Three-Dimensional Imaging Method of Vortex Electromagnetic Wave Radar Combining Integer-Order and Fractional-Order Modes

Abstract

The three-dimensional imaging method of a vortex electromagnetic wave radar combining integer-order and fractional-order modes of the present invention includes Step 1: obtaining radar target echo data with combined integer-order and fractional-order mode numbers; Step 2: realizing the "coarse imaging" of the radar target in range-azimuth angle; Step 3: dividing scatterers into the first type of scatterers and the second type of scatterers; Step 4: performing a butterfly operation on the fractional-order echo data to obtain its sum and difference echo data; Step 5: solving the elevation angle and azimuth angle of the first type of scatterers in the radar target; Step 6: solving the elevation angle information of the second type of scatterers in the radar target; Step 7: fusing the first type of scatterers and the second type of scatterers in Steps 5 and 6 to realize the three-dimensional reconstruction of the radar target. It does not increase the requirement for the number of array elements and the complexity of the array structure, providing a new technical approach for three-dimensional imaging based on vortex electromagnetic waves.

Description

Technical Field

[0001] The present invention relates to signal and information processing technologies, and particularly to a three-dimensional imaging method for a vortex electromagnetic wave radar that combines integer-order and fractional-order modes. Background Art

[0002] Since 1992, when L. Allen et al. first revealed the optical vortex phenomenon, this physical property of the vortex has received extensive attention. According to classical electrodynamics theory, electromagnetic fields also have spin angular momentum and orbital angular momentum. By analogy with optical vortices, microwaves carrying these two types of angular momentum are called vortex electromagnetic waves. Among them, the orbital angular momentum corresponds to the change in the phase of the electromagnetic wavefront. By changing the orbital angular momentum, modulation of the wavefront phase can be achieved, and integer multiples of the mode numbers satisfy orthogonal relationships with each other. This wavefront phase modulation ability provides a new degree of freedom in addition to the time domain, frequency domain, and polarization domain, attracting attention in the fields of communication and radar and resulting in a large number of research results, especially in the field of radar imaging technology.

[0003] The reconstruction of the azimuth image of a radar target by planar wave radar imaging technology depends on the size of the synthetic aperture or real aperture, and there are certain limitations in the real-time performance and quality of imaging. Different from planar wave radar imaging technology, vortex electromagnetic wave imaging technology no longer depends on the aperture size but on the range of mode numbers. This means that vortex electromagnetic waves can be used to achieve real-time imaging of radar targets or imaging of targets with no relative motion to the radar, meeting the requirements of specific detection scenarios. Existing technologies have constructed echo models of single-transmission and multi-reception, and multi-transmission and multi-reception of vortex electromagnetic waves based on a uniform circular array (UCA for short), and experimentally verified the two-dimensional imaging ability of integer-order vortex electromagnetic waves for radar targets. However, the resolution of the two-dimensional imaging results is limited by the range of mode numbers and the Bessel function in the echo signal amplitude term; currently, the orthogonality of integer-order vortex electromagnetic waves can be utilized to achieve high-resolution two-dimensional reconstruction of radar targets through methods such as fast Fourier transform.

[0004] In fact, in addition to integer orders, fractional orders can also be generated for the mode numbers of vortex electromagnetic waves, and fractional-order vortex electromagnetic waves also satisfy orthogonality in the mode number domain. Using fractional-order vortex electromagnetic waves can increase the range of imaging mode numbers, enhance the anti-noise performance of vortex electromagnetic waves, and thus improve the imaging quality. A concentric circular array can be used, with adjacent circular arrays for reception and transmission, thereby realizing the equivalence of fractional-order vortex electromagnetic waves, further increasing the range of mode numbers, and improving the azimuth resolution; for the noise effect in a complex environment, applying fractional-order vortex electromagnetic waves has high-performance two-dimensional imaging ability at low signal-to-noise ratios.

[0005] However, the existing technologies still focus on improving two-dimensional imaging capabilities for the application of fractional-order vortex electromagnetic waves. Compared with two-dimensional imaging results, three-dimensional reconstruction of radar targets can obtain richer characteristic information such as the relative spatial dimensions and types of radar targets. Existing vortex electromagnetic wave imaging technologies do not have the ability to resolve the elevation angle of radar targets, thus unable to obtain the three-dimensional spatial structure of radar targets and more abundant characteristic information. Summary of the Invention

[0006] The object of the present invention is to overcome the deficiencies in the above-mentioned existing technologies and propose a three-dimensional imaging method for a vortex electromagnetic wave radar that combines integer-order and fractional-order modes. First, based on the multiple-input multiple-output (MIMO) mode of a uniform circular array (UCA), a radar target echo model containing integer-order and fractional-order modes is constructed. Secondly, the integer-order and fractional-order echo data are processed separately. By performing a fast Fourier transform (FFT) on the integer-order echo data, a two-dimensional rough imaging result of the radar target in the range-azimuth angle dimension is obtained, and the target scattering points are classified and divided according to the rough imaging result. By performing a butterfly operation on the fractional-order echo data, the sum and difference of the echo signals of the two orders are obtained; then, according to the characteristics of different types of scattering points, based on the rough imaging result and the properties of the fractional-order Bessel function, different imaging processes are designed using the sum and difference of the fractional-order echo signals to achieve three-dimensional reconstruction of different types of scattering points, and the azimuth angle and elevation angle resolutions of different types of scattering points are analyzed.

[0007] The present invention is implemented as follows:

[0008] A three-dimensional imaging method for a vortex electromagnetic wave radar that combines integer-order and fractional-order modes, comprising the following steps:

[0009] Step 1: Obtain radar target echo data combining integer-order and fractional-order mode numbers based on the multiple-input multiple-output (MIMO) mode of a uniform circular array (UCA);

[0010] Step 2: Process the integer-order mode echo data using a fast Fourier transform to achieve "rough imaging" of the radar target in range-azimuth angle;

[0011] Step 3: According to the "rough imaging" result, taking the range cell as the division object, divide the scattering points into the first type of scattering points and the second type of scattering points;

[0012] Step 4: Perform a butterfly operation on the fractional-order echo data to obtain the sum and difference echo data sum;

[0013] Step 5: Solve the elevation angle and azimuth angle of the first type of scattering points in the radar target in sequence to achieve three-dimensional reconstruction of this type of scattering points;

[0014] Step 6: Utilize the azimuth information in the "coarse imaging" to solve for the elevation angle information of the second type of scattering points in the radar target, and achieve the three-dimensional reconstruction of this type of scattering points;

[0015] Step 7: Integrate the first type of scattering points and the second type of scattering points in Steps 5 and 6 to achieve the three-dimensional reconstruction of the radar target.

[0016] Furthermore, the specific steps of Step 1 are as follows:

[0017] Assume that the vortex electromagnetic wave is generated by a UCA array, where the UCA array is a circular planar array with a radius of a composed of N independent transceiver antenna elements. The center of the UCA array is placed at the coordinate origin, and the nth element of the UCA array is denoted as S n , and its corresponding transmitted signal is s n (t); if the signal of the nth element is phase-modulated, the modulation phase is Then the transmitted signal of the nth element can be expressed as:

[0018]

[0019] where s(t) is a chirp signal, K is the frequency modulation rate, T is the transmitted signal pulse width, f c is the signal center frequency, α is the mode number, t is the fast time, and j is the imaginary number; then the transmitted signal s T (t) of the UCA array can be expressed as:

[0020]

[0021] Then for the spatial point where r p is the distance from point P to the origin O, θ p is the angle between point P and the positive direction of the Z axis, is the angle between point P and the positive direction of the X axis in the XOY plane. Based on the MIMO transceiver mode of the UCA array, the total echo signal received at point P can be expressed as:

[0022]

[0023] where τ p is the signal time delay and σ is the normalized scattering coefficient of point P, c is the speed of light, k is the wave number, J α (·) is the first kind of Bessel function of order α, and at this time α takes integer values; by performing amplitude modulation and phase modulation on the signals transmitted by each independent element of the UCA array, the vortex electromagnetic wave with a fractional order mode number can be obtained. Similarly, for the spatial point its echo signal can be approximately expressed as:

[0024]

[0025] At this time, the value of the mode number α is a non-integer; it can be seen from formulas (3) and (4) that for a radar target composed of M scattering points, its target echo can be uniformly expressed as:

[0026]

[0027] If the range of integer-order mode numbers generated by the UCA is [-l, l], and the fractional-order mode numbers are respectively Then the echo signals of radar targets of different orders can be written in matrix form:

[0028] S = [s M (t, α1), s M (t, α2),..., s M (t, α 2l ), s M (t, α 1 / 2 ), s M (t, α -1 / 2 )] T (6).

[0029] Furthermore, the specific steps of step 2 include the following steps:

[0030] Select the echo signals of integer-order radar targets to form a new echo data matrix S in = [s M (t, α1),....., s M (t, α 2l )] T , and through analysis, it can be seen that S in still shows a two-dimensional rectangular distribution in the fast time-mode number domain; first, select the center point P c of the imaging target area as the reference point, then the echo signals of the reference point P c at different mode numbers can be expressed as:

[0031]

[0032] where s Pc (t, α n ) is the echo signal of the reference point P c at the nth-order mode number; by performing matched filtering on S in in the range dimension, the range information of the radar target can be obtained; the data after matched filtering can be expressed as:

[0033] S Match = [s Match (t, α1), s Match(t, α2),..., s Match (t, α 2l )] T (8)

[0034] where psf t (t - τ p ) is the point spread function; it can be seen from formula (8) that for S Match Performing fast Fourier transform in the mode number domain can obtain the azimuth angle of the radar target; then through the above processing, the two-dimensional imaging result of the radar target with respect to range-azimuth angle can be obtained.

[0035] Further, step 3 specifically includes the following steps:

[0036] Taking the range cell as the object, divide the target scatter points according to the imaging result of "coarse imaging". If there is only a single scatter point on a certain range cell, then this type of scatter point is denoted as the first type of scatter point P'; conversely, if two or more scatter points are on the same range cell, then this type of scatter point is denoted as the second type of scatter point P'';

[0037] Suppose there are L1 first-type scatter points and L2 second-type scatter points, then L1 + L2 = M.

[0038] Further, step 4 specifically includes the following steps:

[0039] By processing the integer-order echo data, only the two-dimensional imaging result of "coarse imaging" of the radar target can be obtained. To obtain the elevation angle information of the radar target, the echo data of the mode number forms a fractional-order echo data matrix S fr = [s M (t, α 1 / 2 ), s M (t, α -1 / 2 )] T ; when the mode number α is 1 / 2, the first-kind Bessel function J α (·) can be expressed by elementary functions as:

[0040]

[0041] where z is the variable of the Bessel function;

[0042] Then the radar target echo received when the mode number can be respectively expressed as:

[0043]

[0044] Taking the transmitted signal as the reference signal, for The echo signal at time t is de-linearized and its expression in the difference frequency domain is obtained by fast Fourier transform:

[0045]

[0046] Where R Δ =r p -r ref , r p is the distance from point P to the origin O, r ref is the transmitted signal; because the reference signal is the transmitted signal, i.e. r ref =0, then R Δ =r p ; This means that the distance information of the radar target is solved by using the line frequency solution and the fast Fourier transform in the distance dimension; if the scattering points of the radar target are distributed in different distance units, each peak of the one-dimensional range image represents a scattering point;

[0047] According to formulas (13) and (14), When , the amplitude of each scattering point on the one-dimensional distance image is:

[0048]

[0049] Set the mode number to α 1 / 2 and α -1 / 2 By dividing the amplitude of the same distance unit when , we can get:

[0050]

[0051] but

[0052]

[0053] Formula (18) can be used to solve the target pitch angle information corresponding to different distance units;

[0054] Although the target azimuth has been obtained through coarse imaging processing, in order to achieve fine imaging of the target, The sum and difference of the echo signals of the two modes are used to solve the azimuth of the target; the equations (13) and (14) are expressed as The echo signal S M (f,α 1 / 2 ), S M (f,α -1 / 2 ) performs butterfly operation, where S add =S M (f,α 1 / 2 )+S M (f,α -1 / 2 ), S sub =S M (f,α1 / 2 ) - S M (f, α -1 / 2 );then the signal S add can be expressed as:

[0055]

[0056] Let Expand the exponential term using Euler's formula , then we can get:

[0057]

[0058] Then formula (19) can be further expressed as:

[0059]

[0060] If only considering the amplitude of the one - dimensional range profile, then the amplitude of the range profile in different range cells of formula (21) is:

[0061]

[0062] Similarly, S sub is expressed as:

[0063]

[0064] Then After the echo signal difference processing of, the amplitude of the range profile in different range cells of formula (23) is:

[0065]

[0066] Dividing the amplitudes in the same range cell of formula (22) and (24), the square of the ratio can be expressed as:

[0067]

[0068] Furthermore, step 5 specifically includes the following steps:

[0069] The elevation angle information of the radar target has been solved through formula (18), then by organizing formula (25), the expression of the target azimuth angle can be obtained:

[0070]

[0071] According to formula (18) and (26), it can be known that by jointly processing the echo signals of the semi - odd mode numbers α 1 / 2 , α -1 / 2 , the azimuth angle and elevation angle information of the radar target can be solved.

[0072] Further, step 6 specifically includes the following steps:

[0073] The above signal processing flow is based on the premise that the scattering points are distributed in different range cells, that is, it is applicable to the defined first type of scattering points; if the target scattering point belongs to the second type of scattering points, the azimuth angle information obtained from the two-dimensional imaging result of "coarse imaging" needs to be used. Express formula (26) as:

[0074]

[0075] It can be seen from formula (27) that by using the azimuth angle information of "coarse imaging", the respective elevation angles of different scattering points in the same range cell can be solved, and the three-dimensional resolution ability for the second type of scattering points is achieved.

[0076] Further, step 7 specifically includes the following steps:

[0077] Since the radar target scattering points must belong to the defined first type of scattering points or the second type of scattering points, through the above analysis, the three-dimensional reconstruction of the radar target can be realized by formulas (18), (26), and (27).

[0078] The beneficial effects of the present invention are as follows: The three-dimensional reconstruction of the radar target is realized through the two-stage imaging processing of the combined integer-order and fractional-order mode number vortex electromagnetic waves. The radar target scattering points are divided according to the coarse imaging result, and at the same time, the properties of the fractional-order Bessel function are utilized to further achieve the elevation angle resolution for different types of scattering points. The simulation experiment shows the effectiveness of the vortex electromagnetic wave three-dimensional reconstruction method proposed by the present invention. Compared with the vortex electromagnetic wave two-dimensional imaging method, the method of the present invention does not increase the requirements for the number of array elements and the complexity of the array structure, providing a new technical approach for the three-dimensional imaging based on vortex electromagnetic waves. Brief Description of the Drawings

[0079] Figure 1 It is the flowchart of the three-dimensional imaging method of the present invention;

[0080] Figure 2 It is the geometric schematic diagram of the UCA and the target;

[0081] Figure 3 It is the butterfly operation diagram based on semi-odd numbers;

[0082] Figure 4 It is the calculation error Δx in different elevation angle intervals;

[0083] Figure 5 It is the calculation error Δy in different azimuth angle intervals;

[0084] Figure 6 It is the calculation error of the azimuth angle and the elevation angle at the same angular resolution;

[0085] Figure 7 is the target ideal scattering point model;

[0086] Figure 8 is the display image of the target scattering point, where Figure 8 a is the one-dimensional range image of the target scattering point, Figure 8 b is the one-dimensional azimuth image of the target scattering point;

[0087] Figure 9 is the one-dimensional range image of the echo signal; where Figure 9 a is the one-dimensional range image of the sum of two fractional-order echo signals, Figure 9 b is the one-dimensional range image of the difference between two fractional-order echo signals;

[0088] Figure 10 is the two-dimensional imaging result of the target scattering point; where Figure 10 a is the two-dimensional imaging result obtained by using the first type of scattering point solution method for all target scattering points, Figure 10 b is the two-dimensional imaging result of the first type of scattering points divided according to the rough imaging result;

[0089] Figure 11 The average errors and average variances of the azimuth angle and elevation angle are statistically calculated under different signal-to-noise ratio conditions; where Figure 11 a is the average error of the elevation angle and azimuth angle under different signal-to-noise ratios, Figure 11 b is the average variance of the elevation angle and azimuth angle under different signal-to-noise ratios;

[0090] Figure 12 is the three-dimensional imaging result of the first type of scattering points;

[0091] Figure 13 is the two-dimensional imaging result of the second type of scattering points;

[0092] Figure 14 are the average error, average variance and mean square error of the elevation angle of the second scattering point; where Figure 14 a is the average error of the elevation angle under different signal-to-noise ratios, Figure 14 b is the average variance of the elevation angle under different signal-to-noise ratios, Figure 14 c is the average mean square error of the elevation angle under different signal-to-noise ratios;

[0093] Figure 15 is the three-dimensional imaging result of the target scattering point. Specific embodiments

[0094] The present invention will be further described below in conjunction with the accompanying drawings and examples of the present invention.

[0095] Three-dimensional imaging method for vortex electromagnetic wave radar combining integer-order and fractional-order modes, including

[0096] Step 1: Obtain the radar target echo data S with combined integer-order and fractional-order mode numbers based on the multiple-input multiple-output (MIMO) mode of a uniform circular array (UCA).

[0097] Step 2: Use the fast Fourier transform (FFT) to process the integer-order mode echo data S in to achieve "coarse imaging" of the radar target range-azimuth angle.

[0098] Step 3: According to the "coarse imaging" result, divide the scatter points into the first type of scatter points and the second type of scatter points with the range cell as the division object.

[0099] Step 4: Perform butterfly operations on the fractional-order echo data S fr to obtain its sum and difference echo data S add and S sub .

[0100] Step 5: Solve the elevation angle and azimuth angle of the first type of scatter points in the radar target through formulas (18) and (26) in sequence to achieve three-dimensional reconstruction of this type of scatter points.

[0101] Step 6: Use the azimuth angle information in the "coarse imaging" to solve the elevation angle information of the second type of scatter points in the radar target through formula (27) to achieve three-dimensional reconstruction of this type of scatter points.

[0102] Step 7: Integrate the first type of scatter points and the second type of scatter points in Steps 5 and 6 to achieve three-dimensional reconstruction of the radar target.

[0103] Specifically

[0104] Vortex electromagnetic waves can be generated by a circular array antenna. As Figure 2 shown, the UCA array is a circular planar array with a radius of a composed of N independent transceiver antenna elements, and the center of the UCA array is placed at the coordinate origin. The nth element of the UCA array is denoted as S n , and its corresponding transmitted signal is s n (t). If the signal of the nth element is phase-modulated, the modulation phase is then the transmitted signal of the nth element can be expressed as:[[]]

[0105]

[0106] where s(t) is a linear frequency modulation signal, K is the frequency modulation rate, T is the transmitted signal pulse width, f c is the signal center frequency, and α is the mode number. Then the transmitted signal s T (t) of the UCA array can be expressed as:[[]]

[0107]

[0108] Then for a spatial point where r p is the distance from point P to the origin O, and θ p is the angle between point P and the positive direction of the Z-axis, and is the angle between point P and the positive direction of the X-axis on the XOY plane. Based on the MIMO transceiver mode of the UCA array

[20] , the total echo signal received at point P can be expressed as:

[0109]

[0110] where τ p is the signal time delay and σ is the normalized scattering coefficient of point P, c is the speed of light, and k is the wave number. J α (·) is the Bessel function of the first kind of order α, and at this time α takes integer values. By performing amplitude modulation and phase modulation on the signals emitted by each independent array element of the UCA array, a vortex electromagnetic wave with a fractional-order mode number can be obtained. Similarly, for a spatial point its echo signal can be approximately expressed as:

[0111]

[0112] At this time, the mode number α takes non-integer values. From formulas (3) and (4), it can be seen that for a radar target composed of M scattering points, its target echo can be uniformly expressed as:

[0113]

[0114] If the range of integer-order mode numbers generated by the UCA is [-l, l], and the fractional-order mode numbers are respectively then the echo signals of radar targets of different orders can be written in matrix form:

[0115] S = [s M (t, α1), s M (t, α2),..., s M (t, α 2l ), s M (t, α 1 / 2 ), s M (t, α -1 / 2 )] T (6)

[0116] Three-dimensional imaging method

[0117] According to formula (6), the echo data in S is distributed in a two-dimensional rectangular shape in the time-mode number domain. Using a two-dimensional fast Fourier transform can only obtain the two-dimensional imaging result of the radar target with respect to range-azimuth angle, and it does not have the ability to resolve the elevation angle of the radar target. To achieve the resolution of the target elevation angle and thus reconstruct the three-dimensional spatial structure of the radar target, first, a two-dimensional fast Fourier transform is applied to the integer-order echo data set to obtain the two-dimensional imaging result of the radar target with respect to range-azimuth angle. This imaging step is called "coarse imaging"; second, according to the imaging result of "coarse imaging", the target scattering points are divided into two categories with respect to range cells. The first type of scattering points can be separated in the range cell, and the second type of scattering points cannot be separated in the range cell, that is, there are two or more scattering points in a single range cell; finally, using the echo data of the th order mode number, the elevation angle information of the two types of scattering points is solved respectively, and then the three-dimensional spatial reconstruction of the radar target is realized.

[0118] "coarse imaging"

[0119] Select the echo signals of the integer-order radar target to form a new echo data matrix S in =[s M (t,α1),.....,s M (t,α 2l )] T , it can be analyzed that S in is still distributed in a two-dimensional rectangular shape in the fast time-mode number domain. First, select the center point P c of the imaging target area as the reference point. Then, the echo signals of the reference point P c at different mode numbers can be expressed as:

[0120]

[0121] where is the echo signal of the reference point P c at the nth order mode number. By performing matched filtering on S in in the range dimension, the range information of the radar target can be obtained. The data after matched filtering can be expressed as:

[0122] S Match =[s Match (t,α1),s Match (t,α2),...,s Match (t,α 2l )] T (8)

[0123] where psf t (t-τ p) is the point spread function. It can be seen from formula (8) that for S Match The azimuth angle of the radar target can be obtained by using the fast Fourier transform in the mode number domain. Then, through the above processing, the two-dimensional imaging result of the radar target with respect to range-azimuth angle can be obtained.

[0124] Taking the range cell as the object, the imaging result of the "coarse imaging" divides the target scatterers. If there is only one scatterer on a certain range cell, this type of scatterer is denoted as the first type of scatterer P'; conversely, if two or more scatterers are on the same range cell, this type of scatterer is denoted as the second type of scatterer P". Suppose there are L1 first-type scatterers and L2 second-type scatterers, then L1 + L2 = M.

[0125] Three-dimensional imaging

[0126] By processing the integer-order echo data, only the two-dimensional imaging result of the "coarse imaging" of the radar target can be obtained. To obtain the elevation angle information of the radar target, the mode number of the echo data constitutes the fractional-order echo data matrix S fr = [s M (t, α 1 / 2 ), s M (t, α -1 / 2 )] T . When the mode number α is 1 / 2, the first kind of Bessel function J α (·) can be expressed by elementary functions as:

[0127]

[0128] Then when the mode number the received radar target echo can be respectively expressed as:

[0129]

[0130] Taking the transmitted signal as the reference signal, for the echo signal at that time is de-chirped, and its expression in the difference frequency domain is obtained by using the fast Fourier transform:

[0131]

[0132] where R Δ = r p - r ref , because the reference signal is the transmitted signal, that is, r ref = 0, then R Δ = r p. That is to say, by sequentially using the dechirping frequency and the fast Fourier transform in the distance dimension, the distance information of the radar target can be solved. If the scattering points of the radar target are distributed in different range cells, each peak in the one-dimensional range profile represents a scattering point. According to formulas (13) and (14), at the amplitude of each scattering point on the one-dimensional range profile is:

[0133]

[0134] Dividing the amplitudes of the same range cell when the mode numbers are α 1 / 2 and α -1 / 2 can obtain:

[0135]

[0136] Then

[0137]

[0138] The target elevation angle information corresponding to different range cells can be solved through formula (18). Although the target azimuth angle has been obtained through coarse imaging processing, for fine imaging of the target, the azimuth angle of the target can be solved by the sum and difference of the echo signals of the modes. Performing a butterfly operation on the echo signals S at M (f, α 1 / 2 ), S M (f, α -1 / 2 ) represented by formulas (13) and (14), as shown in Figure 3 , where S add = S M (f, α 1 / 2 ) + S M (f, α -1 / 2 ), S sub = S M (f, α 1 / 2 ) - S M (f, α -1 / 2 ). Then the signal S add can be expressed as:

[0139]

[0140] Let Using Euler's formula to expand the exponential term can obtain:

[0141]

[0142] Then formula (19) can be further expressed as:

[0143]

[0144] If only the amplitude of the one-dimensional range profile is considered, the amplitude of the range profile in different range cells of formula (21) is:

[0145]

[0146] Similarly, it can be known that S sub can be expressed as:

[0147]

[0148] Then After the echo signal difference processing of, the amplitude of the range profile in different range cells of formula (23) is:

[0149]

[0150] Dividing the amplitudes in the same range cell of formulas (22) and (24), the square of the ratio can be expressed as:

[0151]

[0152] The elevation angle information of the radar target has been solved through formula (18). Then, by arranging formula (25), the expression of the target azimuth angle can be obtained:

[0153]

[0154] According to formulas (18) and (26), it can be known that by jointly processing the echo signals of the semi-odd mode numbers α 1 / 2 , α -1 / 2 , the azimuth angle and elevation angle information of the radar target can be solved.

[0155] However, the above signal processing flow is based on the premise that the scatterers are distributed in different range cells, that is, it is applicable to the first type of scatterers defined in the present invention. If the target scatterers belong to the second type of scatterers, the azimuth angle information obtained from the two-dimensional imaging result of "coarse imaging" needs to be used Express formula (26) as:

[0156]

[0157] As can be seen from Equation (27), by using the azimuth information of the "coarse image", the respective elevation angles of different scatterers on the same range bin can be solved, and the three-dimensional resolution ability for the second type of scatterers is achieved. Since the scatterers of the radar target must belong to the first type of scatterers or the second type of scatterers defined in the present invention, based on the above analysis, the three-dimensional reconstruction of the radar target can be realized through Equations (18), (26), and (27), except that the solution processes for different types of scatterers are different. By analyzing Equations (18), (26), and (27), it can be known that the elevation angle and azimuth angle of the target are obtained by using the amplitude of the range bin. However, the amplitude of the range bin is easily affected by factors such as noise and is unstable. Given that the range information of the target can be obtained through only one pulse, multiple pulses can be transmitted to obtain multiple sets of range information, and then the average value of the obtained range information can be calculated to reduce the influence of factors such as noise on the stability of the algorithm, as Figure 1 shown.

[0158] According to the above steps, the three-dimensional reconstruction of the radar target can be realized. Now, the resolutions of the method of the present invention for the target range, azimuth angle, and elevation angle will be specifically analyzed respectively. The method of the present invention realizes the solution of range information by using the FFT algorithm in the range dimension. Its range resolution depends on the point spread function and is inversely proportional to the signal transmission bandwidth B, and can be expressed as:

[0159]

[0160] Due to the different types of scatterers, there are also differences in the solution processes for the azimuth angle and elevation angle of the scatterers, and the scatterers need to be classified and analyzed. First, analyze the second type of scatterers. The azimuth angle of the second type of scatterers is obtained by performing a fast Fourier transform in the mode number domain. The azimuth resolution of its multiple transmit and receive mode can be expressed as:

[0161]

[0162] Using the obtained azimuth angle information of the scatterers, the elevation angle information of the scatterers is further solved through Equation (27). By analyzing Equation (27), it can be known that the elevation angle θ of the scatterers is solved through the arcsine function. Assuming that the required elevation angle resolution is ρ θ , then it is required that the calculation error Δx of the elevation angle satisfies:

[0163] Δx ≤ sin(θ + ρ θ ) - sinθ (30)

[0164] According to the properties of trigonometric functions, the value of Δx is different in different interval ranges of the elevation angle , as Figure 4 shown. From Figure 4It can be seen that when the pitch angle is small, the value of Δx is relatively large, and vice versa, the value of Δx is relatively small.

[0165] Next, analyze the first type of scatter points. Different from the second type of scatter points, the first type of scatter points utilizes the properties of Bessel functions of semi-odd orders. First, the pitch angle information of the scatter points is obtained by solving through formula (18). By comparing and analyzing formulas (18) and (27), it can be seen that the pitch angle information of the first type of scatter points is also obtained by solving through the arcsine function, so it is the same as the pitch angle of the second type of scatter points. Its pitch angle resolution depends on Δx and needs to satisfy formula (30). Secondly, after obtaining the pitch angle information of the first type of scatter points, the azimuth angle of the first type of scatter points can be solved through formula (26). Analyzing formula (26), it can be seen that the azimuth angle of the scatter points is obtained through the arctangent function. If the azimuth angle resolution is then the calculation error Δy of the azimuth angle needs to satisfy:

[0166]

[0167] Similarly, it can be known that the value of Δy is also different in different interval ranges of the azimuth angle at , as shown in Figure 5 . It can be seen from Figure 5 that when the azimuth angle is small, the value of Δy is small, which is opposite to the value of Δx corresponding to the pitch angle. Comparing the calculation errors of the azimuth angle and the pitch angle in different angular intervals under the same angular resolution, as shown in Figure 6 . It can be seen from Figure 6 that under the requirement of the same angular resolution, the requirement for the calculation error of the azimuth angle is significantly higher than that of the pitch angle. That is, on the premise of meeting the pitch angle resolution requirement, the azimuth angle resolution of the first type of scatter points is significantly better than the pitch angle resolution.

[0168] From the analysis of the three-dimensional reconstruction processing flow of the first type of scatter points, it can be seen that for the first type of scatter points, the azimuth angle information of the scatter points can be obtained in the "coarse imaging", and the same azimuth angle information of the scatter points can also be obtained during the three-dimensional reconstruction process. From the solution process of the azimuth angle information, the resolution of the azimuth angle obtained in the "coarse imaging" process should satisfy formula (29), which is related to the range of the modes experienced by the target; the resolution of the azimuth angle obtained during the three-dimensional reconstruction process should satisfy formula (31), which is related to the calculation error of the angle. When the calculation error of the angle meets certain conditions, especially when the azimuth angle is large, the azimuth angle resolution of the first type of scatter points by the method of the present invention is higher than the azimuth angle resolution of the "coarse image".

[0169] Experimental simulation

[0170] Assume that the UCA array consists of 50 array elements, the center of the array is placed at the origin of coordinates, the radius of the array is 0.1 m, the range of integer-order mode numbers is [-20, 20], and the fractional-order mode number is The transmitted signal is a chirp signal with a center carrier frequency of 10 GHz and a signal bandwidth of 100 MHz. There are 7 independent scatterers in the target area, as Figure 7 shown, and the coordinates of the 7 independent scatterers in the rectangular coordinate system are P1(80, 100, 250), P2(140, 100, 200), P3(150, 150, 190), P4(120, 120, 180), P5(120, 150, 120), P6(220, 80, 60), P7(220, 60, 80).

[0171] Coarse imaging result

[0172] Using the integer-order echo data S in , by performing fast Fourier transform in the fast-time domain and the mode number domain respectively, the distance and azimuth angle information of the target scatterers can be solved, as Figure 8 shown. It can be seen from Fig. a that by converting the 7 scatterers from the rectangular coordinate system to the spherical coordinate system, the distances of scatterers P6 and P7 from the center O of the UCA array are the same, both being 241.66 m, and the distances of the other 5 scatterers from the center O of the UCA array are different, that is, the 7 independent scatterers are distributed on 6 different range cells. From Figure 8 Fig. b, it can be seen that under the simulation conditions, the azimuth resolution meets the requirement of distinguishing the azimuth angles of 7 independent scatterers. Through the above processing, the coarse imaging result of the target scatterers can be obtained. From the coarse imaging result, the 5 scatterers from P1 to P5 are distributed on different range cells respectively, and there is only a unique scatterer on the range cell, meeting the conditions of the first type of scatterers; scatterers P6 and P7 are distributed on the same range cell, meeting the conditions of the second type of scatterers. Through the above analysis, P1 to P5 are classified as the first type of scatterers, and P6 and P7 are classified as the second type of scatterers.

[0173] Fractional-order echo processing

[0174] According to the coarse imaging result, the target scatterers are divided into two types of scatterers. To further solve the elevation angle information of the target scatterers, first, the echo data with the mode number of is demodulated, and then the butterfly operation as Figure 2 shown is performed on the two fractional-order echo data to obtain S add and S sub respectively. As Figure 9 shown, where Figure 9 Fig. a is the one-dimensional range image of the sum S add of the two fractional-order echo signals, Figure 9b is the difference S between two fractional - order echo signals sub of the one - dimensional range profiles. It can be seen from Figure 9 that the distribution of the target scattering points in the range cells of S add is the same as that in its one - dimensional range profile, but the amplitudes of the range cells are different. By using the amplitude difference of the same range cells between S sub and S add and combining the characteristics of the fractional - order Bessel function, the elevation angle information of the target scattering points can be solved. sub

[0175] Reconstruction of the elevation angle and azimuth angle of the first - type scattering points

[0176] According to the three - dimensional reconstruction process of the first - type scattering points, using the echo signal S with the fractional - order of the mode number M (f,α ±1 / 2 ), the sum signal S add and the difference signal S sub of the two fractional - order signals, and combining the characteristics of the fractional - order of the Bessel function, the elevation angle and azimuth angle of the target scattering points are solved according to formulas (18) and (26). Since the two - dimensional angle - solving method proposed in this paper uses the amplitude information of the range cells for solving, the amplitude information of the signal is vulnerable to interference and fluctuates. From the ranging principle of the target, the radar can obtain the range information of the target scattering points using only one pulse. The method of averaging the range - amplitude information of multiple pulses can be used to reduce the interference of amplitude fluctuations and thus improve the accuracy of the two - dimensional angle reconstruction of the target. Under the condition of a signal - to - noise ratio of 5 dB, 1000 pulses are transmitted to range the target scattering points and average them. According to the imaging process of the first - type scattering points, the two - dimensional imaging results of the target scattering points are solved, as shown in Figure 10 . Among them Figure 10 a is the two - dimensional imaging result obtained by using the first - type scattering point solving method for all target scattering points Figure 10 b is the two - dimensional imaging result of the first - type scattering points divided according to the rough imaging result.

[0177] It can be seen from Figure 10 a and Figure 10 b that the reconstruction method for the first - type scattering points in this paper can accurately reconstruct this type of scattering points. However, for the second - type scattering points P6 and P7, only the azimuth angle and elevation angle information can be solved at the same range cells, and the solved elevation angle and azimuth angle information is not the true information of the target. That is to say, if the target scattering points are not classified, only using the first - type scattering point reconstruction method, there is no resolution ability for the second - type scattering points in the azimuth angle dimension and elevation angle dimension.

[0178] ​Meanwhile, consider the accuracy of reconstructing the elevation angle and azimuth angle of the first type of scatterers under different signal-to-noise ratio (SNR) conditions. Assume the SNR range is from -10 dB to 15 dB, and the average errors and average variances of the azimuth angle and elevation angle are respectively statistically calculated, as Figure 11 shown. Among them, Figure 11 a is the average error of the elevation angle and azimuth angle under different SNRs, Figure 11 b is the average variance of the elevation angle and azimuth angle under different SNRs. It can be seen from Figure 11 that above an SNR of -5 dB, the accuracy of reconstructing the elevation angle and azimuth angle of the first type of scatterers is relatively stable. The maximum variance of the azimuth angle does not exceed 0.001π, and the maximum variance of the elevation angle does not exceed 0.005π. By comparison, it is found that under the condition of the same calculation error, the estimation accuracy of the target azimuth angle is significantly better than that of the target elevation angle.

[0179] After realizing the two-dimensional angle reconstruction of the first type of scatterers and combining with the one-dimensional range profile of the scatterers, the three-dimensional reconstruction of the first type of scatterers can be achieved, as Figure 12 shown. It can be seen from Figure 12 that the three-dimensional imaging method for the first type of scatterers in this paper can relatively accurately achieve the three-dimensional reconstruction of this type of scatterers.

[0180] Reconstruction of the elevation angle and azimuth angle of the second type of scatterers

[0181] According to the above analysis and simulation experiment results, the three-dimensional reconstruction method for the first type of scatterers is not applicable to the second type of scatterers. Then, for the three-dimensional reconstruction of the second type of scatterers, it is necessary to make full use of the distance r and azimuth angle of the second type of scatterers obtained from the rough imaging result Use formula (27) to solve the elevation angle of the scatterers, and then distinguish the scatterers distributed in the same range cell but with different azimuth angles to achieve the three-dimensional reconstruction of the second type of scatterers. Under the condition of an SNR of 5 dB, still emit 1000 pulses to measure the distance of the target scatterers and take the average, and then according to the imaging process of the second type of scatterers, solve the elevation angle of the target scatterers, as Figure 13 shown. It can be seen from Figure 13 that P6 and P7 are in the same range cell but have different azimuth angles. The three-dimensional imaging method for the second type of scatterers in this paper is used to solve the elevation angles of the two scatterers P6 and P7.

[0182] Similar to the reconstruction method for the first type of scatterers, the reconstruction method for the second type of scatterers also utilizes the amplitude information of the range profile. This requires considering the accuracy of the method for solving the target elevation angle of the second type of scatterers under different SNR conditions at the same time. Assume the SNR range is from 0 dB to 15 dB, and the average error, average variance, and mean square error of the elevation angle are respectively statistically calculated, asFigure 14 as shown. Among them Figure 14 a is the average error of the pitch angle under different signal-to-noise ratios, Figure 14 b is the average variance of the pitch angle under different signal-to-noise ratios, Figure 14 c is the average mean square error of the pitch angle under different signal-to-noise ratios. It can be seen from Figure 14 that above a signal-to-noise ratio of 5 dB, for the second type of scatterers, the accuracy of pitch angle and azimuth angle reconstruction is relatively stable. The maximum average variance of the pitch angle does not exceed 0.005π, the maximum average error does not exceed 0.05π, and the maximum average mean square error does not exceed 0.002. Compared with the first type of scatterers, the reconstruction error of the pitch angle of the second type of scatterers is larger. The azimuth resolution of the second type of scatterers depends on the mode number range, while the azimuth resolution of the first type of scatterers mainly depends on the calculation error of the radar.

[0183] Target three-dimensional image reconstruction

[0184] According to the rough imaging result, the scatterers are divided into the first type of scatterers and the second type of scatterers. Combining the range image and azimuth image information obtained from the rough imaging, the pitch angles of the two types of scatterers are solved according to different imaging processes, so as to realize the three-dimensional reconstruction of the radar target, as Figure 15 shown. It can be seen from Figure 15 that the three-dimensional reconstruction method of vortex electromagnetic wave combining integer-order and fractional-order modes proposed in this paper can better realize the three-dimensional reconstruction of 77 scatterers from P1 to P77.

[0185] The beneficial effects of the present invention are as follows: The three-dimensional reconstruction of the radar target is realized through two-stage imaging processing of the vortex electromagnetic wave by combining integer-order and fractional-order mode numbers. The scatterers of the radar target are divided according to the rough imaging result, and at the same time, the properties of the fractional-order Bessel function are utilized to realize the pitch angle resolution for different types of scatterers. The simulation experiment shows the effectiveness of the three-dimensional reconstruction method of vortex electromagnetic wave proposed in the present invention. Compared with the two-dimensional imaging method of vortex electromagnetic wave, the method of the present invention does not increase the requirement for the number of array elements and the complexity of the array structure, providing a new technical approach for three-dimensional imaging based on vortex electromagnetic wave.

Claims

1. A three-dimensional imaging method for a vortex electromagnetic wave radar based on integer-order and fractional-order modes, comprising the following steps: Step 1: Obtain radar target echo data with combined integer-order and fractional-order mode numbers based on the multiple-transmission and multiple-reception mode of a UCA; Step 2: Process the integer-order mode echo data using a fast Fourier transform to achieve "coarse imaging" of the radar target's range-azimuth angle; Step 3: According to the "coarse imaging" result, divide the scattering points into the first type of scattering points and the second type of scattering points with the range cell as the division object; Step 4: Perform a butterfly operation on the fractional-order echo data to obtain the sum and difference of its echo data; Step 5: Solve the elevation angle and azimuth angle of the first type of scattering points in the radar target in sequence to achieve three-dimensional reconstruction of this type of scattering points; Step 6: Use the azimuth angle information in the "coarse imaging" to solve the elevation angle information of the second type of scattering points in the radar target to achieve three-dimensional reconstruction of this type of scattering points; Step 7: Fuse the first type of scattering points and the second type of scattering points in Steps 5 and 6 to achieve three-dimensional reconstruction of the radar target.

2. The three-dimensional imaging method of a vortex electromagnetic wave radar based on integer-order and fractional-order modes according to claim 1, characterized in that: The specific content of Step 1 includes the following steps: Assume that the vortex electromagnetic wave is generated by a UCA array, where the UCA array is a circular planar array with a radius of a composed of N independent transceiver antenna elements. The center of the UCA array is placed at the origin of coordinates, and the nth element of the UCA array is denoted as S n , and its corresponding transmitted signal is s n (t); if the signal of the nth element is phase - modulated, and its modulation phase is then the transmitted signal of the nth element is expressed as: where \(s(t)\) is a chirp signal, \(K\) is the frequency modulation rate, \(T\) is the pulse width of the transmitted signal, \(f\) c is the center frequency of the signal, \(\alpha\) is the number of modes, \(t\) is the fast time, and \(j\) is the imaginary unit; then the transmitted signal \(s\) T (t) is expressed as: Then for a spatial point where r p is the distance from point P to the origin O, θ p is the angle between point P and the positive direction of the Z-axis, is the angle between point P and the positive direction of the X-axis on the XOY plane. Based on the MIMO transceiver mode of the UCA array, the total echo signal received at point P is expressed as: where τ p is the signal time delay and σ is the normalized scattering coefficient of point P, c is the speed of light, k is the wave number, J α (·) is the Bessel function of the first kind of order α, where α takes integer values at this time; by performing amplitude modulation and phase modulation on the signals emitted by each independent array element of the UCA array, a vortex electromagnetic wave with a fractional mode number can be obtained. Similarly, for a spatial point its echo signal can be approximately expressed as: At this time, the value of the mode number α is non-integer; it can be seen from Formulas (3) and (4) that for a radar target composed of M scattering points, its target echo is uniformly expressed as: If the integer-order mode numbers generated by the UCA range from [-l, l], and the fractional-order mode numbers are respectively Then the echo signals of radar targets with different orders are written in matrix form: S = [s M (t, α1), s M (t, α2),..., s M (t, α 2l ), s M (t, α 1 / 2 ), s M (t, α -1 / 2 )] T (6).

3. The three-dimensional imaging method of a vortex electromagnetic wave radar based on integer-order and fractional-order modes according to claim 1, characterized in that: The specific content of Step 2 includes the following steps: Select the radar target echo signals of integer orders to form a new echo data matrix S in =[s M (t,α1),.....,s M (t,α 2l )] T , It can be analyzed that S in still shows a two-dimensional rectangular distribution in the fast time-mode number domain; First, select the center point P c of the imaging target area as the reference point, then the echo signals of the reference point P c at different mode numbers are expressed as: S Pc = [s Pc (t, α1), s Pc (t, α2),..., s Pc (t, α 2l )] T (7) Among them When it is the nth order mode number, the reference point P c The echo signal of; By performing matched filtering on S in the range dimension in The distance information of the radar target is obtained; The data after matched filtering is expressed as: S Match = [s Match (t, α1), s Match (t, α2),..., s Match (t, α 2l )] T (8) Among them psf t (t - τ p ) is the point spread function; it can be seen from formula (8) that for S Match The azimuth angle of the radar target is obtained by using the fast Fourier transform in the mode number domain; then the two-dimensional imaging result of the radar target with respect to range-azimuth angle is obtained through the above processing.

4. The three-dimensional imaging method of a vortex electromagnetic wave radar based on integer-order and fractional-order modes according to claim 1, characterized in that: The specific content of Step 3 includes the following steps: Divide the target scattering points according to the "coarse imaging" result with the range cell as the object. If there is only a single scattering point on a certain range cell, then this type of scattering point is denoted as the first type of scattering point P′; conversely, if two or more scattering points are on the same range cell, then this type of scattering point is denoted as the second type of scattering point P″; Assume there are L1 first type of scattering points and L2 second type of scattering points, then L1 + L2 = M.

5. The three-dimensional imaging method of the vortex electromagnetic wave radar based on integer-order and fractional-order modes according to claim 1, characterized in that: The specific content of Step 4 includes the following steps: By processing the integer-order echo data, only a two-dimensional imaging result of "coarse imaging" of the radar target is obtained. To obtain the elevation angle information of the radar target, the echo data with the mode number constitute the fractional-order echo data matrix S fr = [s M (t, α 1 / 2 ), s M (t, α -1 / 2 )] T ; when the mode number α is 1 / 2, the first-kind Bessel function J α (·) can be expressed by elementary functions as: where z is the variable of the Bessel function; Then when the number of modes the received radar target echoes are respectively expressed as: Using the transmitted signal as the reference signal, the linear frequency modulation of the echo signal at is solved, and its expression in the difference frequency domain is obtained by using the fast Fourier transform: where R Δ = r p - r ref , r p is the distance from point P to the origin O, and r ref is the transmitted signal; since the reference signal is the transmitted signal, i.e., r ref = 0, then R Δ = r p ; this means that the dechirping and fast Fourier transform are sequentially used in the distance dimension to solve the distance information of the radar target; if the radar target scattering points are distributed in different range cells, each peak of the one-dimensional range profile represents a scattering point. According to formulas (13) and (14), it can be known that at the amplitude of each scattering point on the one-dimensional range profile is: Divide the amplitudes of the same range cell when the number of patterns is α 1 / 2 and α -1 / 2 to obtain: then The target elevation angle information corresponding to different range cells is solved through Formula (18); Although the target azimuth angle has been obtained through rough imaging processing, for fine imaging of the target, the sum and difference of the echo signals in the mode are used to solve the azimuth angle of the target; the echo signals S at M (f,α 1 / 2 ) and S M (f,α -1 / 2 ) are subjected to butterfly operations, where S add = S M (f,α 1 / 2 ) + S M (f,α -1 / 2 ), and S sub = S M (f,α 1 / 2 ) - S M (f,α -1 / 2 ); then the signal S add is expressed as: Let Expand the exponential term using Euler's formula to obtain: then Formula (19) can be further expressed as: If only considering the amplitude of the one-dimensional range image, the amplitude of the range image in different range cells of Formula (21) is: Similarly, it can be known that S sub is expressed as: Then After the echo signal difference processing of, the amplitude of the range profile in different range cells of formula (23) is as follows: Divide the amplitudes within the same range cell of Formulas (22) and (24), and the square of the ratio is expressed as:

6. The three-dimensional imaging method of the vortex electromagnetic wave radar based on integer-order and fractional-order modes according to claim 1, wherein: The specific content of Step 5 includes the following steps: Since the elevation angle information of the radar target has been solved through Formula (18), then Formula (25) is sorted out to obtain the expression of the target azimuth angle: According to formulas (18) and (26), it can be seen that by jointly processing the echo signals of the semi-odd mode numbers α 1 / 2 , α -1 / 2 , the azimuth and elevation angle information of the radar target can be solved and obtained.

7. The three-dimensional imaging method of the vortex electromagnetic wave radar based on integer-order and fractional-order modes according to claim 1, characterized in that: The specific content of Step 6 includes the following steps: The above signal processing flow is based on the premise that the scatterers are distributed in different range cells, that is, it is applicable to the defined first type of scatterers; if the target scatterer belongs to the second type of scatterers, the azimuth information obtained from the two-dimensional imaging result of "coarse imaging" needs to be used. Express formula (26) as: It can be seen from Formula (27) that by using the azimuth angle information of the "coarse imaging", the respective elevation angles of different scattering points on the same range cell are solved.

8. The three-dimensional imaging method of the vortex electromagnetic wave radar based on integer-order and fractional-order modes according to claim 1, characterized in that: The specific content of Step 7 includes the following steps: Because the scattering points of the radar target must belong to the defined first type of scattering points or the second type of scattering points, combined with the above analysis, three-dimensional reconstruction of the radar target is achieved through Formulas (18), (26), and (27).

Images