Stefano Perna

Motion compensation errors: effects on the accuracy of airborne SAR images

This work addresses the study of the effect of residual uncompensated motion errors due to positioning measurement instrument and digital elevation model inaccuracies on the accuracy of airborne synthetic aperture radar (SAR) images. It is shown that these not only introduce phase errors following pure geometric considerations, but they also cause additional aberrations related to their interaction with the SAR processing procedure. Extension to the repeat pass airborne interferometry is also included to show their impact on the resulting interferograms.

Efficient simulation of airborne SAR raw data of extended scenes

In a previous paper, a two-dimensional Fourier domain synthetic aperture radar (SAR) raw signal simulator that exploits the efficiency of fast Fourier transform algorithms was presented. It accounts for the effects of sensor trajectory deviations and is able to generate the raw signal corresponding to extended scenes in a few seconds. However, a narrow-beam-slow-deviation assumption is made; hence, the approach can be applied only to some SAR systems and/or trajectory deviations. To overcome this limitation, in this paper, we show that the narrow-beam-slow-deviation assumption can be relaxed, at the expense of computation efficiency, if use is made of one-dimensional azimuth Fourier domain processing followed by range time-domain integration. The latter approach only requires some reasonable assumptions on the sensor motion and on the SAR system features; hence, it can be used for airborne SAR systems, and turns out to be still much more efficient than the time-domain one; hence, extended scenes can still be considered. Validity limits of the approach are also analytically evaluated, and several simulation results are finally presented to verify the effectiveness of the proposed simulation scheme

SAR Sensor Trajectory Deviations: Fourier Domain Formulation and Extended Scene Simulation of Raw Signal

Synthetic aperture radar (SAR) raw signal simulation is a useful tool for SAR system design, mission planning, processing algorithm testing, and inversion algorithm design. A two-dimensional (2-D) Fourier domain SAR raw signal simulator, exploiting the efficiency of fast Fourier transform algorithms, has been presented some years ago and is able to generate the raw signal corresponding to extended scenes. However, it cannot account for the effects of sensor trajectory deviations with respect to the nominal straight-line path. This paper explores the possibility of extending the efficient Fourier domain simulation approach to the case of sensor trajectory deviations, which is more realistic for airborne SAR systems. We first of all obtain a general and compact Fourier domain formulation of the SAR raw signal in the presence of arbitrary trajectory deviations, and show that in this general case no efficient simulation scheme can be devised. However, we demonstrate that, if a narrow beam and slow trajectory deviation assumption is made, a full 2-D Fourier domain simulation can be used. This approach can be applied only to some SAR systems and/or trajectory deviations, but it has the advantage that processing time is practically not increased with respect to the nominal trajectory case. The validity limits of the approach are analytically evaluated. Some simulation results are finally presented in order to verify the effectiveness of the proposed simulation scheme. In another paper, which is the second part of this work, it will be shown that the narrow beam-slow deviation assumption can be relaxed, at the expense of computation efficiency, if a one-dimensional azimuth Fourier domain processing followed by a range time-domain integration is used

On center-beam approximation in SAR motion compensation

This work provides a geometrical analysis to assess the effects of center-beam approximation, crucial for efficient airborne raw data focusing, on the final image.

A Deterministic Two Dimensional Density Taper Approach for Fast Design of Uniform Amplitude Pencil Beams Arrays

The synthesis of electrically large, aperiodic planar arrays with equi-amplitude excitations plays an increasingly relevant role in satellite applications. Unfortunately, for such a kind of synthesis problems, local optimization procedures may be ineffective, whereas global optimization procedures involve a severe computational effort. To circumvent these problems, a new deterministic approach for fast design of aperiodic concentric ring arrays is proposed. The method exploits easily obtained optimal continuous planar solutions, accounts for the geometric properties of the array element and allows, once the central geometry of the array (that is, at least the most internal ring) is fixed, to compute in a deterministic, iterative, very fast way the whole geometry of the density-tapered concentric ring array. Numerical examples show the effectiveness of the method, which provides in a few seconds layouts of hundreds of elements able to produce directivity patterns that satisfy realistic satellite project requirements.

Advances in the Deterministic Synthesis of Uniform Amplitude Pencil Beam Concentric Ring Arrays

We present some modifications to the deterministic approach (DA) recently proposed for fast design of aperiodic concentric ring arrays. Such modifications are aimed at improving the array performances in terms of directivity, side lobe level (SLL) and number of control points. In particular, an easy implementation of the size-tapering concept is provided within the processing scheme of the DA procedure; moreover, an improved collocation criterion is presented. Finally, a local optimization procedure, tailored to the concentric ring array case, is addressed.

Phase Offset Calculation for Airborne InSAR DEM Generation Without Corner Reflectors

Digital elevation model (DEM) generation through interferometric processing of synthetic aperture radar (SAR) data requires the calculation of a constant phase offset present in the unwrapped interferograms. This operation is usually carried out by exploiting the external information provided by GPS measurements in correspondence of corner reflectors (CRs) properly deployed over the illuminated area. This is, however, expensive in terms of cost and time. Moreover, deployment of CRs along with the corresponding in situ GPS measurements can be difficult (if not impossible) in unfriendly areas or in natural disaster scenarios. To circumvent these limitations, we address in this work the estimation of the required phase offset by exploiting a low-accuracy external DEM, without using CRs. More specifically, a two-step approach is proposed. The first step exploits the synthetic phase computed by means of the external DEM and represents a straightforward extension of the procedure that is usually applied in the presence of CRs. Subsequently, in order to refine the achieved solution, a second step is introduced. It is based on a least squares approach that properly exploits the difference between the available low-accuracy DEM and the interferometric DEM generated by means of the phase offset value roughly estimated through the first step. The presented approach is very easy to implement and allows us to achieve an accurate and fast estimate of the needed phase offset, even in the presence of an external DEM affected by a vertical bias and/or a planar shift. The algorithm performances improve in the presence of a large variation of the look angle, as it generally happens in airborne systems. On the other side, the effectiveness of the algorithm may be impaired by the possible presence of artifacts in the unwrapped interferograms, such as those due to the residual motion errors typical of repeat-pass airborne SAR scenarios. Accordingly, the proposed solution is particularly suitable for single-pass interferometric airborne SAR systems, as demonstrated through the presented experimental results achieved on real data.

Synthesis of Isophoric Sparse Arrays Allowing Zoomable Beams and Arbitrary Coverage in Satellite Communications

In this paper, we address the synthesis of isophoric sparse ring arrays for full Earth coverage from a GEO satellite by means of steerable beams, switchable between two different widths. We show that to achieve such a zooming capability, we cannot simply tailor the array geometry to one of the patterns and then obtaining the beam zooming/shrinking by means of a phase-only control. Hence, we propose a novel synthesis approach that, in order to obtain the required beam zooming/shrinking by means of a phase-only control, tailors the layout geometry simultaneously to both the beams. Numerical results are presented to demonstrate the effectiveness of the proposed approach. The analysis also shows that the required beam re-configurability cannot be achieved for free. In particular, to radiate simultaneously the narrow and wide beams, with a beam-width ratio 1:5, we have to employ a number of control point 80% greater than that necessary to transmit only the narrow beam.

On the Use of Series Expansions for Kirchhoff Diffractals

In recent years, some methods have been devised to evaluate the field scattered by natural surfaces modeled by using fractals. In particular, use of the Kirchhoff approximation allows expressing the field scattered by a fractal surface in terms of two different series expansions. In this paper, the practical applicability of these expansions is addressed. To this aim, we first of all reformulate the derivation of the two series in order to clearly identify the key parameters on which the series behavior depends. Then, we perform a rigorous analysis of the properties of the two series. Based on such an analysis, we present suitable truncation criteria which allow understanding how to practically employ the two series expansions to compute the scattered field with a controlled error. A deep analysis of the range of applicability of the presented truncation criteria is also included. This allows providing a criterion which, given the surface and illumination parameters, and given the required accuracy and the computer floating-point format, allows us to choose which of the two series, if any, can be used, and how it can be properly truncated. Based on the presented analysis, we verify that for values of surface parameters of practical interest and for which the Kirchhoff approach can be used, for reasonable values of the required accuracy, and if the IEEE standard floating-point double-precision numbering format is used, then there is always at least one of the two series that provides an approximation of the scattering integral with the required accuracy.

Azimuth-to-Frequency Mapping in Airborne SAR Data Corrupted by Uncompensated Motion Errors

Airborne synthetic aperture radar (SAR) raw data are affected by motion errors. These are commonly accounted for via standard two-step motion compensation (MOCO) algorithm followed by the Precise Topography- and Aperture-dependent (PTA) procedure proposed some years ago. In this letter, we show how the azimuth-to-frequency mapping used by the PTA approach should be modified to fully account for the presence of uncompensated motion errors.