CN113176566B - Three-dimensional rapid imaging method for MIMO-SAR - Google Patents

Three-dimensional rapid imaging method for MIMO-SAR Download PDF

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CN113176566B
CN113176566B CN202110290721.0A CN202110290721A CN113176566B CN 113176566 B CN113176566 B CN 113176566B CN 202110290721 A CN202110290721 A CN 202110290721A CN 113176566 B CN113176566 B CN 113176566B
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CN113176566A (en
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李超
杨冠
方广有
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Aerospace Information Research Institute of CAS
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    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
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    • G01S13/89Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9094Theoretical aspects
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention provides a three-dimensional rapid imaging method for MIMO-SAR, which utilizes the high efficiency of a frequency domain algorithm, solves the problem of data interpolation in the traditional RMA, avoids the truncation effect of the traditional interpolation mode and interpolation kernel, and can obtain higher imaging quality; meanwhile, the invention also solves the problem of time consumption of wave number domain integration in the traditional PSM algorithm, further exerts the advantage of phase shift substitution interpolation on the premise of ensuring the imaging effect and improves the processing speed.

Description

Three-dimensional rapid imaging method for MIMO-SAR
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a three-dimensional rapid imaging method for an MIMO-SAR.
Background
The most common radar three-dimensional imaging system is that a two-dimensional array is used for realizing the rapid focusing in the direction of azimuth and altitude and combining with a broadband signal to realize the focusing in the direction of distance, and in a millimeter wave/terahertz frequency band, the requirement of spatial sampling rate is limited, the number of array elements required by the two-dimensional array is more, especially the cost of the existing millimeter wave terahertz device is relatively high, so that the cost of building the two-dimensional array system under the existing condition can be increased. Although only a single transceiving array element is adopted for two-dimensional scanning, and a target three-dimensional image can be obtained by combining a broadband signal, the data acquisition time is too long, and the real-time imaging application cannot be realized. At present, the imaging Algorithm based on the MIMO device mostly adopts Range Migration Algorithm (RMA) and Phase Shift Algorithm (PSM) based on the wave number domain to realize rapid imaging, and compared with a Back-projection Algorithm (BPA) based on coherent superposition, the Algorithm has the advantages of high imaging speed and good focusing effect.
Therefore, the prior art has the following technical defects (key parts):
(1) The RM algorithm imaging process based on the wave number domain Fourier transform interpolation relates to the wave number domain interpolation of a transceiver array, the interpolation method determines the imaging efficiency, and the truncation effect of an interpolation kernel reduces the imaging precision;
(2) A PSM algorithm originated from reflection seismology is consistent with the requirement of an RM algorithm on an array, wave field extrapolation is used for replacing interpolation in RMA in the imaging process, integral superposition operation of the last step of the algorithm on wave numbers occupies a large amount of calculation time, and the calculation efficiency is lower than that of RMA.
Disclosure of Invention
In order to solve the problems, the invention provides a three-dimensional rapid imaging method for MIMO-SAR, which avoids the truncation effect of the traditional interpolation mode and interpolation kernel and can obtain higher imaging quality.
A three-dimensional fast imaging method for MIMO-SAR is characterized in that an MIMO antenna array consists of a transmitting antenna sub-array and a receiving antenna sub-array which are positioned in the same straight line, and the imaging result of the MIMO-SAR is obtained
Figure BDA0002982472710000021
The calculation formula of (2) is as follows:
Figure BDA0002982472710000022
wherein the content of the first and second substances,
Figure BDA0002982472710000023
is a one-dimensional inverse Fourier transform,
Figure BDA0002982472710000024
for two-dimensional inverse Fourier transform, FT 3D For three-dimensional Fourier transform, s (x) t ,x r Y, k) are reflection echo signals under the MIMO-SAR system, the rerange represents rearrangement operation,
Figure BDA0002982472710000025
for the spatial coordinates of the target region determined after imaging, M 1 For the first sub-term of the phase shift offset factor,
Figure BDA0002982472710000026
is a second sub-term of the phase shift offset factor and has:
Figure BDA0002982472710000027
Figure BDA0002982472710000028
wherein z is c The distance from the MIMO antenna array to the center of the target area, k is the corresponding wave number when the transmitting antenna sub-array externally radiates frequency stepping signals, k xt For the corresponding spatial wave number, k, in the direction of the sub-array of transmitting antennas xr For receiving the corresponding spatial wave number, k, in the direction of the sub-array of antennas y For the corresponding number of spatial waves, k, in the scanning direction of the synthetic aperture c The number of waves corresponding to the center frequency, j denotes an imaginary unit,
Figure BDA0002982472710000029
expressed in distance z c And the distance coordinate corresponding to the target area when the distance is towards the zero point of the coordinate.
Further, a first sub-term M of the phase shift offset factor 1 With a second sub-term of the phase shift offset factor
Figure BDA00029824727100000210
The acquisition method comprises the following steps:
s1: reflection echo signal s (x) under the MIMO-SAR system t ,x r Y, k) is:
Figure BDA0002982472710000031
wherein O (x ', y ', z ') is the reflectivity of the target region, R T For the distance between each transmit antenna in the transmit antenna sub-array to the target area,R R (x) distance between each receiving antenna in the receiving antenna sub-array and the target area t Y, z = 0) represents the position coordinates of each transmitting antenna in the transmitting antenna sub-array, (x) r Y, z = 0) represents the position coordinates of each receiving antenna in the receiving antenna sub-array;
s2: will reflect the echo signal s (x) t ,x r Y, k) is subjected to three-dimensional Fourier transform to obtain a reflected echo signal s (x) t ,x r Y, k) is expressed in the frequency wavenumber domain as:
Figure BDA0002982472710000032
wherein, P (k) xt ,k xr ,k y ,k)=∫∫∫exp(-jk(R T +R R ))·exp(-jk xt x t )·exp(-jk xr x r )exp(-jk y y)dx t dx r dy;
S3: solving for P (k) by using stationary phase principle xt ,k xr ,k y K), the following dispersion relation is obtained:
Figure BDA0002982472710000033
wherein k is x Representing the corresponding spatial wavenumber, k, in the direction of the MIMO antenna array z Represents the wave number in the distance direction;
s4: suppose that the MIMO-SAR works in the terahertz wave band and obtains the dispersion relation
Figure BDA0002982472710000034
Is approximately expressed by a binomial equation
Figure BDA0002982472710000035
The following were used:
Figure BDA0002982472710000036
s5: approximating a representation according to said binomial
Figure BDA0002982472710000037
Constructing a phase shift offset factor
Figure BDA0002982472710000038
The following were used:
Figure BDA0002982472710000041
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002982472710000042
distance coordinates of the target area are taken as coordinates;
s6: for phase shift offset factor
Figure BDA0002982472710000043
K wave number of (1) according to k = k c +k b Partial variable replacement is performed to split the phase shift offset factor
Figure BDA0002982472710000044
Figure BDA0002982472710000045
Wherein k is b For wave number, M, corresponding to baseband frequency 2 A second sub-term of the phase shift offset factor before reduction;
s7: by k c Substitution of M 2 K in the term denominator, resulting in a second sub-term of the simplified phase shift offset factor
Figure BDA0002982472710000046
Figure BDA0002982472710000047
Further, R T And R R The acquisition method comprises the following steps:
Figure BDA0002982472710000048
Figure BDA0002982472710000049
where (x ', y ', z ') are the coordinates of the target area.
Further, the rearrangement operation specifically comprises:
will be provided with
Figure BDA00029824727100000410
The resulting four-dimensional matrix
Figure BDA00029824727100000411
According to a set dispersion relation
Figure BDA00029824727100000412
Rearranging to obtain a three-dimensional matrix
Figure BDA00029824727100000413
Further, in the MIMO antenna array, the receiving antenna sub-array is located in the middle, and the transmitting antenna sub-array is divided into two parts and arranged at two ends of the receiving antenna sub-array.
Furthermore, the receiving antenna subarray comprises 39 receiving antennas, the transmitting antenna subarray comprises 6 transmitting antennas, the transmitting antennas are evenly divided into two parts and are arranged at two ends of the receiving antennas, meanwhile, the interval between the transmitting antennas is 2.5mm, the interval between the receiving antennas is 7.5mm, and the total length of the MIMO antenna array is 0.3m.
Has the advantages that:
the invention provides a three-dimensional rapid imaging method for MIMO-SAR, which utilizes the high efficiency of a frequency domain algorithm, solves the problem of data interpolation in the traditional RMA, avoids the truncation effect of the traditional interpolation mode and an interpolation kernel, and can obtain higher imaging quality; meanwhile, the invention also solves the problem of time consumption of wave number domain integration in the traditional PSM algorithm, further exerts the advantage of phase shift substitution interpolation on the premise of ensuring the imaging effect and improves the processing speed.
Drawings
FIG. 1 is a schematic diagram of an MIMO-SAR imaging scenario provided by the present invention;
fig. 2 is a schematic diagram of a MIMO antenna array arrangement provided by the present invention;
FIG. 3 is a schematic diagram of a multi-target scene setup provided by the present invention;
FIG. 4 is a schematic diagram of the simulation results of a conventional BPA process;
FIG. 5 is a diagram illustrating simulation results of the present invention;
fig. 6 is a schematic diagram comparing the one-dimensional azimuthal profiles of the conventional BPA process and the present invention along y =0m and z =1.05 m.
Detailed Description
In order to make the technical solutions better understood by those skilled in the art, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.
As shown in the MIMO-SAR imaging scenario of fig. 1, assuming that the distance direction of the plane in which the MIMO array composed of the transmitting antenna sub-array and the receiving antenna sub-array in the same straight line is located at z =0, the transmitting antenna sub-array is located at (x = 0) t Y, z = 0), the receiving antenna sub-array is located at (x) r Y, z = 0). The MIMO array adopts an arrangement mode that transmitting antennas are arranged at two ends and receiving antennas are arranged in the middle. The transmitting antenna sub-array excites the frequency stepping signals, k is the wave number corresponding to the transmitting antenna sub-array radiating the frequency stepping signals with different transmitting frequencies, and the three-dimensional fast imaging method for the MIMO-SAR is explained below by taking the end-to-end transmitting-receiving array as an example.
Step one, a reflection echo obtained after a frequency stepping signal is scattered by a target under an MIMO-SAR system can be expressed as:
Figure BDA0002982472710000061
wherein O (x ', y ', z ') is the reflectivity of the target region, R T For the distance, R, between each transmitting antenna in the sub-array of transmitting antennas and the target area R (x) distance between each receiving antenna in the receiving antenna sub-array and the target area t Y, z = 0) represents the position coordinates of each transmitting antenna in the transmitting antenna sub-array, (x) r Y, z = 0) represents the position coordinates of each reception antenna in the reception antenna sub-array.
R T And R R The acquisition method comprises the following steps:
Figure BDA0002982472710000062
Figure BDA0002982472710000063
where (x ', y ', z ') are the coordinates of the target area.
Step two, the formula (1) is put along (x) t ,x r And y) performing three-dimensional Fourier transform, transforming the echo data into a frequency wavenumber domain, and expressing as follows:
Figure BDA0002982472710000064
wherein P (k) xt ,k xr ,k y K) can be expressed as:
Figure BDA0002982472710000071
wherein k is xt For the corresponding spatial wave number, k, in the direction of the sub-array of transmitting antennas xr For receiving the corresponding spatial wave number, k, in the direction of the sub-array of antennas y For the corresponding space in the scanning direction of the synthetic apertureWave number, k c J represents an imaginary unit for a wave number corresponding to the center frequency.
The integral term in equation (5) can be solved by the stationary phase principle to obtain simplified wavenumber domain data:
Figure BDA0002982472710000072
the dispersion relation satisfied by the wavenumber domain obtainable from equation (6) can be expressed as:
Figure BDA0002982472710000073
wherein k is x Representing the corresponding spatial wavenumber, k, in the direction of the MIMO antenna array z The wave number in the direction of the distance is represented,
Figure BDA0002982472710000074
indicating that a is defined as B.
Step three, in the application of terahertz wave band near field imaging, k is easily satisfied xt ,k xr ,k y Then, the second dispersion relation in (7) can be expressed in a binomial approximation form according to the fresnel approximation principle as follows:
Figure BDA0002982472710000075
then a representation of the phase shift offset factor can be constructed as follows:
Figure BDA0002982472710000081
wherein the content of the first and second substances,
Figure BDA0002982472710000082
representing the distance coordinates of the target area, using the variable k = k c +k b Equation (9) can be further split into:
Figure BDA0002982472710000083
wherein k is c Representing wave number, k, corresponding to the center frequency b For wave number, M, corresponding to baseband frequency 1 For the first sub-term of the phase shift offset factor, M 2 A second sub-term of the phase shift offset factor before reduction;
Figure BDA0002982472710000084
expressed in distance z c And the distance coordinate corresponding to the target area when the distance is towards the zero point of the coordinate. Therefore, according to the Fresnel approximation principle, after the distance wave number is subjected to binomial approximation, the phase shift offset operator is split into three independent exponential terms according to the terahertz waveband narrow-band approximation.
Step four, in the terahertz wave band, the bandwidth is smaller relative to the carrier frequency, namely k b Relative to k c Little change, then M 2 Term available k c Replacing k in the denominator, then M 2 Can be further simplified into:
Figure BDA0002982472710000085
it can be seen that M 1 Distance independent, referred to as fixed distance phase shift factor;
Figure BDA0002982472710000086
and variable k b Independent, called fixed wavenumber phase-shift factor, exp (j 2 k) b z') denotes an inverse fourier transform factor.
Step five, as can be known from the above statements, based on the three exponential terms obtained by the phase shift offset factor splitting, the expression of the MIMO-SAR imaging result based on the efficient PSM can be finally obtained as shown in formula (12):
Figure BDA0002982472710000091
wherein the content of the first and second substances,
Figure BDA0002982472710000092
is a one-dimensional inverse Fourier transform,
Figure BDA0002982472710000093
for two-dimensional inverse Fourier transform, FT 3D For three-dimensional fourier transform, rerange denotes the rebinning operation,
Figure BDA0002982472710000094
the spatial coordinates of the target region are determined after imaging.
It should be noted that the rearrangement operation specifically includes: will be provided with
Figure BDA0002982472710000095
The resulting four-dimensional matrix
Figure BDA0002982472710000096
According to a set dispersion relation
Figure BDA0002982472710000097
Rearranging to obtain a three-dimensional matrix
Figure BDA0002982472710000098
Last pair of
Figure BDA0002982472710000099
Performing two-dimensional inverse Fourier transform to obtain a final reconstructed image
Figure BDA00029824727100000910
Wherein
Figure BDA00029824727100000911
Is represented by k x ,k y The spatial coordinates determined after the inverse fourier transform.
Next, the feasibility of the algorithm is simulated and analyzed by setting specific simulation parameters.
1) And setting simulation parameters shown in table 1:
table 1 example simulation parameter settings
Figure BDA00029824727100000912
2) The MIMO linear array is arranged as shown in fig. 2, the receiving antenna sub-array comprises 39 receiving antennas, the transmitting antenna sub-array comprises 6 transmitting antennas, the transmitting antennas are uniformly divided into two parts and arranged at two ends of the receiving antennas, meanwhile, the interval between the transmitting antennas is 2.5mm, the interval between the receiving antennas is 7.5mm, and the total length of the MIMO antenna array is 0.3m.
3) The multi-target coordinate setting is shown in FIG. 3, the 3-D simulation results of BPA and the proposed algorithm are shown in FIG. 4 and FIG. 5, and the array dimension one-dimensional profile of the two at the central three target points is shown in FIG. 6. Therefore, the method utilizes the high efficiency of the frequency domain algorithm, solves the problem of data interpolation in the traditional RMA, avoids the truncation effect of an interpolation mode and an interpolation kernel, and can obtain higher imaging quality; meanwhile, the invention combines the one-dimensional MIMO linear array and the one-dimensional mechanical scanning technology, realizes three-dimensional imaging by equivalent linear array scanning to two-dimensional synthetic aperture, also solves the problem of time consumption of wave number domain integration in the traditional PSM algorithm, further exerts the advantage of phase shift substitution interpolation on the premise of ensuring the imaging effect, improves the processing speed, can greatly reduce the number of array elements, improves the data acquisition rate and reduces the system cost.
The present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof, and it will be understood by those skilled in the art that various changes and modifications may be made herein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (5)

1. A three-dimensional rapid imaging method for MIMO-SAR is characterized in that an MIMO antenna array consists of a transmitting antenna subarray and a receiving antenna subarray which are positioned on the same straight line, and the imaging result of the MIMO-SAR is obtained
Figure FDA0003901655050000011
The calculation formula of (2) is as follows:
Figure FDA0003901655050000012
wherein the content of the first and second substances,
Figure FDA0003901655050000013
is a one-dimensional inverse Fourier transform,
Figure FDA0003901655050000014
for two-dimensional inverse Fourier transform, FT 3D For three-dimensional Fourier transform, s (x) t ,x r Y, k) is a reflected echo signal under the MIMO-SAR system, wherein x t Representing the x-axis coordinate, x, of each transmit antenna in a sub-array of transmit antennas r X-axis coordinates of each receiving antenna in the receiving antenna sub-array, y-axis coordinates of each antenna in the transmitting antenna sub-array and the receiving antenna sub-array, redundancy represents a rearrangement operation,
Figure FDA0003901655050000015
for the spatial coordinates of the target region determined after imaging, M 1 For the first sub-term of the phase shift offset factor,
Figure FDA0003901655050000016
is a second sub-term of the phase shift offset factor and has:
Figure FDA0003901655050000017
Figure FDA0003901655050000018
wherein z is c The distance from the MIMO antenna array to the center of the target area, k is the corresponding wave number when the transmitting antenna sub-array externally radiates frequency stepping signals, k xt Is the corresponding space wave number, k, in the direction of the transmitting antenna sub-array xr For receiving the corresponding spatial wave number, k, in the direction of the sub-array of antennas y For the corresponding number of spatial waves, k, in the scanning direction of the synthetic aperture c The number of waves corresponding to the center frequency, j denotes an imaginary unit,
Figure FDA0003901655050000019
expressed in distance z c The distance coordinate corresponding to the target area when the distance coordinate is zero;
the rearrangement operation specifically comprises the following steps:
will be provided with
Figure FDA00039016550500000110
The resulting four-dimensional matrix
Figure FDA00039016550500000111
According to a set dispersion relation
Figure FDA00039016550500000112
Rearranging to obtain a three-dimensional matrix
Figure FDA00039016550500000113
2. Three-dimensional fast imaging method for MIMO-SAR according to claim 1, characterized in that said first sub-term M of the phase shift offset factor 1 With a second sub-term of the phase shift offset factor
Figure FDA0003901655050000021
The acquisition method comprises the following steps:
s1: reflection echo signal s (x) under the MIMO-SAR system t ,x r Y, k) is:
Figure FDA0003901655050000022
wherein O (x ', y ', z ') is the reflectivity of the target region, R T For the distance, R, between each transmitting antenna in the sub-array of transmitting antennas and the target area R (xt, y, z) represents the position coordinates of each transmitting antenna in the transmitting antenna sub-array, (x) represents the distance between each receiving antenna in the receiving antenna sub-array and the target area r Y, z) represents the position coordinates of each receiving antenna in the receiving antenna sub-array, where z =0;
s2: will reflect the echo signal s (x) t ,x r Y, k) is subjected to three-dimensional Fourier transform to obtain a reflected echo signal s (x) t ,x r Y, k) is expressed in the frequency wavenumber domain as:
Figure FDA0003901655050000023
wherein, P (k) xt ,k xr ,k y ,k)=∫∫∫exp(-jk(R T +R R ))·exp(-jk xt x t )·exp(-jk xr x r )exp(-jk y y)dx t dx r dy;
S3: solving for P (k) by using stationary phase principle xt ,k xr ,k y K), the following dispersion relation is obtained:
Figure FDA0003901655050000024
wherein k is x Representing the corresponding spatial wavenumber, k, in the direction of the MIMO antenna array z Represents the wave number in the distance direction;
s4: suppose that the MIMO-SAR works in the terahertz wave band and obtains the dispersion relation
Figure DA00039016550532491382
Approximation of binomial equation ofTo represent
Figure FDA0003901655050000026
The following were used:
Figure FDA0003901655050000031
s5: approximating a representation according to said binomial
Figure FDA0003901655050000032
Constructing a phase shift offset factor
Figure FDA0003901655050000033
The following:
Figure FDA0003901655050000034
wherein the content of the first and second substances,
Figure FDA0003901655050000035
distance coordinates of the target area are taken as coordinates;
s6: for phase shift offset factor
Figure FDA0003901655050000036
Wave number k in k = k c +k b Partial variable replacement is performed to split the phase shift offset factor
Figure FDA0003901655050000037
Figure FDA0003901655050000038
Wherein k is b For wave number, M, corresponding to baseband frequency 2 A second sub-term of the phase shift offset factor before reduction;
s7: miningBy k c Substitution of M 2 K in the term denominator, resulting in a second sub-term of the simplified phase shift offset factor
Figure FDA0003901655050000039
Figure FDA00039016550500000310
3. The three-dimensional fast imaging method for MIMO-SAR according to claim 2, characterized in that R T And R R The acquisition method comprises the following steps:
Figure FDA00039016550500000311
Figure FDA00039016550500000312
where (x ', y ', z ') are the coordinates of the target area.
4. The three-dimensional fast imaging method for MIMO-SAR of claim 1, wherein in the MIMO antenna array, the receiving antenna sub-array is located in the middle, and the transmitting antenna sub-array is divided into two parts and arranged at both ends of the receiving antenna sub-array.
5. The three-dimensional fast imaging method for the MIMO-SAR of claim 1, wherein the receiving antenna sub-array comprises 39 receiving antennas, the transmitting antenna sub-array comprises 6 transmitting antennas, and the transmitting antennas are equally divided into two parts and arranged at both ends of the receiving antennas, meanwhile, the interval between the transmitting antennas is 2.5mm, the interval between the receiving antennas is 7.5mm, and the total length of the MIMO antenna array is 0.3m.
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