A 3D imaging method for vortex electromagnetic wave radar based on bistatic mode

Abstract

A three-dimensional imaging method of a vortex electromagnetic wave radar based on a bistatic mode. Step 1: A rectangular coordinate system is constructed with the center of the UCA as the origin. Then, two independent transmitting array elements are set at different positions on the positive X-axis direction, and two transceiver channels TR1 and TR2 are respectively formed with the UCA receiving unit. Step 2: The echo signals of the two dual transceiver channels TR1 and TR2 are respectively subjected to matched filtering in the range dimension to reconstruct the one-dimensional range image of the target. Step 3: The Hilbert transform is respectively used for the two dual transceiver channels TR1 and TR2 in the mode number domain to eliminate the influence of the square term of the Bessel function, and then the FFT transform is used to reconstruct the one-dimensional azimuth image. Step 4: The ranges obtained from TR1 and TR2 and the azimuth are combined to solve the true range and elevation angle of the target, and the three-dimensional coordinates of the target space are reconstructed. It can achieve high resolution for small elevation angle targets without increasing the complexity of the array structure, and the computational amount of the method is significantly better than that of the MUSIC algorithm.

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 based on a bistatic mode. Background Art

[0002] With the diversification of radar target detection requirements, new radar imaging technologies have emerged continuously in the past ten-odd years. Among them, the radar imaging technology based on vortex electromagnetic waves has received extensive attention. Especially in the past ten-odd years, a large number of research results have emerged in the vortex electromagnetic wave imaging technology. "Electromagnetic Vortex Based Radar Target Imaging" published by Guo G R, Hu W D, and Du X Y in the 6th issue of "Journal of University of Defense Technology" in 2013 discloses the experimental verification of the resolution ability of vortex electromagnetic waves for the azimuth angle of radar targets by using the duality relationship between the mode number and the azimuth angle. After that, it is also disclosed that only high-resolution imaging of the azimuth angle of radar targets is achieved by using the Fast Fourier Transform (FFT for short), and the two-dimensional imaging results of the targets are reconstructed, but there is no resolution ability in the elevation angle dimension. "Super-resolution orbital angular momentum based radar targets detection" published by Lin M et al. in the 13th issue of "Electronics Letters" in 2016 discloses that the MUSIC algorithm is used to further improve the azimuth angle resolution of radar targets, and the two-dimensional resolution ability of the azimuth angle and elevation angle of the targets is achieved through two-dimensional space search. However, due to the problem of scatterer correlation, three-dimensional imaging of radar targets cannot be achieved, and the number of array elements of its Uniform Circular Array (UCA for short) receiving unit is very large. In the prior art, the single-station transceiver mode based on the uniform circular array can only achieve two-dimensional imaging of radar targets, but cannot achieve three-dimensional imaging. The three-dimensional imaging results can obtain the relative position, size, and scattering information of the targets in three-dimensional space, providing richer characteristic information for subsequent target recognition. How to achieve three-dimensional imaging of radar targets based on vortex electromagnetic waves and, while reducing the requirement for the number of array elements of the UCA, maintaining the imaging resolution is a problem. Summary of the Invention

[0003] The purpose of the present invention is to overcome the deficiencies in the above-mentioned prior art and propose a three-dimensional imaging method for a vortex electromagnetic wave radar based on a bistatic mode.

[0004] The present invention is realized in the following manner:

[0005] A three-dimensional imaging method of a vortex electromagnetic wave radar based on a bistatic mode, comprising the following steps:

[0006] Step 1: Construct a rectangular coordinate system with the center of the UCA as the origin. Then, set two independent transmitting array elements at different positions on the positive X-axis direction, and respectively form two transceiver channels TR1 and TR2 with the UCA receiving unit;

[0007] Step 2: Adopt matched filtering for the echo signals of the two transceiver channels TR1 and TR2 in the range dimension respectively to reconstruct the one-dimensional range image of the target;

[0008] Step 3: Use the Hilbert transform for the two transceiver channels TR1 and TR2 in the mode number domain respectively to eliminate the influence of the square term of the Bessel function, and then adopt FFT transform to reconstruct the one-dimensional azimuth image;

[0009] Step 4: Combine the ranges and azimuths obtained by TR1 and TR2 and solve for the true range and elevation angle of the target, reconstruct the three-dimensional coordinates of the target space, and form a three-dimensional image.

[0010] Further, the specific steps of Step 1 include the following steps:

[0011] Construct a rectangular coordinate system with the center of the UCA as the origin. The receiving unit is a UCA array, the center of the array is located at the coordinate origin O, the radius of the array is b, and the array is composed of N identical independent array elements S n The transmitting unit is an independent omnidirectional antenna located at the center of the UCA array, that is, at the coordinate origin O. Let the transmitted signal of the transmitting array element O be a linear frequency modulation signal, that is, Linear Frequency Modulation, abbreviated as LFM, denoted as s(t). Let P be an arbitrary independent scattering point in space, denoted as P(r,θ,φ). The target echo signal received by the UCA receiving unit can be expressed as:

[0012] s N (t, l) = σJ l (kbsinθ)s(t - τ)·e jlφ (1)

[0013] where σ is the radar target scattering coefficient, τ is the signal time delay and c is the speed of light, R n is the space propagation distance, l is the mode number, t is the fast time, J l is the l-th order Bessel function of the first kind, k is the range spatial frequency, θ is the elevation angle of the radar target, j is the imaginary number, φLet \(\theta\) be the azimuth of the radar target and \(r\) be the distance to the radar target. At this time, the angle \(\beta\) between the transmission path \(OP\) and the reception path \(SP\) is small, and it can be approximated as a monostatic transceiver mode. The spatial propagation distance \(R\) is approximately \(2r\), so the signal time delay \(\tau=\frac{R}{c}\). n From formula (1), it can be seen that by using the fast Fourier transform in the fast time domain and the mode number domain respectively, the distance \(r\) and azimuth angle \(\varphi\) of the target scattering point \(P\) can be obtained, but the target elevation angle \(\theta\) cannot be calculated from the amplitude term of the echo signal. n Approximately \(2r\), then the signal time delay \(\tau\) From formula (1), it can be seen that by using the fast Fourier transform in the fast time domain and the mode number domain respectively, the distance \(r\) and azimuth angle \(\varphi\) of the target scattering point \(P\) can be obtained, while the target elevation angle \(\theta\) cannot be calculated from the amplitude term of the echo signal.

[0014] Move the transmitting array element from point \(O\) to point \(O'\) on the positive \(x\)-axis. The distance between \(O'\) and the coordinate origin \(O\) is \(d\). Assume that the signal transmitted by the transmitting array element is still the LFM signal \(s(t)\). Then the echo signal received by the array element \(S\) in the receiving unit from the spatially independent point \(P\) can be expressed as: n The echo signal received by the array element \(S\) from the spatially independent point \(P\) can be expressed as:

[0015]

[0016] where \(\tau\) n is the signal propagation time delay, expressed as \(\tau\) n \(=\frac{R}{c}\), \(R_n\) is the signal spatial propagation distance, \(T\) n is the LFM signal pulse width, \(K\) is the chirp rate, p and \(\alpha\) is the angle between the array element \(S\) n and the positive \(x\)-axis in the \(XOY\) plane.

[0017] is the transmitted signal pulse. Then the total echo received by the UCA array composed of \(N\) independent array elements can be expressed as:

[0018] The total echo received by the UCA array composed of \(N\) independent array elements can be expressed as:

[0019]

[0020] The angle \(\beta'\) between the transmission path \(O'P\) and the reception path \(SP\) is large, so it should be a bistatic transceiver mode. The signal propagation distance \(R\) n can be expressed as \(R = R_1+R_2\), where \(R_1\) is the distance from \(O'\) to point \(P\) and \(R_2\) is the distance from point \(P\) to the \(n\)th receiving array element \(S\) in the UCA array. Let the unit vector \(\vec{e}\) n in the direction of the line \(OP\) be expressed as: n \(R = R_1+R_2\), where \(R_1\) is the distance from \(O'\) to point \(P\) and \(R_2\) is the distance from point \(P\) to the \(n\)th receiving array element \(S\) in the UCA array. Let the unit vector \(\vec{e}\) n in the direction of the line \(OP\) be expressed as: in the direction of the line \(OP\) is expressed as:

[0021]

[0022] where is the unit vector in the \(x\)-axis direction, is the unit vector in the \(y\)-axis direction, is the z-axis direction vector, and the straight-line vector from the origin O to the element S in the UCA array n can be expressed as The straight-line vector from point O' to point P can be expressed as where d is the distance between the transmitting element and the coordinate origin, then the distance R1 from O' to P and the distance R2 from P to the element S n are respectively expressed as:

[0023]

[0024]

[0025] According to formulas (5) and (6), the total received echo of the UCA array is expressed as:

[0026]

[0027] where τ′ = R′ / c, and R′ = 2r + dsinθcosφ; let According to the Janoci-Anger formula, s(n) can be expressed as:

[0028]

[0029] where J m (·) is the Bessel function of the first kind of order m. Since has a value only when l - m is an integer multiple of N and is equal to N; at the same time, in the case of a relatively large N, the amplitude of the Bessel function J m (·) when it is of order l is much larger than the amplitudes of other orders. Formula (8) can be approximately expressed as:

[0030] s(n) = Nj l J l (kbsinθ)e jlφ (9)

[0031] Then the echo received by the UCA array is further expressed as:

[0032] s N (t, l) = σ′J l (kbsinθ)s(t - τ′)·e jlφ (10)

[0033] where the scattering coefficient is σ′ = σNj l, According to formula (10), it can be known that the echo sampling data of the target point P in the bistatic mode is still distributed in a two-dimensional rectangle in the frequency-mode number domain. Performing a two-dimensional Fourier transform on it can obtain the range-azimuth angle information of the target; comparing with the echo model of the target point P in the monostatic mode expressed by formula (1), it can be seen that the azimuth angle φ solved in the bistatic mode remains unchanged, and the range changes from r to

[0034] Assume that the radar target consists of M scattering points, denoted as P m (r m , θ m , φ m ). The transmitted signal is an LFM signal s(t). Using the designed bistatic mode, the echo signal received by the UCA array can be expressed as:

[0035]

[0036] where the normalized scattering coefficient of the target σ = σ m j l NJ l (kbsinθ m ), the time delay τ m = R m / c, R m = 2r m + dsinθ m cosφ m ;

[0037] Increase the transmitting element from one element to two elements, that is, set another transmitting element in the positive direction of the X-axis. This element is located at O″ and is at a distance d′ (d′≠d) from the center of the UCA; at this time, the transmitting element located at O′ and the UCA receiving array form a signal transceiver channel 1, denoted as TR1; the transmitting element located at O″ and the UCA receiving array form a signal transceiver channel 2, denoted as TR2.

[0038] Furthermore, the specific steps of step two include the following steps:

[0039] Since the signals of TR1 and TR2 are orthogonal in frequency, process the signals of the two channels TR1 and TR2 respectively as described in step one to obtain the one-dimensional range profiles of the two channels TR1 and TR2;

[0040] Matched filtering is used for the echo signals of the two dual transceiver channels TR1 and TR2 in the distance dimension. The echo signals are distributed in a two-dimensional rectangular shape in the frequency-mode number domain. Assuming the center point of the target area is P0 (r0, θ0, φ0), the echo of P0 received by the UCA array is s0 (t, l). The echo s0 (t, l) of P0 is used as the reference signal. Matched filtering is used to reconstruct the target in the distance dimension. The reconstructed echo signal can be expressed as:

[0041]

[0042] in psf t (·) is the time domain point spread function; From formula (12), we can know that the reconstructed echo signal s Match (t,l) to get the distance information R m ; Using the dual relationship between the mode number l and the azimuth angle φ, the azimuth angle φ can be obtained by fast Fourier transform in the mode number domain m , but because the echo signal amplitude term contains a Bessel function related to the mode number, its influence on the azimuth image needs to be considered; it is known that when kb sinθ>>1, the Bessel function can be approximately expressed as:

[0043]

[0044] From formula (13), we can see that the Fourier transform result of the Bessel function in the mode number domain will form a zero point at its zero frequency and The narrow-band spectrum components are symmetrically distributed at the frequencies, and the frequency displacement is independent of the pitch angle θ; therefore, the amplitude term J l (kbsinθ m )J l (kbsinθ0) is approximately J l 2 (kbsinθ0), then the amplitude term of the vortex electromagnetic wave echo signal contains the Bessel function J l The square term of (·).

[0045] Further, the step three specifically includes the following steps:

[0046] First, the echo signal is subjected to Hilbert transform, and then the echo signal is subjected to Fast Fourier Transform in the mode number domain. The displacement is effectively eliminated, and only the real azimuth angle information of the target exists in the azimuth image imaging result;

[0047] After the above processing in the frequency-mode number domain, the two-dimensional imaging results of range and azimuth can be obtained. According to formula (12), the azimuth angle obtained by solving is equal to the azimuth angle φ of the target scattering point.m Same, distance R m Not equal to the distance r of the target scattering point m Instead, it contains the three-dimensional spatial information of the target scattering point; from the expression Looking at it, d is a known quantity, and at the same time, the target azimuth angle φ m Can also be solved, then the distances of M target scattering points can be expressed as:

[0048] r + A·θ = R (14)

[0049] Where r = [r1, r2, … r m T Is the distance vector of the target scattering point, Is the weight coefficient vector of the equation system, θ = [sinθ1, sinθ2, … sinθ m Is the vector about the elevation angle of the scattering point, R = [R1, R2, … R m T Is the distance vector to be solved;

[0050] Channel TR1 and channel TR2 satisfy the orthogonal relationship in frequency. The center carrier frequencies of the transceiver channels are f1 and f2 respectively. For the echo data of TR2, the above processing method is adopted, and the target distance R m ′ and the azimuth angle φ m , where For channel TR2, the distances of M scattering points can be expressed as:

[0051] r + A′·θ = R′ (15)

[0052] Where Where R′ = [R1′, R2′, … R m ′] T ;

[0053] Combining formulas (14) and (15) can solve the elevation angle of the target as:

[0054]

[0055] After solving the target elevation angle θ = [sinθ1, sinθ1, …, sinθ m , solve the target distance r through formula (14) or (15).

[0056] Furthermore, the specific steps of step four include the following steps:

[0057] For the three-dimensional reconstruction of the target scattering point, it is necessary to solve the distance and elevation angle of the target scattering point from formula (14); for M target scattering points, M groups of (r m , φ​​m ) From formulas (14)-(16), it can be seen that the target distance information R contains the target three-dimensional coordinate information. On the premise that the azimuth angle is resolvable, the resolution ability of the elevation angle depends on the target distance resolution. If it is required that the resolution of the elevation angle is not less than Δθ, then it is necessary to satisfy:

[0058] Δx = sin(θ m + Δθ) - sinθ m ≥ρ R (17)

[0059] Given the distance resolution where B is the bandwidth of the transmitted signal, it can be known that the resolution of the elevation angle is inversely proportional to the signal bandwidth. If the resolution of the elevation angle is Δθ, then the bandwidth B of the transmitted signal needs to satisfy Considering that the value of Δx is different in different interval ranges of the elevation angle θ ; the azimuth angle of the target scattering point has been obtained through the mode number domain fast Fourier transform and the actual distance r and elevation angle θ of the target scattering point are solved according to formulas (14)-(17) to reconstruct the three-dimensional imaging result of the target scattering point in the spherical coordinate system.

[0060] The beneficial effects of the present invention are as follows: The vortex electromagnetic wave radar adopts a bistatic transceiver mode and has the ability to resolve the elevation angle of the radar target, realizing three-dimensional imaging of the radar target. The method of this patent can achieve high resolution for small elevation angle targets without increasing the complexity of the array structure, and the computational amount of the method is significantly better than that of the MUSIC algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is a flowchart of the present invention;

[0062] Figure 2 is a vortex electromagnetic wave transceiver model diagram based on a UCA array;

[0063] Figure 3 is a spectrum diagram of the square Bessel function;

[0064] Figure 4 is an elevation angle resolution diagram in different elevation angle intervals;

[0065] Figure 5 is a one-dimensional distance imaging diagram, Figure 5 a is the one-dimensional distance imaging in the monostatic mode, Figure 5 b is the one-dimensional distance imaging of channel TR1 in the bistatic mode, Figure 5 c is the one-dimensional distance imaging of channel TR2 in the bistatic mode;

[0066] Figure 6 is a distance-azimuth angle imaging result diagram in the bistatic mode,Figure 6 a is the range-azimuth imaging result of the transceiver channel TR1, Figure 6 b is the range-azimuth imaging result of the transceiver channel TR2;

[0067] Figure 7 is the target range-elevation angle imaging result diagram;

[0068] Figure 8 is the elevation angle simulation result diagram when the range dimension error is different unit range cells;

[0069] Figure 9 is the relationship diagram between elevation angle resolution and range dimension resolution;

[0070] Figure 10 is the three-dimensional imaging result diagram. Specific implementation manner

[0071] The present invention will be further described below in conjunction with the accompanying drawings and examples of the present invention.

[0072] A vortex electromagnetic wave bistatic three-dimensional imaging method, the specific steps are as follows:

[0073] Step 1: Construct a rectangular coordinate system with the center of the UCA array as the origin, and then set two independent transmitting array elements at different positions on the positive X-axis direction, and respectively form transceiver channels TR1 and TR2 with the UCA receiving unit;

[0074] Step 2: Adopt matched filtering for the echo signals of TR1 and TR2 in the range dimension respectively to reconstruct the target one-dimensional range image R;

[0075] Step 3: Use the Hilbert transform for TR1 and TR2 respectively in the mode number domain to eliminate the influence of the square term of the Bessel function, and then adopt FFT transform to reconstruct the one-dimensional azimuth image φ;

[0076] Step 4: Use formulas (14)-(17) to jointly solve the true range r and elevation angle θ of the target for the ranges R and azimuth angles φ obtained by TR1 and TR2, and reconstruct the target space three-dimensional coordinates.

[0077] Specifically: The single-transmission multi-reception mode adopted is as Figure 2 shown, the receiving unit is a UCA array, the center of the array is located at the coordinate origin O, the radius of the array is b, and the array is composed of N identical independent array elements S nIt consists of a transmitting unit which is an independent omnidirectional antenna located at the center of the UCA array, i.e., at the coordinate origin O. Let the transmitted signal of the transmitting element O be a linear frequency modulation (LFM) signal, denoted as s(t). Let P be an arbitrary independent scattering point in space, denoted as P(r,θ,φ). The received target echo signal by the UCA receiving unit can be expressed as:

[0078] s N (t, l) = σJ l (kbsinθ)s(t - τ)·e jlφ (1)

[0079] where σ is the radar target scattering coefficient, τ is the signal time delay and c is the speed of light, R n is the space propagation distance, l is the mode number, t is the fast time, J l is the l-th order Bessel function of the first kind, k is the range spatial frequency, θ is the elevation angle of the radar target, j is the imaginary number, φ is the azimuth of the radar target, r is the distance of the radar target; at this time, the included angle β between the transmitting path OP and the receiving path S n P is relatively small and can be approximated as a monostatic transceiver mode. The space propagation distance R n is approximately 2r, then the signal time delay It can be seen from formula (1) that the distance r and azimuth angle φ of the target scattering point P can be obtained by using the fast Fourier transform in the fast time domain and the mode number domain respectively, while the elevation angle θ of the target cannot be solved from the amplitude term of the echo signal; in this transceiver mode, only the two-dimensional imaging result of the target scattering point P can be obtained.

[0080] If the transmitting element is moved from O to O' on the positive X-axis, and the distance between O' and the coordinate origin O is d. Let the signal transmitted by the transmitting element still be the LFM signal s(t), then the echo signal of the spatial independent point P received by the element S n in the receiving unit can be expressed as:

[0081]

[0082] where τ n is the signal propagation time delay, expressed as τ n = R n / c, Rn is the signal space propagation distance, T p is the pulse width of the LFM signal, K is the frequency modulation rate, is the included angle between the element S n and the positive X-axis in the XOY plane, rect[·] is the transmitted signal pulse, f c (t - τ n)K(t - τ n ) 2 is the multiplication between variables; then the total echo received by the UCA array composed of N independent array elements can be expressed as:

[0083]

[0084] From Figure 1 it can be seen that the included angle β′ between the transmitting path O′P and the receiving path S n P is relatively large, so it should be a bistatic transceiver mode; the signal propagation distance R n can be expressed as R n = R1 + R2, where R1 is the distance from O′ to point P, and R2 is the distance from point P to the nth receiving array element S in the UCA array n ; Let the unit vector in the direction of the straight line where OP is located can be expressed as:

[0085]

[0086] where, is the x-axis direction vector, is the y-axis direction vector, is the z-axis direction vector, and the straight line vector from the origin O to the array element S in the UCA array n can be expressed as The straight line vector from point O′ to point P can be expressed as where, d is the distance between the transmitting array element and the coordinate origin, then the distance R1 from O′ to point P and the distance R2 from point P to the array element S n are respectively expressed as:

[0087]

[0088]

[0089] According to formulas (5) and (6), the total echo received by the UCA array can be expressed as:

[0090]

[0091] where τ′ = R′ / c, and R′ = 2r + dsinθcosφ. Let According to the Janoci - Anger formula, s(n) can be expressed as:

[0092]

[0093] where J m (·) is the Bessel function of the first kind of order m. Since It has a value only when l - m is an integer multiple of N and is equal to N. At the same time, when N is a relatively large value, the amplitude of the Bessel function J m when it is of order l is much larger than that of other orders. Equation (8) can be approximately expressed as:

[0094] s(n) = NjlJ l (kbsinθ)e jlφ (9)

[0095] Then the echo received by the UCA array can be further expressed as:

[0096] s N (t, l) = σ′J l (kbsinθ)s(t - τ′)·e jlφ (10)

[0097] where the scattering coefficient is σ′ = σNj l , according to Equation (10), it can be seen that the echo sampling data of the target point P in the bistatic mode is still distributed in a two-dimensional rectangle in the frequency - mode number domain. Performing a two-dimensional Fourier transform on it can obtain the range - azimuth angle information of the target. Comparing with the echo model of the target point P in the monostatic mode expressed by Equation (1), it can be seen that the azimuth angle φ solved in the bistatic mode remains unchanged, and the range changes from r to

[0098] Bistatic 3D Imaging of Vortex Electromagnetic Waves

[0099] Suppose the radar target consists of M scattering points, denoted as P m (r m , θ m , φ m ). The transmitted signal is an LFM signal s(t). Using the bistatic mode designed in this patent, the echo signal received by the UCA array can be expressed as:

[0100]

[0101] where the normalized scattering coefficient of the target is σ = σ m j l NJl(kbsinθ m ), the time delay τ m = R m / c, R m = 2r m + dsinθ m cosφ mAs can be seen from the previous analysis, the echo signal is distributed in a two-dimensional rectangle in the frequency-mode number domain. Let the center point of the target area be P0(r0, θ0, φ0), then the echo received by the UCA array from P0 is s0(t, l). Taking the echo s0(t, l) of P0 as the reference signal, and using matched filtering in the range dimension to reconstruct the target, the reconstructed echo signal can be expressed as:

[0102]

[0103] where psf t (·) is the time-domain point spread function. From formula (12), it can be seen that the range information R can be obtained from the reconstructed echo signal s Match (t, l). Using the dual relationship between the mode number l and the azimuth angle φ, the azimuth angle φ can be obtained by performing a fast Fourier transform in the mode number domain m . However, since the amplitude term of the echo signal contains the Bessel function related to the mode number, its influence on the azimuth image needs to be considered. It is known that when kb sinθ >> 1, the Bessel function can be approximately expressed as: m As can be seen from formula (13), the Fourier transform result of the Bessel function in the mode number domain will form zeros at its zero frequency and narrowband spectral components symmetrically distributed on both sides

[0104]

[0105] of its frequency, and the frequency shift amount is independent of the elevation angle θ; therefore, J in the amplitude term can be approximated as J l (kbsinθ m )J l (kbsinθ0) is approximately J l 2 (kbsinθ0), then the amplitude term of the vortex electromagnetic wave echo signal contains the square term of the Bessel function J l (·). Considering the influence of the Bessel function on the azimuth image imaging result, Figure 3 the spectrogram of the square Bessel function is given. As can be seen from Figure 3 , the square Bessel function forms narrowband spectral components at . Using the Hilbert transform, the frequency shift problem caused by the Bessel function can be eliminated. First, perform the Hilbert transform on the echo signal, and then perform a fast Fourier transform on the echo signal in the mode number domain. The frequency shift of the echo signal is effectively eliminated, and only the true azimuth angle information of the target exists in the azimuth image imaging result.

[0106] After the above processing in the frequency-mode number domain, a two-dimensional imaging result of the range and azimuth can be obtained. According to formula (12), it can be known that the solved azimuth is the same as the azimuth φ of the target scattering point, and the range R m is not equal to the range r of the target scattering point m but contains the three-dimensional spatial information of the target scattering point; from the expression m , d is a known quantity, and at the same time, the target azimuth φ can also be solved. Then the ranges of M target scattering points can be expressed as: m r + A·θ = R (14)

[0107] where r = [r1, r2, … r

[0108] < m > T is the range vector of the target scattering point, is the weight coefficient vector of the equation set, θ = [sinθ1, sinθ2, … sinθ m < m > T is the vector of the elevation angle of the scattering point, and R = [R1, R2, … R m , φ m ) is the solved range vector; if three-dimensional reconstruction of the target scattering point is desired, the range and elevation angle of the target scattering point need to be solved from formula (14); for M target scattering points, M groups of (r

[0109] , φ m ′) need to be solved, but this cannot be achieved only through formula (14). m If the number of transmitting elements is increased from one to two, that is, another transmitting element is set in the positive direction of the X-axis. This element is located at O″ and is at a distance d′ (d′ ≠ d) from the center of the UCA; at this time, the transmitting element located at O′ and the UCA receiving array form a signal transceiver channel 1, denoted as TR1; the transmitting element located at O″ and the UCA receiving array form a signal transceiver channel 2, denoted as TR2; channel 1 and channel 2 satisfy an orthogonal relationship in frequency, and the center carrier frequencies of the transceiver channels are f1 and f2 respectively; for the echo data of TR2, the above processing method is adopted, and the target range R m ′ and azimuth φ m can be obtained, where for channel TR2, the ranges of M scattering points can be expressed as:

[0110] r + A′·θ = R′ (15)

[0111] where where R′ = [R1′, R2′, … R m ′]< T . Combining formulas (14) and (15), the elevation angle of the target can be solved as:

[0112]

[0113] After solving the target pitch angle θ = [sinθ1, sinθ1, …, sinθ m , the target distance r is solved through formula (14) or (15).

[0114] As can be seen from formulas (14)-(16), the target distance information R contains the target three-dimensional coordinate information. On the premise that the azimuth angle satisfies resolvability, the resolution ability of the pitch angle depends on the target distance resolution. If it is required that the resolution of the pitch angle is not less than Δθ, then it is necessary to satisfy:

[0115] Δx = sin(θ m +Δθ)-sinθ m ≥ρ R (17)

[0116] Known distance resolution where B is the transmit signal bandwidth, it can be known that the resolution of the pitch angle is inversely proportional to the signal bandwidth. If the pitch angle resolution is Δθ, then the transmit signal bandwidth B needs to satisfy Considering that the value of Δx is different in different interval ranges of the pitch angle θ , as shown in Figure 4 , the value of Δx is larger in the small elevation angle interval of the pitch angle θ, while the value of Δx is smaller in the large elevation angle interval. That is to say, the setting of the transmit signal bandwidth needs to take the position of the maximum pitch angle as a reference. At the same time, it can be seen from Figure 4 that the lower the pitch angle resolution, the lower the requirement for the range dimension resolution.

[0117] While the method of this patent realizes the three-dimensional reconstruction of radar targets, under the condition of the same pitch angle resolution, the computational complexity is significantly better than that of the MUSIC algorithm. For a UCA array with N array elements, the computational amount of the MUSIC algorithm is:

[0118] C Music = N 2 (M + 2)+J(N + 1)(N - M) (18)

[0119] where J is the number of pitch angle search points, and Δθ is the pitch angle resolution. The MUSIC algorithm requires the number of array elements to be greater than the number of targets. We set the number of array elements N to be only 1 more than the number of targets M. Then the MUSIC computational amount C Music can be approximately expressed as:

[0120] C Music ≤N 3 +J(N + 1) (19)

[0121] It can be seen from Equation (19) that the computational complexity of the MUSIC algorithm mainly depends on the number of array elements \(N\) and the elevation angle resolution \(\Delta\theta\).

[0122] By analyzing the imaging method in this paper, it can be seen that the imaging algorithm in this paper mainly uses the FFT algorithm in the range dimension and the number of modes dimension, and can be approximately expressed as:

[0123] \(C\approx6N rang \log_2(N rang ) + 2N\log_2(N)+4M\ (20)

[0124] where \(N rang is the number of time-domain sampling points, \(6N rang \log_2(N rang ) is the computational complexity of range reconstruction in the range dimension, \(2N\log_2(N)\) is the computational complexity of azimuth reconstruction in the number of modes dimension. Still assuming that the number of array elements \(N\) is only 1 more than the number of targets \(M\), Equation (20) can be further expressed as:

[0125] \(C\approx6N rang \log_2(N rang ) + 2N(\log_2(N)+2)\ (21)

[0126] It can be seen from Equation (21) that the computational complexity of the algorithm in this paper mainly depends on the number of array elements \(N\) and the number of time-domain sampling points \(N rang . In the range imaging range, the number of time-domain sampling points is proportional to the transmit signal bandwidth, and can be expressed as The elevation angle resolution of the algorithm in this paper depends on the range dimension resolution, that is, the number of sampling points \(N rang will increase as the elevation angle resolution increases.

[0127] Comparing Equation (19) and (21), it can be seen that in the MUSIC algorithm, only the term related to the number of array elements \(N\) is the cubic term, and the remaining terms are the search point number and the quadratic term of the number of array elements \(N\). Under the high elevation angle resolution requirement, the number of array elements \(N\) is large, and the computational complexity increases exponentially; in the algorithm in this paper, only the term related to the number of array elements \(N\) is the linear term, and the remaining terms are the linear terms of the number of sampling points \(N rang . Under the high elevation angle resolution requirement, the computational complexity increases linearly.

[0128] Experimental simulation

[0129] Suppose the UCA array consists of 50 array elements, the center of the array is placed at the origin of coordinates, the array radius \(b = 10\lambda\), and two independent transmit array elements \(O'\) and \(O''\) are placed on the positive X-axis. The two transmit array elements are 2 meters apart. The transmit signal is a chirp signal with a signal bandwidth of 2 GHz. The transmit array element and the UCA array form independent transceiver channels respectively, denoted as TR1 and TR2. There are four scattering points in the target area, which are And the range of the number of modes experienced is [-20, 20].

[0130] One-dimensional range profile of bistatic mode

[0131] The one-dimensional range profile of the target scatterer can be obtained by using the range-Doppler algorithm, as Figure 5 shown. Figure 5 a is the imaging result of the one-dimensional range profile in the monostatic transceiver mode. In the monostatic model, the transmitting array element is located at the center of the UCA array, i.e., the coordinate origin O. It can be seen from the figure that the range profile result is the distance of the scatterer r = [298 300 303 294]; Figure 5 b, Figure 5 c are the imaging results of the one-dimensional range profile of channel TR1 and channel TR2 based on the bistatic transceiver mode of this patent. According to it can be known that the one-dimensional range profile results of channel TR1 and channel TR2 should be: R TR1 = [300.2042 300.9492 305.0014 297.9279], R TR2 = [300.4981 301.0757 305.2682 298.4516].

[0132] Range-elevation angle two-dimensional imaging result of bistatic mode

[0133] According to the three-dimensional imaging method of this patent, after preprocessing the echo signals of the TR1 and TR2 transceiver channels by using the Hilbert transform, the distance R and azimuth angle of the target scatterer can be obtained through the fast Fourier transform. The imaging result is as Figure 6 shown. Figure 6 a, Figure 6 b are the range-azimuth angle two-dimensional imaging results of channel TR1 and channel TR2 respectively.

[0134] According to the range-azimuth angle imaging results of the transceiver channels TR1 and TR2, by using formulas (14)-(17), the actual distance r and elevation angle θ of the target scatterer can be solved. Figure 7 The solution results of the distance-elevation angle of the target scatterer and the true position information of the distance-elevation angle of the target scatterer are given. The rhombus is the true distance-elevation angle of the target, and the circle is the distance-elevation angle of the target obtained by the imaging method in this article.

[0135] From Figure 7It can be seen that the method of this patent can relatively accurately reconstruct the range - elevation angles of scatterers P1, P2, and P3. There is a certain error between the simulation result of scatterer P4 and the actual position of the target. When reconstructing in the range dimension, the signal bandwidth determines the range - dimension resolution and the unit range cell. On the premise of meeting the elevation - angle resolution, the target range may deviate by 1 range cell, and for the dual - transceiver - channel mode proposed in this patent, it will bring a maximum deviation of 2 range cells in range - dimension calculation. For Figure 8 the scatterer P3 in, the theoretical range difference ΔR between channels TR1 and TR2 should be 0.2668 m, corresponding to 8 unit range cells, while the simulated range difference ΔR is 0.2625 m, corresponding to 7 unit range cells. There is an error of 1 unit range cell in the simulation calculation, and the elevation angle of point P3 obtained by the simulation calculation differs from the actual value by 0.007π. On the premise of meeting the elevation - angle resolution, as Figure 7 shown, the elevation - angle calculation error is less than 0.011π.

[0136] Given that the elevation angle of scatterer P4 is and the transmit - signal bandwidth is 2 GHz, and the range - dimension resolution is 0.0375 m. According to formula (17), the corresponding relationship between the elevation - angle resolution of scatterer P4 and the range - dimension resolution is as Figure 9 shown. When the range - dimension resolution is 0.0375 m and the target elevation angle is equal to , the elevation - angle resolution Δθ ∈ [4°, 5°]. The elevation angle of scatterer P4 obtained by the simulation experiment is 59 degrees, differing from the actual elevation angle of scatterer P4 by 4 degrees, and the error conforms to the above - mentioned theoretical analysis.

[0137] 3D imaging results of the bistatic mode

[0138] According to Figure 1 the 3D imaging process, the azimuth angle of the target scatterer has been obtained through the mode - number - domain fast Fourier transform, and the actual range r and elevation angle θ of the target scatterer are solved according to formulas (14) - (17), and the 3D imaging results of the target scatterer in the spherical coordinate system can be reconstructed, as Figure 10 shown. The rhombus represents the actual position of the target scatterer, and the circle represents the reconstructed scatterer position. In the small - elevation - angle range, the method of this patent can relatively accurately reconstruct the 3D imaging results of the radar target.

[0139] The prior art uses the MUSIC algorithm to achieve the resolution of the target elevation angle and azimuth angle through the spatial two-dimensional spectrum estimation. When the signal-to-noise ratio and the number of snapshots are determined, the two-dimensional angular resolution depends on the range of the number of modes. Compared with the prior art, in the case of the same azimuth resolution, the elevation angle resolution of the method of this patent is independent of the number of modes and only related to the bandwidth of the transmitted signal. As shown in Table 1, when the range resolution is 0.0375 m and the azimuth resolution is 0.2π, when the elevation angle resolution ranges from 8° to 3°, the requirements for the range of the number of modes and the computational complexity of the prior art method increase exponentially. When the elevation angle resolution is 3°, the requirement for the range of the number of modes of the prior art method is 4 times that of the patent method, that is to say, the requirement for the number of UCA array elements of the patent method is 1 / 4 of that of the prior art. With the improvement of the elevation angle resolution, the growth rate of the computational complexity of the patent method is significantly lower than that of the prior art algorithm. When the resolution is 3°, the computational complexity is only 1 / 8 of that of the prior art.

[0140] Table 1 Array element quantity and computational complexity at different elevation angle resolutions

[0141]

[0142] The beneficial effects of the present invention are as follows: The vortex electromagnetic wave radar adopts a bistatic transceiver mode and has the ability to resolve the elevation angle of the radar target, realizing three-dimensional imaging of the radar target. The method of this patent can achieve high resolution for small elevation angle targets without increasing the complexity of the array structure, and the computational complexity of the method is significantly better than that of the MUSIC algorithm.

Claims

1. A three-dimensional imaging method for a vortex electromagnetic wave radar based on a bistatic mode, comprising the following steps: Step 1: Construct a rectangular coordinate system with the center of the UCA as the origin. Then, set two independent transmitting array elements at different positions on the positive X-axis direction, and respectively form two transceiver channels TR1 and TR2 with the UCA receiving unit. Step 2: Perform matched filtering on the echo signals of the two transceiver channels TR1 and TR2 in the range dimension respectively to reconstruct the one-dimensional range image of the target. Step 3: Use the Hilbert transform on the two transceiver channels TR1 and TR2 in the mode number domain respectively to eliminate the influence of the square term of the Bessel function, and then use the FFT transform to reconstruct the one-dimensional azimuth image. The specific steps of Step 3 include the following steps: First, perform the Hilbert transform on the echo signal, and then perform the fast Fourier transform on the echo signal in the mode number domain. The displacement of the echo signal frequency is effectively eliminated, and only the true azimuth angle information of the target exists in the azimuth image imaging result; After the above processing in the frequency-mode number domain, a two-dimensional imaging result of the range and azimuth can be obtained. According to formula (12), it can be known that the solved azimuth is the same as the azimuth φ of the target scattering point m while the range R m is not equal to the range r of the target scattering point m but contains the three-dimensional spatial information of the target scattering point; from the expression it can be seen that d is a known quantity, and at the same time the target azimuth φ m can also be solved, then the ranges of M target scattering points can be expressed as: r + A·θ = R (14) where \(r = [r_1, r_2, \ldots, r m T is the distance vector of the target scattering points, is the weight coefficient vector of the equation system, \(\theta = [\sin\theta_1, \sin\theta_2, \ldots, \sin\theta m \) is the vector regarding the elevation angles of the scattering points, \(R = [R_1, R_2, \ldots, R m T is the distance vector to be solved;​​ Channel TR1 and channel TR2 satisfy the orthogonal relationship in frequency. The center carrier frequencies of the transceiver channels are f1 and f2 respectively. By using the above processing method for the echo data of TR2, the target distance R can be obtained. m ′ and azimuth angle φ m , where For channel TR2, the distances of M scatterers can be expressed as: r + A′·θ = R′ (15) wherein where R' = [R1', R2',... R m '] T ; Combining formulas (14) and (15), the pitch angle of the target can be solved as: After solving for the target pitch angle θ = [sinθ1, sinθ1, …, sinθ m , using formula (14) or (15) Solve for the target distance r ; Step 4: Combine the ranges and azimuth angles obtained from TR1 and TR2 and solve the true range and pitch angle of the target to reconstruct the three-dimensional coordinates of the target and form a three-dimensional image. The specific steps of Step 4 include the following steps: To perform three-dimensional reconstruction of the target scattering points, it is necessary to solve for the distance and elevation angle of the target scattering points from Equation (14); for M target scattering points, M sets of (r m , φ m ) need to be solved. From Equations (14)-(16), it can be seen that the target distance information R contains the target three-dimensional coordinate information. On the premise that the azimuth angle is resolvable, the resolution ability of the elevation angle depends on the target distance resolution. If it is required that the resolution of the elevation angle is not less than Δθ, then the following conditions need to be satisfied: Δx = sin(θ m +Δθ) - sinθ m ≥ρ R (17) Known range resolution Where B is the bandwidth of the transmitted signal, it can be known that the resolution of the elevation angle is inversely proportional to the signal bandwidth. If the elevation angle resolution is Δθ, the transmitted signal bandwidth B needs to satisfy Considering that the value of Δx is different in different intervals of the elevation angle θ The azimuth angle of the target scattering point has been obtained through the mode number domain fast Fourier transform And the actual distance of the target scattering point is solved according to formulas (14)-(17) r And the elevation angle θ to reconstruct the three-dimensional imaging result of the target scattering point in the spherical coordinate system.

2. The three-dimensional imaging method of a vortex electromagnetic wave radar based on a bistatic mode according to claim 1, characterized in that: The specific steps of Step 1 include the following steps: A rectangular coordinate system is constructed with the center of the UCA as the origin. The receiving unit is a UCA array. The center of the array is located at the coordinate origin O, and the radius of the array is b. The array consists of N identical independent array elements S n The transmitting unit is an independent omnidirectional antenna located at the center of the UCA array, i.e., at the coordinate origin O. Let the transmitted signal of the transmitting element O be a linear frequency modulation signal, namely Linear Frequency Modulation, abbreviated as LFM, denoted as s(t). Let P be an arbitrary independent scattering point in space, denoted as P(r, θ, φ). The target echo signal received by the UCA receiving unit can be expressed as: s N (t, l) = σJ l (kbsinθ)s(t - τ)·e jlφ (1) where σ is the radar target scattering coefficient, τ is the signal time delay and c is the speed of light, R n is the space propagation distance, l is the number of modes, t is the fast time, J l is the l-th order Bessel function of the first kind, k is the distance spatial frequency, θ is the radar target elevation angle, j is the imaginary number, φ is the radar target azimuth, r is the distance of the radar target; at this time, the angle β between the transmission path OP and the reception path S n P is relatively small and can be approximated as a monostatic transceiver mode. The space propagation distance R n is approximately 2r, then the signal time delay It can be seen from formula (1) that the distance r and azimuth angle φ of the target scattering point P can be obtained by using the fast Fourier transform in the fast time domain and the mode number domain respectively, while the target elevation angle θ cannot be solved from the amplitude term of the echo signal; Move the transmitting array element from point O to point O' on the positive x-axis. The distance between O' and the coordinate origin O is d. Assume that the signal transmitted by the transmitting array element is still the LFM signal s(t). Then, for the array element S in the receiving unit n The echo signal received from the spatially independent point P can be expressed as: where τ n is the signal propagation delay, denoted as τ n = R n / c, where Rn is the signal spatial propagation distance, T p is the LFM signal pulse width, K is the frequency modulation rate, is the angle between the array element S n and the positive X-axis in the XOY plane, rect[·] is the transmitted signal pulse; then the total echo received by the UCA array composed of N independent array elements is expressed as: The emission path O′P and the reception path S n The included angle β′ between P is relatively large, and it should be a bistatic transceiver mode; the signal propagation distance R n can be expressed as R n = R1 + R2, where R1 is the distance from O′ to point P of the signal, and R2 is the distance from point P to the nth reception array element S in the UCA array n Let the unit vector in the direction of the straight line where OP is located, which is expressed as: Among them, is the vector in the x-axis direction, is the vector in the y-axis direction, is the vector in the z-axis direction. The straight-line vector from the origin O to the element S in the UCA array n can be expressed as The straight-line vector from the point O' to the point P can be expressed as Among them, d is the distance between the transmitting element and the coordinate origin. Then, the distance R1 from O' to P and the distance R2 from the point P to the element S n are respectively expressed as: According to formulas (5) and (6), the total echo received by the UCA array is expressed as: wherein τ′ = R′ / c, and R′ = 2r + dsinθcosφ; Let According to the Jacobi-Anger formula, s(n) can be expressed as: where J m () is the Bessel function of the first kind of order m. Since has a value only when l - m is an integer multiple of N and is equal to N; at the same time, in the case where N is a relatively large value, the amplitude of the Bessel function J m (·) at order l is much larger than the amplitudes at other orders, and Equation (8) can be approximately expressed as: s(n) = Nj l J l (kbsinθ)e jlφ (9) Then the echo received by the UCA array is further expressed as: s N (t, l) = σ′J l (kbsinθ)s(t - τ′)·e jlφ (10) where the scattering coefficient is σ′ = σNj l , according to formula (10), it can be known that the echo sampling data of the target point P in the bistatic mode is still distributed in a two-dimensional rectangle in the frequency-mode number domain. Performing a two-dimensional Fourier transform on it can obtain the range-azimuth angle information of the target; comparing with the echo model of the target point P in the monostatic mode expressed by formula (1), it can be seen that the azimuth angle φ solved in the bistatic mode remains unchanged, and the range changes from r to Suppose the radar target consists of M scattering points, denoted as P m (r m , θ m , φ m ). The transmitted signal is an LFM signal s(t). Adopting the designed bistatic mode, the echo signal received by the UCA array can be expressed as: where the target-normalized scattering coefficient σ = σ m j l NJ l (kbsinθ m ), the time delay τ m = R m / c, R m = 2r m + dsinθ m cosφ m ; Increase the transmitting unit from one array element to two array elements, that is, set another transmitting array element on the positive X-axis direction. This array element is located at O″ and is at a distance d′ from the center of the UCA, d′≠d; at this time, the transmitting array element located at O′ and the UCA receiving array form signal transceiver channel 1, denoted as TR1; the transmitting array element located at O″ and the UCA receiving array form signal transceiver channel 2, denoted as TR2.

3. The three-dimensional imaging method of a vortex electromagnetic wave radar based on a bistatic mode according to claim 1, wherein: The specific steps of Step 2 include the following steps: Since the signals of TR1 and TR2 are orthogonal in frequency, the signals of the two channels TR1 and TR2 are processed respectively as described in Step 1 to obtain the one-dimensional range images of the two channels TR1 and TR2. Perform matched filtering on the echo signals of the two double transceiver channels TR1 and TR2 in the range dimension respectively; the echo signals are distributed in a two-dimensional rectangle in the frequency-mode number domain. Let the center point of the target area be P0(r0, θ0, φ0), then the echo received by the UCA array for P0 is s0(t, l). Use the echo s0(t, l) of P0 as the reference signal and perform matched filtering in the range dimension to reconstruct the target. Then the reconstructed echo signal can be expressed as: Among them psf t (·) is the time-domain point spread function; It can be seen from formula (12) that the distance information R can be obtained from the reconstructed echo signal s Match (t, l); By using the dual relationship between the mode number l and the azimuth angle φ, the azimuth angle φ can be obtained by performing a fast Fourier transform in the mode number domain m , but since the amplitude term of the echo signal contains the Bessel function related to the mode number, its influence on the azimuth image needs to be considered; It is known that when kbsinθ >> 1, the Bessel function can be approximately expressed as: m ​ As can be seen from Equation (13), the Fourier transform result of the Bessel function in the mode number domain forms a zero point at its zero frequency and narrowband spectral components symmetrically distributed on both sides of the frequency; moreover, the frequency displacement is independent of the pitch angle θ. Therefore, the J l (kbsinθ m )J l (kbsinθ0) in the amplitude term can be approximated as J l 2 (kbsinθ0). Then, the amplitude term of the vortex electromagnetic wave echo signal contains the square term of the Bessel function J l (·).

Images