As a special multiple-input multiple-output (MIMO) radar networking mode, missile-borne forward-looking synthetic aperture radar (MFL-SAR) has many potential applications. This paper describes and analyzes properties of this new configuration. Range history and Doppler history are analyzed and derived using the designed geometric configuration. Then the expressions of range and Doppler resolution are determined based on the validity of two-dimensional (2D) resolution imaging capability. To help to design the proper system and motion parameters of this configuration, key parameters affecting the imaging ability are found out. Due to high velocities and accelerations of both transmitter and receiver, high-order terms in the slant range equation should be kept to reduce the approximation error. The range resolution and Doppler resolution of MFL-SAR are both space-variant and time-variant owing to the complexity of this configuration. The tiny changes of 2D resolution during the synthetic aperture time should be considered when designing the imaging algorithm of MFL-SAR.
Multiple-input multiple-output (MIMO) [
In order to confirm the validity of application of such MIMO radar networking system to missile-borne platform, the mode of “single-transmitting and single-receiving” is assumed, that is, missile-borne bistatic forward-looking SAR (MBFL-SAR). MBFL-SAR is a new bistatic SAR imaging mode [
Configuration and resolution analysis are the basis of MBFL-SAR imaging study, and some researches have been published. Three different bistatic forward-looking SAR configurations have been analyzed, and the optimal geometry configurations have been proposed in [
In this paper, we describe and analyze this special configuration. Geometric configuration and signal model of MBFL-SAR are introduced in Section
MBFL-SAR configuration is shown in Figure
Geometric configuration of MBFL-SAR.
The locations of transmitter and receiver at
The position of transmitter
Then we can obtain the expression of instantaneous bistatic slant range as
Suppose that the transmitted waveform is the linear frequency modulation (LFM), and scattering from
To design imaging algorithms for MBFL-SAR more conveniently, it is important to take efficient approximation of
Parameters used in the simulations.
Wavelength | 0.02 m |
Bandwidth | 50 MHz |
Sampling frequency | 100 MHz |
Pulse duration | 2 |
PRF | 9 KHz |
|
20° |
|
25 km |
|
20 km |
|
(0, 1500, −1000) m/s |
|
(0, −50, 30) m/s2 |
|
(0, 1500, −1000) m/s |
|
(0, −50, 30) m/s2 |
Approximation errors of the bistatic slant range.
Up to quadratic term
Up to the third term
It can be seen that the maximum approximation error when keeping the terms up to the quadratic term is about 0.02 m, nearly the value of wavelength, so it is necessary to keep the higher term. When keeping the terms up to the third term, the maximum approximation error is only 2.44 × 10−6 m, which is much less than the value of wavelength. Therefore, expanding (
Doppler frequency can be obtained through derivation of slant range and is expressed as
Doppler centroid represents echo Doppler frequency at the moment beam center cross target, given by
Doppler centroid represents correlativity only to motion parameters and irrelevance to location of targets in the traditional case where monostatic SAR moves with invariant velocity along a straight line or the case where transmitter and receiver move with equal velocities along parallel trajectories in traditional airborne bistatic SAR system. However, it can be seen from (
Doppler frequency rate is the change rate of Doppler frequency and can be expressed as
We can find from (
Range walk ratio represents the range walk increment of echo signal in per time unit; it can be obtained as
Similar to Doppler centroid, range walk ratio in MBFL-SAR configuration is also space-variant. Such space-variance leads to the result that MBFL-SAR does not have azimuth-invariant property, which is important to conventional algorithms in monostatic SAR and airborne bistatic SAR in parallel and velocity-equivalent mode. So space-variance must be considered when the range cell migration correction is achieved.
In this section, 2D imagingresolution of MBFL-SAR is analyzed. The expressions of range resolution and Doppler resolution are determined using gradient method [
Assume that
According to the geometrical relationship in Figure
Substituting (
According to gradient method in [
As shown in the coordinate system in Figure
Again, using the gradient method, the Doppler resolution can be obtained as
Similarly,
In this section, several examples are provided to illustrate the resolution ability in the MBFL-SAR. Below are some simulation results of the resolution capability and 2D resolution. Parameters used in the simulations are listed in Table
MBFL-SAR range contours and Doppler frequency contours when
MBFL-SAR range resolution and Doppler resolution when
Range resolution
Doppler resolution
MBFL-SAR range resolution and Doppler resolution at different
Range resolution
Doppler resolution
To further analyze the signal properties of MBFL-SAR, several simulations about airborne bistatic forward-looking SAR (ABFL-SAR) are also realized, where the velocities of the transmitter and receiver are 150 m/s and 100 m/s with included angle of 20 degrees, and the heights are 5 km and 2 km, respectively. Doppler frequency and RWR comparisons of five-point targets 150 m apart from each other in the imaging area are conducted between ABFL-SAR and MBFL-SAR during the same synthetic aperture time. The results are given in Figures
Doppler frequency comparison between ABFL-SAR and MBFL-SAR.
ABFL-SAR
MBFL-SAR
RWR comparison between ABFL-SAR and MBFL-SAR.
ABFL-SAR
MBFL-SAR
RCC comparison between ABFL-SAR and MBFL-SAR.
ABFL-SAR
MBFL-SAR
MBFL-SAR range contours and Doppler frequency contours when
Figure
Some simulations are also achieved to analyze range resolution and Doppler resolution of MBFL-SAR at different
Because of the presence of high velocities and accelerations in MBFL-SAR configuration, Doppler frequencies of targets in the imaging area have greater changes than ABFL-SAR. And range cell migrations (RCMs) are also more severe during the same synthetic aperture time; that is to say, RWRs are greater. As shown in Figure
Applications of MIMO radar networking technology to radar imaging can improve the performance of radar imaging resolution, targets detection, recognition, and tracking. As a special MIMO radar networking system, MBFL-SAR is a special mode of bistatic forward-looking imaging by combining geometry configuration of bistatic motion with forward-looking mode and has potential of being applied to missile precision terminal guidance. Properties of MBFL-SAR are analyzed in this paper. The high velocities and the two square-root terms lead to the presence of high-order terms in slant range history and Doppler history which cannot be ignored. Simulations have been done to illustrate the resolution ability of this configuration, and both range resolution and Doppler resolution are space-variant and time-variant. The tiny changes of the values of 2D resolution in this configuration during short synthetic aperture time and comparisons with ABFL-SAR can be used to design imaging algorithms in this special configuration. Research on the properties of MBFL-SAR configuration validates the efficiency of the application of MIMO radar networking to radar imaging, which also provides theoretical groundwork for the whole system parameter design and imaging algorithms of MBFL-SAR.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China under Grant nos. 61001211 and 61303035, the Fundamental Research Funds for the Central Universities (K5051202016), and the Science Foundation for Navigation (20110181004).