uniform concentric ring antenna array and uniform linear antenna array is: By performing a two-dimensional Fourier transform on the echo signal received by a uniform linear antenna array, a two-dimensional imaging result of the target in a Cartesian coordinate system with respect to range and azimuth can be obtained. Furthermore, the azimuth resolution is related to the length of the linear array. Proportional, its resolution is expressed as:

[0041] (13)

[0042] in, The wavelength of the transmitted signal, The center position of the target area in the azimuth dimension;

[0043] For the echo signal received by a uniform concentric circular ring antenna array, Fourier transform is used to obtain the target azimuth image in spherical coordinates. The target azimuth resolution obtained based on the Fourier transform algorithm is expressed as:

[0044] (14)

[0045] Analysis of equation (14) shows that the target azimuth resolution is proportional to the number of observed modes, while the number of vortex electromagnetic wave modes that a uniform concentric ring antenna array can generate depends on the total number of antenna array elements. That is, the azimuth resolution is proportional to the total number of elements of the uniform concentric ring antenna array. Considering that the imaging results of the two vortex electromagnetic wave imaging methods need to be correlated with scattering points in the future, the azimuth resolution of the two vortex electromagnetic wave imaging methods needs to be kept consistent. It is necessary to increase the number of elements of the uniform concentric ring antenna array to improve the azimuth resolution. In order to improve the imaging resolution in the azimuth dimension, the total number of elements and complexity of the hybrid array of uniform concentric ring antenna array and uniform linear antenna array will increase sharply, thereby affecting the signal processing efficiency based on the hybrid array of uniform concentric ring antenna array and uniform linear antenna array.

[0046] S32 Analysis of the amplitude spatial distribution of vortex electromagnetic waves shows that the main lobe illumination direction of vortex electromagnetic waves is also affected by the mode value, which in turn affects the number of target observation modes. In order to further improve the azimuth resolution, a uniform concentric ring antenna array is used to increase the number of observation modes.

[0047] A uniform concentric ring antenna array is an antenna array composed of multiple ring arrays with different radii centered at a fixed point. The antenna array generates a large number of modes of vortex electromagnetic waves with a fixed main lobe illumination direction by optimizing transmission resources. The hybrid array of uniform concentric ring antenna array and uniform linear antenna array is improved into a hybrid antenna array of concentric ring antenna array and uniform linear antenna array to obtain a higher azimuth resolution. The complexity of the hybrid antenna array of concentric ring antenna array and uniform linear antenna array increases significantly. In order to reduce the complexity of the hybrid antenna array of concentric ring antenna array and uniform linear antenna array, a uniform symmetrical concentric ring antenna array for vortex electromagnetic wave three-dimensional imaging is adopted on the basis of the hybrid antenna array of concentric ring antenna array and uniform linear antenna array. The array elements on each ring antenna array in the hybrid antenna array must satisfy uniform symmetrical distribution, and there must be two array elements symmetrical about the origin O on the X-axis.

[0048] S33 Analysis of the uniformly symmetrical concentric ring antenna array shows that the uniformly symmetrical concentric ring antenna array is composed of It consists of a uniformly symmetrical concentric circular ring antenna array with the same center but different radii. The number of array elements in each uniformly symmetrical concentric circular ring antenna array is: ,in ,and For an even number of uniform, symmetrical, concentric circular ring antenna arrays, the spacing between each array should satisfy the following:

[0049] (15)

[0050] in, The interval between each ring, Let M be the minimum interval between the rings, and M be any positive integer; since the elements of each uniformly symmetrical concentric ring antenna array satisfy a symmetrical and uniform distribution, then the first element and the second element of each uniformly symmetrical concentric ring antenna array... Each element should be located in On the axis, in the A uniform, symmetrical, concentric circular ring antenna array composed of several rings has Individual elements The array elements are linearly distributed along the axis; the receiving array elements located on the X-axis and the elements located at the origin of the coordinate system... The transmitting elements form a linearly distributed transmit / receive antenna array. A linear antenna array satisfying linear distribution is constructed from a uniformly symmetrical concentric ring array. The complexity of the uniformly symmetrical concentric ring antenna array is then analyzed. Under the condition of the same azimuth resolution, the total length of the uniformly symmetrical concentric ring antenna array is... , Let be the maximum radius of the uniformly symmetrical concentric circular ring antenna array, and let be the length of the hybrid antenna array of uniformly concentric circular ring antenna array and uniformly linear antenna array. The total number of elements in a uniformly symmetrical concentric circular ring antenna array is The total number of elements in a hybrid antenna array of uniform concentric ring antenna array and uniform linear antenna array is the minimum. Compared to a hybrid antenna array consisting of a uniform concentric ring antenna array and a uniform linear antenna array, a uniform symmetrical concentric ring antenna array has a shorter length. The total number of array elements will be reduced by at least ;

[0051] S34 It is known that in the direction of illumination of the main lobe of the vortex electromagnetic wave Represented as:

[0052] (16)

[0053] in, The direction of the main lobe illumination of the vortex electromagnetic wave, and the modal values. , wave number and the radius of the circular array ;

[0054] According to equation (16), by scheduling circular arrays of different diameters, vortex electromagnetic waves of different mode values ​​can be received in a time-division manner. The echo received by a uniformly symmetrical concentric circular array antenna is expressed as:

[0055] (18)

[0056] Unlike vortex electromagnetic wave imaging methods based on Fourier transform, the echo signal Bessel function in the amplitude term Since b is no longer a constant, the target distance and azimuth information can still be obtained by using the vortex electromagnetic wave two-dimensional imaging method based on Fourier transform.

[0057] S35 employs the minimum-mode vortex electromagnetic wave two-dimensional imaging method based on real-valued processing to process the echo signal received by a uniformly symmetrical concentric circular ring antenna array. The echo signal received by the uniformly symmetrical concentric circular ring antenna array is then expressed as:

[0058] (19)

[0059] in, Unlike equation (4), the guiding vector in equation (19) middle The diameter b of the uniform symmetrical concentric ring antenna array is no longer a constant. When using the spatial average sliding algorithm to divide the signal subarray, the diameter b is used as the division standard, and the azimuth and elevation angle information of the target can still be obtained.

[0060] S36 Based on the analysis of uniformly symmetrical concentric circular ring antenna arrays, it can be seen that each uniformly symmetrical concentric circular ring antenna array has two array elements distributed on the linear antenna array, and about the origin... The signals received by two array elements symmetrically distributed on the same circular ring of diameter are 180° out of phase. Assuming the transmitted signal is a linear frequency modulated signal... The echo signal received by the array element in the positive X-axis direction is denoted as The echo signal received by the array element in the negative X-axis direction should be denoted as... Based on the modal values ​​carried by the echo signal After uniform phase compensation, the echo signal received by the array elements in the negative X-axis direction is... ;

[0061] Based on the analysis of the optimization model of equation (19), it can be seen that the linear array constructed in the uniform symmetrical concentric ring antenna array may not meet the uniform distribution. Considering the distribution characteristics of the linear array elements, the back projection algorithm is used to process the echo signal received by the linear array to realize two-dimensional imaging of the radar target.

[0062] Furthermore, the complexity is further optimized in S33:

[0063] To further optimize the complexity of the uniform symmetrical concentric ring antenna array, the total number of array elements is further optimized using a vortex electromagnetic wave transmission resource optimization method. It is known that in the direction of illumination of the main lobe of the vortex electromagnetic wave Represented as:

[0064] (16)

[0065] Analysis of equation (16) reveals that the irradiation direction of the main lobe of the vortex electromagnetic wave is... With modal values , wave number and the radius of the circular array Related, azimuth imaging resolution of uniform symmetrical concentric ring antenna array With array length Related, while the array length constructed by a uniformly symmetrical concentric circular ring antenna array is According to equation (14), the azimuth resolution obtained based on Fourier transform is... With the number of observed modes Correlation, and the number of observed modes The number of circular antenna arrays Relatedly, considering the consistency of the azimuth resolution of different imaging methods for the imaging area, the azimuth resolution of the imaging area center based on the linear distribution antenna array imaging method is shown in Equation (13), and the azimuth resolution of the vortex electromagnetic wave imaging method based on Fourier transform using the single-transmitter multi-receiver observation model is shown in Equation (14).

[0066] Let the elevation angle of the center point of the observed imaging region be... The azimuth resolution of the imaging region center based on the imaging method of uniform symmetric concentric ring antenna array The azimuth resolution of the vortex electromagnetic wave imaging method based on Fourier transform, employing a single-transmitter, multiple-receiver observation model, is [value missing]. Then, for a uniformly symmetrical concentric ring antenna array, the total number of array elements is... The optimization model is expressed as:

[0067] (17)

[0068] in, Let be the diameter of the i-th circular antenna array. To obtain the total number of modes for the i-th circular ring antenna array, equation (17) is the total number of array elements of a uniformly symmetrical concentric circular ring antenna array. To optimize the target.

[0069] Furthermore, the backward projection algorithm in S36 is specifically as follows:

[0070] S361 uses the nearest distance as a reference point to cluster the compressed echo data, divides the imaging scene into a network to obtain the coordinates of all network points, starting from the azimuth starting point;

[0071] S362 calculates the distances between the radar and all grid points in the current azimuth direction and calculates the delay time of all grid points relative to the nearest reference point. ;

[0072] S363 utilizes the delay time of each grid point The corresponding echo value is calculated by interpolation and then superimposed with the echo value of the previous direction to that grid point.

[0073] S364 Check if all grid points have been traversed. If so, proceed to S365; otherwise, proceed to S363 to find the next grid point.

[0074] S365 Check if all directions have been traversed. If so, proceed to S366. Otherwise, proceed to S362 to find the next direction.

[0075] S366 obtains the image of the imaging scene area.

[0076] Furthermore, S4 specifically includes:

[0077] By utilizing coordinate system transformation relationships to reconstruct the three-dimensional imaging results of the target in the rectangular coordinate system, spatial information of the radar target in the spherical coordinate system obtained by different imaging methods on the echo signals received by a uniformly symmetrical concentric circular ring antenna array is presented. and , by azimuth Correlate the scattering points to obtain the target's three-dimensional spatial information in spherical coordinates. In azimuth angle When associating scattering points, for the same azimuth angle Multiple false scattering points will appear at the scattering point; a back projection algorithm is used for a uniform symmetrical concentric ring antenna array to obtain the range and azimuth information of the radar target in a rectangular coordinate system. Using the conversion formula between spherical coordinates and rectangular coordinates, the target spherical coordinate information is converted... Convert to rectangular coordinate information The formula for converting between spherical coordinates and rectangular coordinates is given as follows:

[0078] (20)

[0079] Then, the range and azimuth information in the radar Cartesian coordinate system are obtained through a back projection algorithm. As prior information, the determination is specifically represented as follows:

[0080] (twenty one)

[0081] (twenty two)

[0082] in, The threshold for judgment is defined as the distance resolution in the distance dimension and the azimuth resolution in the azimuth dimension; this threshold is used for the transformed target Cartesian coordinate information. Simultaneously, scattering points that do not satisfy equations (21) and (22) are eliminated, and finally, the three-dimensional imaging result of the target is obtained. .

[0083] The advantages of this invention are as follows: a uniform symmetrical concentric ring array, which enables the array elements to form a uniform linear array for radar target observation in space. The array structure of the uniform symmetrical concentric ring array is further optimized by utilizing the characteristics of the back projection algorithm, which effectively reduces the antenna complexity and the total number of array elements. Attached Figure Description

[0084] Figure 1 A geometric schematic diagram of a single-transmitter multiple-receiver observation model based on a uniform circular array is shown.

[0085] Figure 2 A geometric schematic diagram of the UCA-ULA hybrid array model is shown;

[0086] Figure 3 A geometric schematic diagram of a uniform symmetrical concentric circular ring antenna array is shown.

[0087] Figure 4 A geometric schematic diagram of the observation model based on a uniform symmetrical concentric ring array is shown.

[0088] Figure 5 The steps of the backward projection algorithm are shown;

[0089] Figure 6(a) shows the target scattering point model, Figure 6(b) shows the two-dimensional imaging result when the virtual array elements are uniformly distributed, Figure 6(c) shows the imaging result when 22 virtual array elements are lost consecutively, Figure 6(d) shows the imaging result when 22 virtual array elements are lost in 5 blocky regions and the blocky regions are sparsely distributed, and Figure 6(e) shows the imaging result when 22 virtual array elements are lost randomly.

[0090] Figure 7 A flowchart of a vortex electromagnetic wave three-dimensional imaging method based on a uniform symmetrical concentric ring array is shown.

[0091] Figure 8(a) shows the imaging results based on Fourier transform, displaying the two-dimensional imaging results of the target in the spherical coordinate system with respect to range and azimuth; Figure 8(b) shows the imaging results based on the RV-MVM algorithm, displaying the two-dimensional imaging results of the target in the spherical coordinate system with respect to azimuth and pitch; Figure 8(c) shows the imaging results based on the back projection algorithm, displaying the two-dimensional imaging results of the target in the rectangular coordinate system with respect to range and azimuth.

[0092] Figure 9 The image shows the 3D imaging result after correlation processing;

[0093] Figure 10 The image shows a two-dimensional projection of the associated reconstructed scattering points in a Cartesian coordinate system;

[0094] Figure 11 The image shows the imaging results of the vortex electromagnetic wave three-dimensional imaging method based on a uniform symmetrical concentric ring array. Detailed Implementation

[0095] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0096] A three-dimensional imaging method for vortex electromagnetic waves based on a uniform symmetrical concentric ring array specifically includes the following steps:

[0097] S1 Constructs a uniform concentric circular ring antenna array. For the echo signal received by the uniform concentric circular ring antenna array, a two-dimensional imaging method based on Fourier transform vortex electromagnetic waves is used to obtain the range and azimuth information of the radar target in a spherical coordinate system. ;

[0098] S2. Then, for the echo signal received by the uniform concentric ring antenna array, a fast two-dimensional imaging method based on minimum mode vortex electromagnetic waves with real-valued processing is used to obtain the azimuth and elevation angle information of the radar target in the spherical coordinate system. ;

[0099] S3 constructs a hybrid array of uniform concentric ring antenna array and uniform linear antenna array. This hybrid array is then optimized into a uniform symmetrical concentric ring antenna array. Based on the mode values ​​carried by the vortex electromagnetic waves, phase compensation is performed on the array elements distributed along the negative X-axis in the uniform symmetrical concentric ring antenna array. Finally, a back projection algorithm is used to obtain the range and azimuth information of the radar target in a Cartesian coordinate system. ;

[0100] S4 performs correlation processing on the obtained two-dimensional imaging results of the radar target, reconstructs the three-dimensional imaging results of the target in the rectangular coordinate system using coordinate system transformation relationships, and filters out false scattering points in the reconstructed three-dimensional imaging results according to the resolution in the rectangular coordinate system to obtain accurate three-dimensional imaging results of the target.

[0101] S1 specifically includes:

[0102] The S11 spatial spectrum estimation algorithm uses the phase difference of the received signal caused by the positional differences of each element in the antenna array to estimate the arrival parameters of the target, such as the target elevation angle, azimuth angle, and the number of targets. The Multiple Signal Classification (MUSIC) algorithm is one of the classic spatial spectrum estimation algorithms. It processes the covariance matrix of the signal received by the antenna array. This algorithm first performs eigenvalue decomposition on the covariance matrix of the received signal to obtain the signal subspace and the noise subspace orthogonal to it. Finally, it uses the orthogonality of the two subspaces to estimate the characteristic parameters of the arrival signal.

[0103] Construct a uniform concentric circular ring antenna array, and let the mathematical model for estimating the direction of arrival be expressed as:

[0104] (1)

[0105] in, The signal data vector received by a uniform concentric circular ring antenna array. For spatial array manifold vectors, It is a spatial signal vector. For noise data vectors of a uniform concentric circular ring antenna array Indicated as fast time, express The pitch angle of the point;

[0106] S12 Considering the complexity of the uniform concentric ring antenna array in the observation model, a single-transmitter, multiple-receiver observation model based on the uniform concentric ring antenna array is adopted. The transmitting element is an independent omnidirectional antenna located at the origin of the coordinate system. The receiving unit is a uniform concentric circular ring antenna array, and the center of the array is also located at the origin of the coordinate system. The receiving unit array consists of The array consists of n identical antenna elements, and the nth element is denoted as . The radius of the annular array is b; for example Figure 1 As shown;

[0107] set up Let be any scattering point in space, where, express Point to the center of the circular array Distance between points express The pitch angle of the point, express The azimuth angle of the point is the angle received by the uniform concentric circular ring antenna array. The normalized echo signal of a point is represented as: (2)

[0108] in, The radar cross section of the scattering point. For modal number, Represented as wave number, For a Bessel function of the first kind, In order to transmit signals, This is a noise signal;

[0109] S13 Assume the radar target is... Composed of 18 ideal scattering points, the radar target echo is represented as:

[0110] (3)

[0111] in, , , The first The distance, azimuth, and elevation angles of each scattering point in spherical coordinates. For the first The radar cross section (RCS) of each scattering point;

[0112] Analyzing the radar target echo signal represented by equation (3), it can be seen that the exponential terms contained in the radar target echo signal are respectively and The radar target range can be seen from the exponential term. With the frequency of the transmitted signal Radar target azimuth angle Modal values ​​of vortex electromagnetic waves These parameters are in a dual relationship; a two-dimensional Fourier transform is used on the radar target echo signal to obtain the radar target range and azimuth information. However, the radar target elevation angle... Included in echo amplitude In some cases, the two-dimensional fast Fourier transform cannot decouple the amplitude of the echo signal, thus it cannot obtain the elevation angle information of the radar target. In other words, the Fourier transform imaging method does not have the ability to resolve elevation angles.

[0113] S2 specifically includes:

[0114] S21 treats each scattering point of the radar target as an independent radiation source and uses the MUSIC algorithm to estimate the arrival parameters of the equivalent radiation sources in order to obtain radar target information on the target elevation and azimuth angles.

[0115] According to equation (1), let the vortex electromagnetic wave mode value The range of values ​​is Then equation (2) can be further expressed as:

[0116] (4)

[0117] in, , As the guide vector, For the echo signal vector, the first... The steering vector and echo vector corresponding to each signal are respectively and , This represents the number of sampling points for the echo signal;

[0118] S22 According to the MUSIC algorithm, the covariance matrix of the target signal received by the uniform concentric ring antenna array needs to be obtained; assuming the noise interference is Gaussian white noise, different mode values The covariance matrix of the target signal is expressed as:

[0119] (5)

[0120] in, Let be the covariance matrix of the signal. For noise energy, The identity matrix; typically, the target signal received by a uniform concentric circular ring antenna array is complex, and considering the actual length of the received signal, the covariance matrix is... Represented as:

[0121] (6)

[0122] in, The target signal received by the uniform concentric circular ring antenna array; through the analysis of equation (6), and Considered as the two basic elements storing target spatial information, according to equation (6), the real part and the imaginary part of the covariance matrix of the target signal are respectively expressed as: (7)

[0123] (8)

[0124] As can be seen from equations (7) and (8), the real or imaginary part of the covariance matrix of the echo signal completely contains the spatial information of the target; therefore, processing the real or imaginary part of the covariance matrix alone can obtain the spatial information of the target, and the target azimuth and elevation angle information can be obtained by performing a two-dimensional spatial peak search. The search process is expressed as follows:

[0125] (9)

[0126] (10)

[0127] in, for or The noise subspace eigenvector matrix obtained by eigenvalue decomposition. The guiding vector of the signal subspace;

[0128] S23 When the number of radar target scattering points is unknown, the problem of unknown target scattering points is solved by using the weighted MUSIC algorithm (WMUSIC), a generalized form of the MUSIC algorithm. Using the weighted MUSIC algorithm, equation (9) is expressed as: (11)

[0129] in, , For noise subspace The first line, For noise subspace remove The rest If so, the spatial spectrum estimation formula based on the minimum modulus algorithm weighted MUSIC algorithm is expressed as:

[0130] (12)

[0131] To mitigate the impact of unknown spatial spectrum estimation computation and target number on the performance of the MUSIC algorithm, real-valued processing and minimum-mode weighted MUSIC algorithms can be employed to improve performance. Therefore, the minimum-mode vortex electromagnetic wave two-dimensional imaging algorithm (RV-MVM) based on real-valued processing can achieve high-resolution and rapid imaging of radar targets.

[0132] S3 specifically includes:

[0133] The azimuth angle of a radar target in spherical coordinates can be obtained by employing a fast two-dimensional imaging method using minimum-mode vortex electromagnetic waves based on real-valued processing. and pitch angle The vortex electromagnetic wave imaging method using Fourier transform can utilize the duality of the echo signal in the frequency domain and modal domain to decouple and obtain the radar target's range in spherical coordinates. and azimuth Therefore, using only one of the above vortex electromagnetic wave imaging methods can only obtain a two-dimensional imaging result of the radar target. Using both vortex electromagnetic wave imaging methods simultaneously, and utilizing the correlation of scattering points, a three-dimensional imaging result of the target can be obtained, but the obtained three-dimensional imaging result will contain false scattering points. To eliminate false scattering points in the three-dimensional imaging result, the two-dimensional spatial information of scattering points acquired by a uniformly linearly distributed MIMO radar can be used to remove false scattering points. The transmitting and receiving units of a MIMO radar consist of antenna arrays containing multiple elements, which are often distributed in equally spaced linear or planar arrays. Based on the principle of phase approximation center, a MIMO radar can acquire a far greater number of virtual observation channels than actual observation channels. By jointly processing the data from multiple virtual observation channels, it can be approximately equivalent to the imaging aperture for target observation. Therefore, a MIMO radar has the capability for real-time imaging of radar targets and can be applied to imaging scenarios with high real-time requirements. By combining and optimizing the design of a uniform circular ring antenna array with a MIMO antenna array, and by applying vortex electromagnetic waves to the MIMO radar, two-dimensional imaging results of the target under different systems can be obtained, and three-dimensional imaging of the target can be achieved.

[0134] S31 Constructing a hybrid array of uniform concentric circular array (UCA) and uniform linear array (ULA), such as... Figure 2 As shown. Both the uniform concentric ring antenna array and the uniform linear antenna array are receiving elements. The uniform concentric ring antenna array consists of... A uniform linear antenna array consists of M antenna elements uniformly distributed on a ring of diameter b. On the straight line, the transmitting element is an omnidirectional antenna located at the origin of the coordinate system. Analysis of the complexity of the hybrid array of uniform concentric ring antenna array and uniform linear antenna array shows that the total length of the antenna array in the hybrid array is... The total number of antenna array elements in the hybrid array of uniform concentric ring antenna array and uniform linear antenna array is: By performing a two-dimensional Fourier transform on the echo signal received by a uniform linear antenna array, a two-dimensional imaging result of the target in a Cartesian coordinate system with respect to range and azimuth can be obtained. Furthermore, the azimuth resolution is related to the length of the linear array. Proportional, its resolution is expressed as:

[0135] (13)

[0136] in, The wavelength of the transmitted signal, The center position of the target area in the azimuth dimension;

[0137] For the echo signal received by a uniform concentric circular ring antenna array, Fourier transform is used to obtain the target azimuth image in spherical coordinates. The target azimuth resolution obtained based on the Fourier transform algorithm is expressed as:

[0138] (14)

[0139] Analysis of equation (14) shows that the target azimuth resolution is proportional to the number of observed modes, while the number of vortex electromagnetic wave modes that a uniform concentric ring antenna array can generate depends on the total number of antenna array elements. That is, the azimuth resolution is proportional to the total number of array elements of the uniform concentric ring antenna array. Although the RV-MVM algorithm can obtain a higher target azimuth resolution than the Fourier transform within the same number of modes, considering that the imaging results of the two vortex electromagnetic wave imaging methods need to be correlated with scattering points in the future, the azimuth resolution of the two vortex electromagnetic wave imaging methods needs to be kept consistent. It is necessary to increase the number of array elements of the uniform concentric ring antenna array to improve the azimuth resolution. In order to improve the imaging resolution in the azimuth dimension, the total number of array elements and complexity of the uniform concentric ring antenna array-uniform linear antenna array hybrid array (UCA-ULA) will increase sharply, thereby affecting the signal processing efficiency based on the uniform concentric ring antenna array-uniform linear antenna array hybrid array.

[0140] S32 Analysis of the amplitude spatial distribution of vortex electromagnetic waves shows that the main lobe illumination direction of vortex electromagnetic waves is also affected by the mode value, which in turn affects the number of target observation modes. In order to further improve the azimuth resolution, a concentric circular ring antenna array is used to increase the number of observation modes.

[0141] A concentric circular array (CCA) is an antenna array composed of multiple circular arrays of different radii centered at a fixed point. This antenna array generates a large number of modes of vortex electromagnetic waves with a fixed main lobe illumination direction by optimizing transmission resources. The UCA-ULA is improved into a hybrid antenna array of concentric circular array and uniform linear array (CCA-ULA) to obtain higher azimuth resolution. However, the complexity of this hybrid antenna array increases significantly. To reduce the complexity of the hybrid antenna array, a uniform symmetrical concentric circular array for vortex electromagnetic wave three-dimensional imaging is adopted based on the hybrid antenna array. The array elements on each circular array in this hybrid antenna array must satisfy a uniform symmetrical distribution, and there must exist two array elements symmetrical about the origin O on the X-axis.

[0142] S33 Analysis of the uniformly symmetrical concentric ring antenna array shows that the uniformly symmetrical concentric ring antenna array is composed of It consists of a uniformly symmetrical concentric circular ring antenna array with the same center but different radii. The number of array elements in each uniformly symmetrical concentric circular ring antenna array is: ,in ,and For an even number of uniform, symmetrical, concentric circular ring antenna arrays, the spacing between each array should satisfy the following:

[0143] (15)

[0144] in, The interval between each ring, Let M be the minimum interval between the rings, and M be any positive integer; since the elements of each uniformly symmetrical concentric ring antenna array satisfy a symmetrical and uniform distribution, then the first element and the second element of each uniformly symmetrical concentric ring antenna array... Each element should be located in On the axis, in the A uniform, symmetrical, concentric circular ring antenna array composed of several rings has Individual elements The array elements are linearly distributed along the axis; the receiving array elements located on the X-axis and the elements located at the origin of the coordinate system... The transmitting elements form a linearly distributed transmit / receive antenna array. A linear antenna array satisfying linear distribution is constructed from a uniformly symmetrical concentric ring array. The complexity of the uniformly symmetrical concentric ring antenna array is then analyzed. Under the condition of the same azimuth resolution, the total length of the uniformly symmetrical concentric ring antenna array is... , Let be the maximum radius of the uniformly symmetrical concentric circular ring antenna array, and let be the length of the hybrid antenna array of uniformly concentric circular ring antenna array and uniformly linear antenna array. The total number of elements in a uniformly symmetrical concentric circular ring antenna array is The total number of elements in a hybrid antenna array of uniform concentric ring antenna array and uniform linear antenna array is the minimum. Compared to a hybrid antenna array consisting of a uniform concentric ring antenna array and a uniform linear antenna array, a uniform symmetrical concentric ring antenna array has a shorter length. The total number of array elements will be reduced by at least ;

[0145] To further optimize the complexity of the uniform symmetrical concentric ring antenna array, the total number of array elements in the uniform symmetrical concentric ring array is further optimized using the vortex electromagnetic wave transmission resource optimization method. ,

[0146] S34 It is known that in the direction of illumination of the main lobe of the vortex electromagnetic wave Represented as:

[0147] (16)

[0148] Analysis of equation (16) reveals that the irradiation direction of the main lobe of the vortex electromagnetic wave is... With modal values , wave number and the radius of the circular array Related, azimuth imaging resolution of uniform symmetrical concentric ring antenna array With array length Related, while the array length constructed by a uniformly symmetrical concentric circular ring antenna array is According to equation (14), the azimuth resolution obtained based on Fourier transform is... With the number of observed modes Correlation, and the number of observed modes The number of circular antenna arrays Relatedly, considering the consistency of the azimuth resolution of different imaging methods for the imaging area, the azimuth resolution of the imaging area center based on the linear distribution antenna array imaging method is shown in Equation (13), and the azimuth resolution of the vortex electromagnetic wave imaging method based on Fourier transform using the single-transmitter multi-receiver observation model is shown in Equation (14).

[0149] Let the elevation angle of the center point of the observed imaging region be... The azimuth resolution of the imaging region center based on the imaging method of uniform symmetric concentric ring antenna array The azimuth resolution of the vortex electromagnetic wave imaging method based on Fourier transform, employing a single-transmitter, multiple-receiver observation model, is [value missing]. Then, for a uniformly symmetrical concentric ring antenna array, the total number of array elements is... The optimization model is expressed as:

[0150] (17)

[0151] in, Let be the diameter of the i-th circular antenna array. To obtain the total number of modes for the i-th circular ring antenna array, equation (17) is the total number of array elements of a uniformly symmetrical concentric circular ring antenna array. To optimize the target, the linear array formed by the multiplexed elements in the designed uniformly symmetrical concentric circular ring antenna array on the X-axis may not satisfy the requirement of uniform distribution. If imaging methods based on Fourier transform or sparse regularization are still used to image the echo signals received by the non-uniformly distributed linear array, the resolution of the imaging results will be affected. Therefore, considering the non-uniform distribution of the linear array elements, a back projection algorithm is used to process the echo signals received by the non-uniformly distributed linear antenna array, avoiding a decrease in the resolution of the range-azimuth two-dimensional imaging results of the target.

[0152] The uniform, symmetrical, concentric ring array described above observes radar targets, and its observation model is as follows: Figure 4 As shown, considering the fixed illumination direction of the main lobe of the vortex electromagnetic wave; according to equation (16), it can be seen that by scheduling circular arrays of different diameters, vortex electromagnetic waves of different mode values ​​can be received in a time-division manner. The echo received by the uniformly symmetrical concentric circular array antenna is expressed as:

[0153] (18)

[0154] Unlike vortex electromagnetic wave imaging methods based on Fourier transform, the echo signal Bessel function in the amplitude term In this case, b is no longer a constant, but the vortex electromagnetic wave imaging method based on Fourier transform obtains the target azimuth angle by utilizing the dual relationship between the azimuth angle and the mode in the phase term of the echo signal. Therefore, the target distance and azimuth angle information can still be obtained by using the vortex electromagnetic wave two-dimensional imaging method based on Fourier transform.

[0155] S35 employs the minimum-mode vortex electromagnetic wave two-dimensional imaging method based on real-valued processing to process the echo signal received by a uniformly symmetrical concentric circular ring antenna array. The echo signal received by the uniformly symmetrical concentric circular ring antenna array is then expressed as:

[0156] (19)

[0157] in, Unlike equation (4), the guiding vector in equation (19) middle The diameter b of the uniform symmetrical concentric ring antenna array is no longer a constant. When using the spatial average sliding algorithm to divide the signal subarray, the diameter b is used as the division standard, and the azimuth and elevation angle information of the target can still be obtained.

[0158] S36 Based on the analysis of uniformly symmetrical concentric circular ring antenna arrays, it can be seen that each uniformly symmetrical concentric circular ring antenna array has two array elements distributed on the linear antenna array, and about the origin... The signals received by two array elements symmetrically distributed on the same circular ring of diameter are 180° out of phase. Assuming the transmitted signal is a linear frequency modulated signal... The echo signal received by the array element in the positive X-axis direction is denoted as The echo signal received by the array element in the negative X-axis direction should be denoted as... Based on the modal values ​​carried by the echo signal After uniform phase compensation, the echo signal received by the array elements in the negative X-axis direction is... ;

[0159] Analysis of the optimization model in equation (19) shows that the linear array constructed in a uniformly symmetrical concentric ring antenna array may not satisfy the uniform distribution. Considering the distribution characteristics of the linear array elements, a back projection algorithm is used to process the echo signal received by the linear array to achieve two-dimensional imaging of the radar target. The steps of the back projection algorithm are as follows: Figure 5 As shown.

[0160] The problem of non-uniform distribution of the linear array can be equivalent to the problem of element loss of a uniformly distributed linear array. Then, the non-uniformly distributed linear array may have the following three situations: (1) continuous loss of array elements; (2) block loss of array elements, and the block area satisfies the sparse distribution condition; (3) random loss of array elements. If the transmitted signal is an LFM signal with a carrier frequency of 10 GHz and a signal bandwidth of 4 GHz, under the condition of a uniformly distributed linear array with 4 transmitters and 32 receivers, the back projection algorithm can achieve two-dimensional imaging of the target in both the case of uniform distribution of virtual array elements and the three non-uniform distribution cases, as shown in Figures 6(a)-6(e). It can be seen from Figures 6(a)-6(e) that the non-uniform distribution of the virtual array elements of the linear array has little impact on the back projection algorithm, and the imaging effect of the back projection algorithm is the best in the case of sparse loss of array elements.

[0161] The back projection algorithm in S36 is specifically as follows:

[0162] S361 uses the nearest distance as a reference point to cluster the compressed echo data, divides the imaging scene into a network to obtain the coordinates of all network points, starting from the azimuth starting point;

[0163] S362 calculates the distances between the radar and all grid points in the current azimuth direction and calculates the delay time of all grid points relative to the nearest reference point. ;

[0164] S363 utilizes the delay time of each grid point The corresponding echo value is calculated by interpolation and then superimposed with the echo value of the previous direction to that grid point.

[0165] S364 Check if all grid points have been traversed. If so, proceed to S365; otherwise, proceed to S363 to find the next grid point.

[0166] S365 Check if all directions have been traversed. If so, proceed to S366. Otherwise, proceed to S362 to find the next direction.

[0167] S366 obtains the image of the imaging scene area. Set the delay time for all grid points relative to the nearest reference point.

[0168] Specifically, S4 is:

[0169] By utilizing coordinate system transformation relationships to reconstruct the three-dimensional imaging results of the target in the rectangular coordinate system, spatial information of the radar target in the spherical coordinate system obtained by different imaging methods on the echo signals received by a uniformly symmetrical concentric circular ring antenna array is presented. and , by azimuth Correlate the scattering points to obtain the target's three-dimensional spatial information in spherical coordinates. In azimuth angle When associating scattering points, for the same azimuth angle Multiple false scattering points will appear at the scattering point; a back projection algorithm is used for a uniform symmetrical concentric ring antenna array to obtain the range and azimuth information of the radar target in a rectangular coordinate system. Using the conversion formula between spherical coordinates and rectangular coordinates, the target spherical coordinate information is converted... Convert to rectangular coordinate information The formula for converting between spherical coordinates and rectangular coordinates is given as follows:

[0170] (20)

[0171] Then, the range and azimuth information in the radar Cartesian coordinate system are obtained through a back projection algorithm. As prior information, the determination is specifically represented as follows:

[0172] (twenty one)

[0173] (twenty two)

[0174] in, The threshold for judgment is defined as the distance resolution in the distance dimension and the azimuth resolution in the azimuth dimension; this threshold is used for the transformed target Cartesian coordinate information. Simultaneously, scattering points that do not satisfy equations (21) and (22) are eliminated, and finally, the three-dimensional imaging result of the target is obtained. The 3D imaging algorithm process is as follows: Figure 7 As shown.

[0175] Simulation Experiment

[0176] According to the three-dimensional imaging method based on a uniform symmetrical concentric ring antenna array, the uniform concentric ring antenna array is used as both the transmitting and receiving unit. By solving the optimization model of equation (20), the concentric ring array is composed of 8 ring arrays, and the total number of array elements of the concentric ring array is 136. The transmitted signal parameters remain unchanged, and four scattering points are set in space. to The spatial location information of the four scattering points in the spherical coordinate system and the rectangular coordinate system is shown in Table 1.

[0177] according to Figure 7 As shown in the three-dimensional imaging process based on a uniform symmetrical circular ring antenna array, it is necessary to perform Fourier transform, RV-MVM algorithm and back projection algorithm on the echo received by the antenna array to obtain the two-dimensional imaging result about the target, as shown in Figure 8.

[0178] Table 1 Spatial coordinate information of scattering points

[0179] .

[0180] By azimuth Figure 8(a) and 8(b) The two-dimensional imaging results are correlated to obtain the correlated three-dimensional imaging results, such as... Figure 9 As shown in the diagram. The circles represent the actual scattering points, and the rhombuses represent the reconstructed scattering points. From... Figure 9 It can be seen that, in addition to the true scattering point, there are two false scattering points. This is due to the duplicate association that occurs when multiple scattering points exist in the same azimuth unit during correlation processing based solely on azimuth angle.

[0181] To eliminate false scattering points after correlation processing, the three-dimensional spherical coordinate information of the correlated scattering points is converted into three-dimensional rectangular coordinate information using equation (20), such as... Figure 10 As shown in the figure. The circle represents the true scattering point obtained through the back projection algorithm, and the rhombus represents the two-dimensional projection of the associated reconstructed scattering point into the rectangular coordinate system after the coordinate system transformation formula.

[0182] The obtained true scattering points in the range-azimuth 2D spatial information and the associated reconstructed scattering points projected in the range-azimuth 2D spatial information are processed according to equations (21) and (22) to eliminate false scattering points caused by the association processing. Finally, the target 3D imaging result after eliminating false scattering points is obtained, as shown in the figure. Figure 11 As shown, the circle represents the actual scattering point, and the star represents the scattering point reconstructed by the three-dimensional imaging method proposed in this patent, demonstrating the effectiveness of the vortex electromagnetic wave three-dimensional imaging algorithm based on a uniform symmetrical concentric ring antenna array proposed in this patent.

[0183] The advantages of this invention are as follows: a uniform symmetrical concentric ring array, which enables the array elements to form a uniform linear array for radar target observation in space. The array structure of the uniform symmetrical concentric ring array is further optimized by utilizing the characteristics of the back projection algorithm, which effectively reduces the antenna complexity and the total number of array elements.

Claims

1. A three-dimensional imaging method for vortex electromagnetic waves based on a uniform symmetrical concentric ring array, specifically including the following steps: S1 Constructs a uniform concentric circular ring antenna array. For the echo signal received by the uniform concentric circular ring antenna array, a two-dimensional imaging method based on Fourier transform vortex electromagnetic waves is used to obtain the range and azimuth information of the radar target in a spherical coordinate system. ; S1 specifically includes: S11 Construct a uniform concentric circular ring antenna array. Let the mathematical model for estimating the direction of arrival be expressed as: (1) in, The signal data vector received by a uniform concentric circular ring antenna array. For spatial array manifold vectors, For spatial signal vectors, For a uniform concentric circular ring antenna array noise data vector, Indicated as fast time, express The pitch angle of the point; S12 Considering the complexity of the uniform concentric ring antenna array in the observation model, a single-transmitter, multiple-receiver observation model based on the uniform concentric ring antenna array is adopted. The transmitting element is an independent omnidirectional antenna located at the origin of the coordinate system. The receiving unit is a uniform concentric circular ring antenna array, and the center of the array is also located at the origin of the coordinate system. The receiving unit array consists of The array is composed of n identical antenna elements, and the nth element is denoted as nn. The radius of the circular array is b; set up Let be any scattering point in space, where, express Point to the center of the circular array Distance between points express The pitch angle of the point, express The azimuth angle of the point is the angle received by the uniform concentric circular ring antenna array. The normalized echo signal of a point is represented as: (2) in, The radar cross section of the scattering point. Modal values, Represented as wave number, For a Bessel function of the first kind, In order to transmit signals, This is a noise signal; S13 Assume the radar target is... Composed of 18 ideal scattering points, the radar target echo signal is expressed as: (3) in, , , The first The distance, azimuth, and elevation angles of each scattering point in spherical coordinates. For the first Radar scattering cross section of each scattering point; Analyzing the radar target echo signal represented by equation (3), it can be seen that the exponential terms contained in the radar target echo signal are respectively and The radar target range can be seen from the exponential term. With the frequency of the transmitted signal Radar target azimuth angle Modal values ​​of vortex electromagnetic waves They are in a dual relationship, and the radar target range and azimuth information are obtained by using two-dimensional Fourier transform on the radar target echo signal; S2. Then, for the echo signal received by the uniform concentric ring antenna array, a fast two-dimensional imaging method based on minimum mode vortex electromagnetic waves with real-valued processing is used to obtain the azimuth and elevation angle information of the radar target in the spherical coordinate system. ; S3 constructs a hybrid array of uniform concentric ring antenna array and uniform linear antenna array. This hybrid array is then optimized into a uniform symmetrical concentric ring antenna array. Based on the mode values ​​carried by the vortex electromagnetic waves, phase compensation is performed on the array elements distributed along the negative X-axis in the uniform symmetrical concentric ring antenna array. Finally, a back projection algorithm is used to obtain the range and azimuth information of the radar target in a Cartesian coordinate system. ; S4 performs correlation processing on the obtained two-dimensional imaging results of the radar target, reconstructs the three-dimensional imaging results of the target in the rectangular coordinate system using coordinate system transformation relationship, and filters out false scattering points in the reconstructed three-dimensional imaging results according to the resolution in the rectangular coordinate system to obtain accurate three-dimensional imaging results of the target. Specifically, S4 is: By utilizing coordinate system transformation relationships to reconstruct the three-dimensional imaging results of the target in the rectangular coordinate system, spatial information of the radar target in the spherical coordinate system obtained by different imaging methods on the echo signal received by a uniform concentric circular ring antenna array is presented. and , by azimuth Correlate the scattering points to obtain the target's three-dimensional spatial information in spherical coordinates. In azimuth angle When associating scattering points, for the same azimuth angle Multiple false scattering points will appear at the scattering point; a back projection algorithm is used for a uniform symmetrical concentric ring antenna array to obtain the range and azimuth information of the radar target in a rectangular coordinate system. Using the conversion formula between spherical coordinates and rectangular coordinates, the target spherical coordinate information is converted... Convert to rectangular coordinate information The formula for converting between spherical coordinates and rectangular coordinates is given as follows: (20) Then, the range and azimuth information in the radar Cartesian coordinate system are obtained through a back projection algorithm. As prior information, the determination is specifically represented as follows: (21) (22) in, The threshold for judgment is the converted target rectangular coordinate information. Simultaneously, scattering points that do not satisfy equations (21) and (22) are eliminated, and finally, the three-dimensional imaging result of the target is obtained. .

2. The vortex electromagnetic wave three-dimensional imaging method based on a uniform symmetrical concentric ring array as described in claim 1, characterized in that: S2 specifically includes: S21 treats each scattering point of the radar target as an independent radiation source and uses the MUSIC algorithm to estimate the arrival parameters of the equivalent radiation sources in order to obtain radar target information on the target elevation and azimuth angles. According to equation (1), let the vortex electromagnetic wave mode value The range of values ​​is Then equation (2) can be further expressed as: (4) in, , As the guide vector, For the echo signal vector, the first... The steering vector and echo vector corresponding to each signal are respectively and , This represents the number of sampling points for the echo signal; S22 According to the MUSIC algorithm, the covariance matrix of the target signal received by the uniform concentric ring antenna array needs to be obtained; assuming the noise interference is Gaussian white noise, different mode values The covariance matrix of the target signal is expressed as: (5) in, Let be the covariance matrix of the signal. For noise energy, The identity matrix is ​​used; typically, the target signal received by a uniform concentric circular ring antenna array is complex, and considering the actual length of the received signal, the covariance matrix is ​​used. Represented as: (6) in, The target signal received by the uniform concentric circular ring antenna array; through the analysis of equation (6), and Considered as the two basic elements for storing target spatial information, according to equation (6), the real part and the imaginary part of the covariance matrix of the target signal are respectively expressed as: (7) (8) As can be seen from equations (7) and (8), the real or imaginary part of the covariance matrix of the echo signal completely contains the spatial information of the target; therefore, processing the real or imaginary part of the covariance matrix alone can obtain the spatial information of the target, and the target azimuth and elevation angle information can be obtained by performing a two-dimensional spatial peak search. The search process is expressed as follows: (9) (10) in, for or The noise subspace eigenvector matrix obtained by eigenvalue decomposition. This is the guiding vector of the signal subspace; S23 When the number of radar target scattering points is unknown, the problem of unknown target scattering points is solved by using the minimum modulus algorithm weighted MUSIC algorithm, a generalized form of the MUSIC algorithm. When using the minimum modulus algorithm weighted MUSIC algorithm, equation (9) is expressed as: (11) in, , For noise subspace The first line, For noise subspace remove The rest If so, the spatial spectrum estimation formula based on the minimum modulus algorithm weighted MUSIC algorithm is expressed as: (12)。 3. The vortex electromagnetic wave three-dimensional imaging method based on a uniform symmetrical concentric ring array as described in claim 1, characterized in that: S3 specifically includes: S31 Constructs a hybrid array of uniform concentric circular ring antenna array and uniform linear antenna array. Both the uniform concentric circular ring antenna array and the uniform linear antenna array serve as receiving elements. The uniform concentric circular ring antenna array consists of... A uniform linear antenna array consists of M antenna elements uniformly distributed on a ring of diameter b. On the straight line, the transmitting element is an omnidirectional antenna located at the origin of the coordinate system. Analysis of the complexity of the hybrid array of uniform concentric ring antenna array and uniform linear antenna array shows that the total length of the antenna array in the hybrid array is... The total number of antenna array elements in the hybrid array of uniform concentric ring antenna array and uniform linear antenna array is: By performing a two-dimensional Fourier transform on the echo signal received by a uniform linear antenna array, a two-dimensional imaging result of the target in a Cartesian coordinate system with respect to range and azimuth can be obtained. Furthermore, the azimuth resolution is related to the length of the linear array. Proportional, its resolution is expressed as: (13) in, The wavelength of the transmitted signal, The center position of the target area in the azimuth dimension; For the echo signal received by a uniform concentric circular ring antenna array, Fourier transform is used to obtain the target azimuth image in spherical coordinates. The target azimuth resolution obtained based on the Fourier transform algorithm is expressed as: (14) Analysis of equation (14) shows that the target azimuth resolution is proportional to the number of observed modes, while the number of vortex electromagnetic wave modes that a uniform concentric ring antenna array can generate depends on the total number of antenna array elements. That is, the azimuth resolution is proportional to the total number of elements of the uniform concentric ring antenna array. Considering that the imaging results of the two vortex electromagnetic wave imaging methods need to be correlated with scattering points in the future, the azimuth resolution of the two vortex electromagnetic wave imaging methods needs to be kept consistent. It is necessary to increase the number of elements of the uniform concentric ring antenna array to improve the azimuth resolution. In order to improve the imaging resolution in the azimuth dimension, the total number of elements and complexity of the hybrid array of uniform concentric ring antenna array and uniform linear antenna array will increase sharply, thereby affecting the signal processing efficiency based on the hybrid array of uniform concentric ring antenna array and uniform linear antenna array. S32 Analysis of the amplitude spatial distribution of vortex electromagnetic waves shows that the main lobe illumination direction of vortex electromagnetic waves is also affected by the mode value, which in turn affects the number of target observation modes. In order to further improve the azimuth resolution, a uniform concentric ring antenna array is used to increase the number of observation modes. A uniform concentric ring antenna array is an antenna array composed of multiple ring arrays with different radii centered at a fixed point. The antenna array generates a large number of modes of vortex electromagnetic waves with a fixed main lobe illumination direction by optimizing transmission resources. The hybrid array of uniform concentric ring antenna array and uniform linear antenna array is improved into a hybrid antenna array of concentric ring antenna array and uniform linear antenna array to obtain a higher azimuth resolution. The complexity of the hybrid antenna array of concentric ring antenna array and uniform linear antenna array increases significantly. In order to reduce the complexity of the hybrid antenna array of concentric ring antenna array and uniform linear antenna array, a uniform symmetrical concentric ring antenna array for vortex electromagnetic wave three-dimensional imaging is adopted on the basis of the hybrid antenna array of concentric ring antenna array and uniform linear antenna array. The array elements on each ring antenna array in the hybrid antenna array must satisfy uniform symmetrical distribution, and there must be two array elements symmetrical about the origin O on the X-axis. S33 Analysis of the uniformly symmetrical concentric ring antenna array shows that the uniformly symmetrical concentric ring antenna array is composed of It consists of a uniformly symmetrical concentric circular ring antenna array with the same center but different radii. The number of array elements in each uniformly symmetrical concentric circular ring antenna array is: ,in ,and For an even number of uniform, symmetrical, concentric circular ring antenna arrays, the spacing between each array should satisfy the following: (15) in, The interval between each ring, Let M be the minimum interval between the rings, and M be any positive integer; since the elements of each uniformly symmetrical concentric ring antenna array satisfy a symmetrical and uniform distribution, then the first element and the second element of each uniformly symmetrical concentric ring antenna array... Each element should be located in On the axis, in the A uniform, symmetrical, concentric circular ring antenna array composed of several rings has Individual elements The array elements are linearly distributed along the axis; the receiving array elements located on the X-axis and the elements located at the origin of the coordinate system... The transmitting elements form a linearly distributed transmit / receive antenna array. A linear antenna array satisfying linear distribution is constructed from a uniformly symmetrical concentric ring array. The complexity of the uniformly symmetrical concentric ring antenna array is then analyzed. Under the condition of the same azimuth resolution, the total length of the uniformly symmetrical concentric ring antenna array is... , Let be the maximum radius of the uniformly symmetrical concentric circular ring antenna array, and let be the length of the hybrid antenna array of uniformly concentric circular ring antenna array and uniformly linear antenna array. The total number of elements in a uniformly symmetrical concentric circular ring antenna array is The total number of elements in a hybrid antenna array of uniform concentric ring antenna array and uniform linear antenna array is the minimum. Compared to a hybrid antenna array consisting of a uniform concentric ring antenna array and a uniform linear antenna array, a uniform symmetrical concentric ring antenna array has a shorter length. The total number of array elements will be reduced by at least ; S34 It is known that in the direction of illumination of the main lobe of the vortex electromagnetic wave Represented as: (16) in, The direction of the main lobe illumination of the vortex electromagnetic wave, and the modal values. , wave number and the radius of the circular array ; According to equation (16), by scheduling circular arrays of different diameters, vortex electromagnetic waves of different mode values ​​can be received in a time-division manner. The echo received by a uniformly symmetrical concentric circular array antenna is expressed as: (18) Unlike vortex electromagnetic wave imaging methods based on Fourier transform, the echo signal Bessel function in the amplitude term Since b is no longer a constant, the target distance and azimuth information can still be obtained by using the vortex electromagnetic wave two-dimensional imaging method based on Fourier transform. S35 employs the minimum-mode vortex electromagnetic wave two-dimensional imaging method based on real-valued processing to process the echo signal received by a uniformly symmetrical concentric circular ring antenna array. The echo signal received by the uniformly symmetrical concentric circular ring antenna array is then expressed as: (19) in, Unlike equation (4), the guiding vector in equation (19) middle The diameter b of the uniform symmetrical concentric ring antenna array is no longer a constant. When using the spatial average sliding algorithm to divide the signal subarray, the diameter b is used as the division standard, and the azimuth and elevation angle information of the target can still be obtained. S36 Based on the analysis of uniformly symmetrical concentric circular ring antenna arrays, it can be seen that each uniformly symmetrical concentric circular ring antenna array has two array elements distributed on the linear antenna array, and about the origin... The signals received by two array elements symmetrically distributed on the same circular ring of diameter are 180° out of phase. Assuming the transmitted signal is a linear frequency modulated signal... The echo signal received by the array element in the positive X-axis direction is denoted as The echo signal received by the array element in the negative X-axis direction should be denoted as... Based on the modal values ​​carried by the echo signal After uniform phase compensation, the echo signal received by the array elements in the negative X-axis direction is... ; Based on the analysis of the optimization model of equation (19), it can be seen that the linear array constructed in the uniform symmetrical concentric ring antenna array may not meet the uniform distribution. Considering the distribution characteristics of the linear array elements, the back projection algorithm is used to process the echo signal received by the linear array to realize two-dimensional imaging of the radar target.

4. The vortex electromagnetic wave three-dimensional imaging method based on a uniform symmetrical concentric ring array as described in claim 3, characterized in that: Further optimization of complexity is performed in S33: To further optimize the complexity of the uniform symmetrical concentric ring antenna array, the total number of array elements is further optimized using a vortex electromagnetic wave transmission resource optimization method. It is known that in the direction of illumination of the main lobe of the vortex electromagnetic wave Represented as: (16) Analysis of equation (16) reveals that the irradiation direction of the main lobe of the vortex electromagnetic wave is... With modal values , wave number and the radius of the circular array Related, azimuth imaging resolution of uniform symmetrical concentric ring antenna array With array length Related, while the array length constructed by a uniformly symmetrical concentric circular ring antenna array is ; According to equation (14), the azimuth resolution obtained based on Fourier transform is... With the number of observed modes Correlation, and the number of observed modes The number of circular antenna arrays Relatedly, considering the consistency of the azimuth resolution of different imaging methods for the imaging area, the azimuth resolution of the imaging area center based on the linear distribution antenna array imaging method is shown in Equation (13), and the azimuth resolution of the vortex electromagnetic wave imaging method based on Fourier transform using the single-transmitter multi-receiver observation model is shown in Equation (14). Let the elevation angle of the center point of the observed imaging region be... The azimuth resolution of the imaging region center based on the imaging method of uniform symmetric concentric ring antenna array The azimuth resolution of the vortex electromagnetic wave imaging method based on Fourier transform, employing a single-transmitter, multiple-receiver observation model, is [value missing]. Then, for a uniformly symmetrical concentric ring antenna array, the total number of array elements is... The optimization model is expressed as: (17) in, Let be the diameter of the i-th circular antenna array. To obtain the total number of modes for the i-th circular ring antenna array, equation (17) is the total number of array elements of a uniformly symmetrical concentric circular ring antenna array. To optimize the target.

5. The vortex electromagnetic wave three-dimensional imaging method based on a uniform symmetrical concentric ring array as described in claim 3, characterized in that: The back projection algorithm in S36 is specifically as follows: S361 uses the nearest distance as a reference point to cluster the compressed echo data, divides the imaging scene into a network to obtain the coordinates of all network points, starting from the azimuth starting point; S362 calculates the distances between the radar and all grid points in the current azimuth direction and calculates the delay time of all grid points relative to the nearest reference point. ; S363 utilizes the delay time of each grid point The corresponding echo value is calculated by interpolation and then superimposed with the echo value of the previous direction to that grid point. S364 Check if all grid points have been traversed. If so, proceed to S365; otherwise, proceed to S363 to find the next grid point. S365 Check if all directions have been traversed. If so, proceed to S366. Otherwise, proceed to S362 to find the next direction. S366 obtains the image of the imaging scene area.

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