Fast Fourier Transform

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Understanding By Design

Communication systems: An introduction to signals and noise in electrical communication

The proliferation of wireless services is driving innovative phased array solutions that are able to provide better cost/performance tradeoffs. In this context, the use of irregular array architectures provides a viable solution. This paper reviews and highlights some of the most recent advances in this field, including clustered, thinned, sparse, and time-modulated arrays, and their proposed design methodologies.

Unconventional Phased Array Architectures and Design Methodologies—A Review

Longer wavelength synthetic aperture radars (SARs) are precious in the remote sensing of forested areas, being sensitive to contributions from the whole vegetation layer and from the ground below. The electromagnetic properties of such contributions are retrieved from multipolarimetric acquisitions, whereas their vertical structure is retrieved from multibaseline acquisitions through tomographic imaging. Combining baseline and polarization diversity provides most information, allowing the decomposition of the SAR signal into ground- and volume-only contributions. A formal treatment of this problem is provided with the algebraic synthesis technique, which extends the concepts of PolInSAR. The decomposition, however, is shown to be ambiguous in that different solutions are equally consistent with the data. The main goal of this paper is to discuss this topic in light of the experimental results from a tomographic and polarimetric analysis of the boreal forest within the Krycklan River catchment, Northern Sweden, investigated at P- and L-bands during the ESA campaign BioSAR 2008. Different solutions to the decomposition problem will be discussed by examining the corresponding vertical structures accessible through tomographic techniques. Elements are shown supporting the idea that ground-volume interactions play a nonnegligible role at P-band, and a solution is proposed to isolate contributions from direct volume backscattering. The retrieval of forest top height is discussed as well, leading to the conclusion that such parameter is robust against erroneous choices in the identification of volume-only contributions, thus corroborating the PolInSAR approach for the analysis of single-baseline data.

Multibaseline Polarimetric SAR Tomography of a Boreal Forest at P- and L-Bands

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.

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

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

Efficient simulation of airborne SAR raw data of extended scenes

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.

On center-beam approximation in SAR motion compensation

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

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

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.

Stefano Perna

Papers

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

Efficient simulation of airborne SAR raw data of extended scenes

On center-beam approximation in SAR motion compensation

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

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