Bistatic Point Target Reference Spectrum Research Articles

Range‐resolution improvement for spaceborne/airborne bistatic synthetic aperture radar using stepped‐frequency chirp trains

In this paper, a stepped-frequency spaceborne/airborne bistatic synthetic aperture radar (SFSA-BiSAR) configuration is proposed to show to improve the range resolution of BiSAR. First, the geometry and the signal model of SFSA-BiSAR are formulated, and then an analytical bistatic point target reference spectrum (BPTRS) is derived. Second, based on the developed BPTRS, two imaging algorithms called combination-before-focusing algorithm (CBFA) and combination-after-focusing algorithm (CAFA) are proposed to obtain BiSAR images with improved range resolution. CBFA uses sub-band combination to obtain synthetic BPTRS, and then uses a new bistatic frequency-domain algorithm (BFDA) to obtain the improved BiSAR image, whereas CAFA first uses the BFDA to focus all the sub-pulses, and then uses sub-image combination to obtain the improved BiSAR image. Both of the two algorithms can focus the SFSA-BiSAR signal well and comparison simulations are performed to verify the authors' conclusion. Computation loads are also calculated to compare the two algorithms and show that CAFA uses less floating-point operations than CBFA. Besides, some important parameters of SFSA-BiSAR are analysed both theoretically and numerically to provide a reference for system design.

Focusing bistatic forward-looking synthetic aperture radar based on modified Loffeld’s bistatic formula and chirp scaling algorithm

A focusing solution for bistatic forward-looking synthetic aperture radar (BFSAR) is presented. Forward-looking imaging is highly desirable in some potential applications, such as self-landing in bad weather, military surveillance, and navigation. Unfortunately, monostatic synthetic aperture radar reaches its limit when it is used in a forward-looking configuration. BFSAR can provide a high-resolution image in the forward-looking direction. However, due to the special forward-looking geometry, many proposed methods of deriving a bistatic point target reference spectrum (BPTRS) cannot handle the BFSAR data well. A modified Loffeld's bistatic formula (MLBF) for a forward-looking configuration is proposed first; it can get an accurate BPTRS of BFSAR. Then, a chirp scaling algorithm (CSA) based on MLBF is derived. CSA without interpolation allows high performance. Numerical simulations show that the proposed focusing solution can handle the BFSAR data well and achieve a high- resolution focused image. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. (DOI: 10.1117/1.JRS.8.083586)

BISTATIC FORWARD-LOOKING SYNTHETIC APERTURE RADAR IMAGING BASED ON THE MODIFIED LOFFELD'S BISTATIC FORMULA

Bistatic forward-looking SAR (BFSAR) has many potential applications, such as self- landing in bad weather and military detection. Therefore, BFSAR receives considerable attention recently. The imaging algorithms for BFSAR are the di-culties of the study. The original Lofield's Bistatic Formula (LBF) can handle most general bistatic SAR conflgurations well. But in some complex bistatic geometries, such as high squint or forward-looking cases, the performance of LBF is degenerated. Some extended LBF (ELBF) methods have been developed, which improve the performance of LBF in some special geometries, but still not the forward-looking conflguration. In this paper, we modify the LBF method and try to solve the instantaneous azimuth frequencies of transmitter and receiver directly. Then, we can obtain a bistatic point target reference spectrum (BPTRS), which is accurate enough for forward-looking conflguration. A range Doppler algorithm (RDA) based on this BPTRS is derived. Finally, simulations validate the accuracy of the modifled Lofield's Bistatic Formula (MLBF) and efiectiveness of imaging algorithm.

Spaceborne/airborne bistatic synthetic aperture radar focusing on an analytical bistatic point target reference spectrum

An analytical bistatic point target reference spectrum (BPTRS) is proposed. The BPTRS is derived from the one-to-one relationship between slow time and Doppler frequency with no Taylor series expansions. Based on the BPTRS, a two-dimensional frequency-domain focusing algorithm for spaceborne/airborne bistatic synthetic aperture radar is developed. The algorithm exploits a range-dependent sub-blocks processing method to perform range cell migration correction and quadratic Doppler term compensation, and then a scaled inverse Fourier transformation and a sinc interpolation are used to correct the geometric distortions in azimuth and range, respectively. Some simulation experiments are also presented to verify their performance.

Bistatic FMCW SAR Signal Model and Imaging Approach

The bistatic configuration of frequency-modulated continuous wave (FMCW) synthetic aperture radar (SAR) offers considerable capabilities, reliability and flexibility in designing the compact size and low cost remote sensing systems. Furthermore, the spacial separation between transmitter and receiver avoids the antenna isolation problem. A signal model is proposed here to accurately formulate the bistatic slant range history in FMCW SAR configuration, where the motion during the long pulse duration is taken into account. Moreover, based on the preceding model, an optimization approach is presented to deal with the double square root (DSR) term, and thus an accurate FMCW bistatic point target reference spectrum (BPTRS) is derived. The proposed spectrum can not only address the signal characteristics of bistatic FMCW SAR, but also significantly simplify the bistatic FMCW SAR processing, which will really push the applications of FMCW SAR in the remote sensing field. Furthermore, based on the proposed signal model, the application of an improved range-Doppler algorithm (RDA) is further proposed to focus the bistatic FMCW SAR data. Simulation experiments are carried out to verify the accuracy of this novel formulation and highlight the performance of the proposed focusing approach.

Model and signal processing of bistatic frequency-modulated continuous wave synthetic aperture radar

Bistatic frequency-modulated continuous wave (FMCW) synthetic aperture radar (SAR) mounts the radar transmitter and receiver on separate platforms, which offers considerable capabilities, reliability and flexibility in designing FMCW SAR missions. Moreover, the spatial separation achieves better isolation between transmission and reception channels compared with the monostatic FMCW SAR where the two separate dedicated antennas are fixed on one platform. In this study, a bistatic FMCW SAR signal model is proposed to formulate the bistatic slant range history in bistatic FMCW configuration. Based on the preceding model, an approach is presented to deal with the double-square-root (DSR) term, and thus an accurate FMCW bistatic point target reference spectrum (BPTRS) is derived. Besides accurately addressing the signal characteristics of bistatic FMCW SAR, the proposed spectrum also significantly simplifies the signal processing of bistatic FMCW SAR, which will really push the applications of bistatic FMCW SAR in remote sensing fields. Furthermore, based on the proposed BPTRS, an extended inverse chirp-Z transform (EICZT) algorithm is proposed to process the bistatic FMCW SAR data by introducing a perturbation function to deal with the range-variance of second- and third-order range–azimuth coupling terms. Two simulation experiments are carried out to verify the accuracy of this novel formulation and highlight the performance of the proposed focusing approach.

BISTATIC FMCW SAR RAW SIGNAL SIMULATOR FOR EXTENDED SCENES

By mounting the transmitter and receiver of Frequency Modulated Continuous Wave (FMCW) Synthetic Aperture Radar (SAR) system on separate platforms, bistatic FMCW SAR ofiers more considerable capabilities, reliability and ∞exibility while maintaining the small size, low cost and agile reaction. The bistatic FMCW SAR raw signal simulator is highly required to quantitatively support the design of bistatic FMCW SAR, to help mission planning, test processing algorithms, and analyze jamming and noises. Bistatic FMCW SAR raw signal can be exactly simulated target-by-target in time domain but with extremely time and memory consuming, especially when extended scenes are considered. In this paper, bistatic FMCW SAR signal model and Bistatic Point Target Reference Spectrum (BPTRS) is proposed, based on which a raw signal simulator is developed in the 2-D frequency domain for the flrst time, where Chirp-Z Transform (CZT) is used to formulate the range migration terms. By taking advantage of Fast Fourier Transform (FFT), the proposed raw signal simulator highly reduces the computational load with respect to the time domain approach. The simulated raw data is verifled by analyzing the corresponding images focused by Range Doppler Algorithm (RDA).

Processing the Azimuth-Variant Bistatic SAR Data by Using Monostatic Imaging Algorithms Based on Two-Dimensional Principle of Stationary Phase

This paper presents a new bistatic point target reference spectrum. It is derived by using the 2-D principle of stationary phase which is first applied in the synthetic aperture radar (SAR) community. The spectrum contains two hyperbolic range-azimuth coupling terms and thus is very similar to the monostatic spectrum. It shows the characteristic of the conventional monostatic SAR besides an additional azimuth scaling term. Therefore, it makes the common Doppler-based monostatic processing algorithms readily suitable to handle the Bistatic SAR (BiSAR) data in the moderate-squint azimuth-variant configurations with two moving platforms. Based on the spectrum, two Doppler-based monostatic imaging algorithms [i.e., range-Doppler algorithm (RDA) and chirp-scaling algorithm (CSA)] are readily implemented to deal with the moderate-squint azimuth-variant BiSAR data. Compared to the processing procedure for the monostatic SAR, the RDA and CSA for the BiSAR need only the adjustment of Doppler parameters. Finally, the potential and limitation of the spectrum are analyzed, and the real raw data in the spaceborne/airborne configurations are used to validate the proposed spectrum and processing methods.

RANGE DOPPLER ALGORITHM FOR BISTATIC SAR PROCESSING BASED ON THE IMPROVED LOFFELD'S BISTATIC FORMULA

This paper presents a new range Doppler algorithm (RDA) for bistatic synthetic aperture radar (SAR) processing in a general conflguration based on a bistatic point target reference spectrum: the improved extended Lofield's bistatic formula (ILBF). The ILBF spectrum is proved to be comparably accurate with the spectrum derived using the method of series reversion (MSR). Based on the expansion of the ILBF spectrum, a new bistatic RDA is developed to process the azimuth invariant and variant bistatic SAR data. Compared with existing bistatic RDA, the new algorithm has a simpler formulation and is able to cope with moderate or high squint bistatic SAR data. The simulated data in the azimuth invariant and variant bistatic conflgurations are used to validate the new algorithm.

Frequency-Domain Bistatic SAR Processing for Spaceborne/Airborne Configuration

This paper focuses on the bistatic synthetic aperture radar (BiSAR) signal processing in the spaceborne/airborne configuration. Due to the extreme differences in platform velocities and slant ranges, the airborne system operates in the inverse sliding spotlight mode, while the spaceborne system works in the sliding spotlight mode to achieve a tradeoff between the azimuth scene size and azimuth resolution. Such a mode is generally called double sliding spotlight mode. In this configuration, the echoed signal has two characteristics. Firstly, both transmitter and receiver have very short synthetic aperture times. Secondly, the airborne platform operates with wide squint difference, while the spaceborne platform works in the small squint case. According to these two features, we use different Taylor expansions to address the slant range histories of transmitter and receiver. Based on the presented model, a two-dimensional space-variant bistatic point target reference spectrum (BPTRS) is derived. Furthermore, we linearize the BPTRS to derive the transfer function of the baseband scene. From the transfer function, the signal features of the spaceborne/airborne configuration become very clear. Using the transfer function, the two-dimensional inverse scaled Fourier transform (ISFT) is used to focus the bistatic signal in the spaceborne/airborne configuration.

Extending Loffeld's bistatic formula for the general bistatic SAR configuration

This study derives an accurate bistatic point target reference spectrum based on a zeroth-order polynomial model. The spectrum contains only two hyperbolic square root terms that are very analogous in form to the analytical monostatic spectrum. The new formulation can be considered as an improvement of the Loffeld's bistatic formula (LBF) and allows it to handle a wider range of bistatic configurations. The original LBF works well only in the case where the contributions of transmitter and receiver to the total Doppler modulation are approximately equal. An earlier paper on the extended LBF (EBLF) uses time bandwidth product (TBP) to weight the azimuth phase modulation from each platform. However, this extension is valid only in the low squint bistatic geometry. Both LBF and ELBF are expanded up to the quadratic term to derive an approximate bistatic spectrum; however, they do not show a good focusing performance in the more complex bistatic geometry, for example, the high squint case. This is due to the inaccurate individual time-Doppler correspondences. In this study, a norm in Euclidean space is defined to derive the optimal individual time-Doppler correspondences. Using the accurate individual time-Doppler correspondences, a zeroth-order polynomial model can be used to readily derive a more accurate bistatic spectrum. Two simulation experiments in the high squint geometry are used to verify the accuracy of this new formulation. The first experiment uses a parallel-track spaceborne/spaceborne configuration, and the second experiment involves an orthogonal-track airborne/airborne case.

Focusing Bistatic SAR Data in Airborne/Stationary Configuration

This paper presents a frequency-domain-based focusing algorithm for the bistatic synthetic aperture radar (BiSAR) data in airborne/stationary configuration. In this bistatic configuration, only the moving platform contributes to the azimuth modulation, whereas the stationary platform introduces a range offset (RO) to the range migration trajectories of targets at the same range. The offset is determined by the azimuth position of different targets with respect to the stationary platform. Since the RO is position dependent, monostatic SAR imaging algorithms are not able to focus the bistatic data collected in this configuration. In this paper, an analytical bistatic point-target reference spectrum is derived, and then, a frequency-domain-based algorithm is developed to focus the bistatic data. It uses an interpolation-free wavenumber-domain algorithm as a basis and performs a range-variant interpolation to correct the position-dependent RO in the image domain after coarse focusing. The proposed algorithm is validated by the simulated data and the real BiSAR data acquired by the Forschungsgesellschaft fu?r Angewandte Naturwissenschaften's airborne SAR system, PAMIR, in December 2007. In this BiSAR experiment, an X-band transmitter was stationary operated on a hill with PAMIR as the receiver mounted on a Transall C-160.

Focusing Spaceborne/Airborne Hybrid Bistatic SAR Data Using Wavenumber-Domain Algorithm

This paper focuses on the bistatic synthetic aperture radar (SAR) data processing in a spaceborne/airborne hybrid bistatic configuration. Due to the extreme differences in platform velocities and slant ranges, the airborne system operates in the inverse sliding-spotlight mode, while the spaceborne system works in the sliding-spotlight mode to achieve a tradeoff between azimuth scene size and azimuth resolution. In this extreme bistatic configuration, our original bistatic formula shows a limitation of accurately describing the bistatic point-target reference spectrum, owing to the assumption of equal contributions of transmitter and receiver to the total Doppler spectrum. We extend our previous formula using the weighting operation where the weighting factor is the ratio of the azimuth time-bandwidth product (TBP) of the platform to the total azimuth TBP. In this paper, the bistatic-deformation and azimuth-dependent range-cell-migration terms were removed with phase multiplications performed blockwise in range-azimuth subsections. The remaining quasi-monostatic term shows the characteristic of the conventional monostatic SAR besides an additional azimuth-scaling term. For the monostatic characteristic, any precision monostatic SAR processing algorithms can handle. In this paper, we prefer the wavenumber-domain algorithm (also known as Omega-K), since it can accurately correct the range dependence of the range-azimuth coupling, as well as the azimuth-frequency dependence. For the azimuth-scaling term, an inverse scaled Fourier transformation is performed to correct it. Finally, a hybrid spaceborne/airborne simulation experiment is conducted to validate the proposed processing procedure.

A Bistatic Point Target Reference Spectrum for General Bistatic SAR Processing

A bistatic point target reference spectrum (BPTRS) based on Loffeld's bistatic formula (LBF) is derived in this letter. For LBF, the same contributions of the transmitter and receiver to the total azimuth modulation are assumed. This assumption results in the failure of LBF in the extreme configuration (i.e., spaceborne/airborne configuration). For general bistatic configurations, the azimuth modulations are unequal for the transmitter and receiver due to the different slant ranges and velocities. Therefore, the azimuth time-bandwidth products (TBPs) from the transmitter and receiver are different; in some cases (e.g., spaceborne/airborne case), one of them might be very small, which might even result in a serious error of the principle of stationary phase. This letter uses TBP to weight the azimuth phase modulation contributions of the transmitter and receiver to the common azimuth spectrum to approximately obtain the point of stationary phase of the total azimuth phase history. Simulations show that the proposed BPTRS can work well for spaceborne/airborne configurations.