A point target reference spectrum based on Loffeld's bistatic formula (LBF) for hybrid configurations

In this paper, an omega-K imaging algorithm to focus the raw data of translational invariant (TI) bistatic synthetic aperture radar (BSAR) is proposed. The method utilizes a point target reference spectrum of generalized Loffeld's bistatic formula (GLBF). Without the bistatic deformation term, GLBF is the latest development of Loffeld's bistatic formula. It is comparable in precision with the method of series reversion (MSR), but it has a much simpler form than MSR and a similar form to a monostatic case. Based on the spatial linearization of GLBF, the Stolt transformation relationship is derived. The method can consider the linear spatial variation of Doppler parameters, which is always ignored in previous publications about bistatic omega-K algorithms. This method can handle the cases of TI BSAR with high squint angles and large bistatic degrees. In addition, a compensation method for the phase error caused by the linearization is discussed. Numerical simulations and experimental data processing verify the effectiveness of the proposed method.

Focusing bistatic synthetic aperture radar (SAR) data in frequency domain requires two-dimensional (2D) point target reference spectrum (PTRS). Lofield's bistatic formula (LBF) and the Method of Series Reversion (MSR) have been introduced recently to compute PTRS of bistatic SAR. In this paper, flrstly we generalize the original LBF (OLBF) by introducing the Doppler contribution functions of transmitter and receiver. Thus, OLBF and its derivatives (e.g., extended LBF) can be viewed as special forms of the generalized LBF with constant Doppler contributions. Based on this, secondly the ideal LBF (ILBF) with no computing error, except the error resulting from the principle of stationary phase, is also presented. The ILBF reveals that the theoretical PTRS of bistatic SAR consists of only two monostatic terms, but it does not include bistatic deformation term in comparison with OLBF. It supplies us with a target when we deduce the PTRS for bistatic SAR. Finally, to get the precise analytical PTRS for general bistatic SAR, an approximated ILBF (AILBF) is proposed. It expresses the Doppler contributions of the transmitter and receiver as power series and can approach the ILBF very well. AILBF can keep the precision as MSR and inherit a simple form from LBF. In addition, error limit for the validity of bistatic PTRS is also given. The results in this paper can be used to develop imaging algorithms for extreme bistatic (e.g., spaceborne/airborne) and high squint (e.g., bistatic forward-looking) cases.

With the Loffeld's bistatic formula, the point target reference spectrum (PTRS) of multireceiver synthetic aperture sonar (SAS) can be decomposed into the quasi monostatic term and bistatic deformation (BD) term. The former term is analogous to the monostatic SAS PTRS while the latter one describes the bistatic phase introduced by the bistatic displacement between the transmitter and receiver. The multireceiver SAS echo signal can be transformed into monostatic SAS equivalent data after correcting the BD term. Based on the range sub‐block processing method, this data transformation is conducted by using the preprocessing step. Then, fast imaging processors based on monostatic SAS system can be directly exploited to process the monostatic SAS equivalent data. In this paper, the authors mainly focus on the application of non‐linear chirp scaling algorithm. At last, the simulations and real data are used to validate the presented method. The processing results show that the imaging performance of presented method is nearly close to that of traditional method. Besides, the imaging efficiency is highly improved compared to the phase centre approximation (PCA) method.

The individual azimuth contribution of transmitter and receiver phase terms has been optimized by weighting them unequally based on a weighting factor mu, in Loffeld's bistatic formula (LBF). Analytical results are verified with the simulations.

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.

A weighting solution based on the original Loffeld's bistatic formula (LBF) is addressed briefly in this paper to deal with the cases with noticeable difference between transmitter and receiver's velocities. The published LBF-based approaches use range blocks to deal with the range variance. Alternatively, a new wavenumber domain algorithm is proposed by using the linearization of bistatic range, which follows the same routine of the monostatic Omega-K algorithm. The approximation in this range linearization is examined with space-surface hybrid and airborne bistatic configurations. Due to large phase error for the airborne case, a second phase multiply have to be used in its focusing. This approach results in a good focusing performance over simulated data.

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.

With appropriate geometry configurations, bistatic Synthetic Aperture Radar (SAR) can break through the limitations of monostatic SAR for forward-looking imaging. Thanks to such a capability, bistatic forward-looking SAR (BFSAR) has extensive potential applications. This paper develops a frequency-domain imaging algorithm for translational invariant BFSAR. The algorithm uses the method of Lengendre polynomials expansion to compute the two dimensional point target reference spectrum, and this spectrum is used to perform the range cell migration correction (RCMC), secondary range compression and azimuth compression. In particular, the Doppler-centroid and bistatic-range dependent interpolation for residual RCMC is presented in detail. In addition, a method that combines the ambiguity and resolution theories to determine the forward-looking imaging swath is also presented in this paper.

In Radar remote sensing, the electromagnetic (em) modeling of scattering contributions from natural or man-made scatterers has often to deal with coupling scattering mechanisms due to the underlying reflecting surface (ground or water). For the monostatic configuration, this contribution is commonly associated with the so-called double bounce scattering mechanism, which is also known to be located in synthetic aperture radar (SAR) images at the vertical projection of the scatterer onto the ground. To explore this phenomenon in the more general case of bistatic SAR but also for triple bounce scattering, a new formalism using virtual scatterers is introduced in this paper. Based upon image theory and on far-field assumption, these virtual points are defined by simple interaction scatterers located on the reflecting surface, and involving the same traveling wave path than the considered scattering mechanism. Depending only on the incidence and scattering angles, elegant formulae in their simplicity are highlighted to construct these fictitious scatterers. The resulting reduction of multiple to simple interaction scattering mechanisms simplifies the finding of their location within bistatic SAR images, generalizing thereby migration effects associated to coupling mechanisms in the bistatic configuration.

Range cell migration correction (RCMC) is the key process in the imaging formation of the bistatic SAR. Due to the existence of double-square-root in the bistatic range equation, the RCMC in the general bistatic SAR configuration is more complicated than the traditional monostatic method. In this letter, the range cell migration of bistatic SAR system is analysed in detail, and a novel data transformation is derived. From the derivation, we find that the original keystone transform is only a special case of our proposed transformation, so that we called it the generalized keystone transform. Compared with the original keystone transform, this generalized method can correct more complex range cell migration nicely. After the generalized keystone transform processing, the range cell migration is eliminated closely, and the focused image with full range and Doppler resolution can be obtained using the fast Fourier transform. Finally, a hybrid spaceborne/airborne bistatic SAR numerical simulation is performed to validate the proposed processing procedure.

The forward-looking imaging problem of synthetic aperture radar (SAR) can be resolved by adopting the bistatic configuration. A bistatic configuration with a stationary transmitter and a forward-looking receiver is introduced and the two-dimensional spectrum is derived, and then an improved nonlinear chirp scaling algorithm is used to focus the data. The imaging quality is compared with the traditional nonlinear chirp scaling algorithm; the simulation results verify the 2D imaging ability of the proposed method.

A disadvantage of monostatic SAR is that it cannot image the forward-looking area. In this paper, the possibility of forward-looking imaging with bistatic configuration is verified using DVB-T signals as transmitting signals. The Back Projection (BP) method is used to perform the imaging in each configuration and the point spread functions (PSFs) are presented. The forward-looking imaging ability is analyzed in terms of the resolution for each configuration. From the simulation, we realized forward-looking imaging with bistatic Radar in configuration 3, that is, the squint angle has been reduced to zero. The result show that bistatic forward-looking imaging is feasible and the resolution can achieve the requirement.

The use of a bistatic antenna configuration for ground moving target indication in an ultra-wideband and widebeam synthetic aperture radar system is discussed. To suppress the strong clutter signal the radar channels have a strict requirement on equality. In a bistatic system they are not equal, and the author investigates how to compensate for the bistatic configuration. Bistatic effects on clutter scattering cannot be compensated, and an attempt is therefore made to estimate the bistatic scattering influence of the ground moving target indication. The bistatic to monostatic synthetic aperture inversion in a wide antenna beam is derived in both the time and the frequency domain. The mismatch between the radar channels will cause clutter leakage. The pulse compressed impulse response leakage is determined both for the time and frequency domains.

A bistatic synthetic aperture radar uses a separated transmitter and receiver flying on different platforms to achieve benefits like exploitation of additional information contained in the bistatic reflectivity of targets, reduced vulnerability for military applications, forward looking SAR imaging or increased RCS. A particular constellation, where the transmitter is in space and the receiver near or on the earth surface (e.g. aircraft, tower) is called a hybrid bistatic SAR system. Besides technical challenges, like the synchronization of transmitter and receiver, the overlap of the two antenna footprints is of vital importance. Due to the extreme platform velocity differences, SAR modes with flexible steering of the antenna beams are necessary. The sliding spotlight mode offers such a beam steering, where the antenna footprint velocity can be chosen slower or faster than the platform velocity. If both transmitter and receiver use this mode it is called double sliding spotlight mode, which will be investigated in this paper using the example of the satellite TerraSAR-X and the airborne SAR system PAMIR. Several aspects like the ground resolution, Doppler frequency and Doppler-bandwidth will be analyzed.

The TanDEM-X mission has the goal to deliver a digital elevation model (DEM) that fulfils HRTI-3 quality requirements on a global scale. The interferometric height is determined by the phase difference between the two acquired images and the spatial geometry. Baseline errors intrinsic of the bi-static SAR configuration combined with errors and drifts of the radar instrument introduce phase inaccuracies in the interferogram. Therefore, an accurate calibration of the interferometric system parameters and independent height references are required. In order to validate the DEM calibration concept with real interferometric data, a measurement campaign was carried out with the experimental airborne radar system (E-SAR) of the German Aerospace Center (DLR) in Oberpfaffenhofen. This paper will present some of the various results from these interferometric experiments, stressing on the quality assessment of the ICESat GLAS14 elevation data, which will be a key aspect in a successful TanDEM-X DEM generation.