Fast Fourier Transform

Ways of efficiently computing the discrete Fourier transform (DFT) when the number of input and output data points differ are discussed. The two problems of determining whether the length of the input sequence or the length of the output sequence is reduced can be found to be duals of each other, and the same methods can, to a large extent, be used to solve both. The algorithms utilize the redundancy in the input or output to reduce the number of operations below those of the fast Fourier transform (FFT) algorithms. The usual pruning method is discussed, and an efficient algorithm, called transform decomposition, is introduced. It is based on a mixture of a standard FFT algorithm and the Horner polynomial evaluation scheme equivalent to the one in Goertzel's algorithms. It requires fewer operations and is more flexible than pruning. The algorithm works for power-of-two and prime-factor algorithms, as well as for real-input data. >

Efficient computation of the DFT with only a subset of input or output points

Fully polarimetric synthetic aperture radar (SAR) data analysis has found wide application for terrain classification, land-use, soil moisture, and ground cover classification. Critical to all analyses and applications is accurate calibration of the relative amplitudes of and phases between the various polarimetric channels. Here we propose an a posteriori method imposing only the weakest of constraints, scattering reciprocity, on the polarimetric data. Calibration parameters are self-consistently estimated from full 4/spl times/4 polarimetric covariance matrices. Whilst the complete set of calibration parameters is underdetermined, we give several reasonable heuristic methods to provide a complete calibration. Stronger constraints reduce the number of independent parameters and provide an overdetermined set of equations but at a cost - the loss of polarimetric fidelity when the underlying assumptions are violated. Without recourse to in situ calibration targets, the extent of the polarimetric distortion that results from polarimetric calibration remains unknown. We apply our new method to simulated data, anechoic chamber data and polarimetric SAR imagery. We also present comparisons with alternate calibration methods and different approximate solutions of the new technique.

Orientation angle preserving a posteriori polarimetric SAR calibration

Polarization properties of radar waves that are scattered from atmospheric objects are of great interest in meteorological studies. However, polarimetric radar measurements are often not sufficiently accurate for retrieving physical properties of targets. To compensate for errors, radar polarimetric calibration is applied. Typical calibrations are performed based on measurements of point targets with known scattering matrices located in the boresight of the antenna. Such calibration takes into account the polarization state of the antenna pattern only at one point. Since radar measurements of atmospheric phenomena involve distributed targets that fill the full antenna beam, point target radar calibrations are inadequate for meteorological studies. This paper explains in detail the effects of the complete antenna patterns on weather echoes. It is shown that the conventional polarimetric calibration can be significantly improved by incorporating light-rain (,20 dBZ) zenith-pointing measurements into the calibration procedure. As a result, the sensitivity of cross-polar measurements can be improved by 7 dB on average. Also it is shown that the bias in co-cross-polar correlation coefficient can be reduced.

Improved polarimetric calibration for atmospheric radars

To provide meaningful data, polarimetric ground penetrating radar (GPR) requires accurate calibration of channel imbalance and crosstalk not only in the amplitude term but also in the phase term. Currently, calibration techniques usually ignore higher-order terms to simplify equations. These techniques, though very easy to perform, provide less accurate calibration results for the crosstalk. To improve the accuracy of calibration, we have derived a new mathematical formulation to calibrate a polarimetric GPR system. We measured several scattering matrices to obtain the necessary calibration parameters. The calibration technique was tested from measurements conducted on a 22.5° oriented dihedral corner reflector from 1 to 6 GHz with a step of 0.1 GHz. The calibrated results are found to be consistent with the theoretically values, especially for the crosstalk.

Calibration With High-Order Terms of Polarimetric GPR

Based on the existing mathematical formalisms of radar polarimetry, it is necessary to perform accurate and diversified polarimetric measurements in the real world to thoroughly investigate signature definition, identification, and classification of radar targets. For this study the Delft Atmospheric Research Radar (DARR) is used. This ground-based polarimetric FM-CW radar operates in the S-band. The purpose of the present paper is the polarimetric calibration of the DARR. Among the passive reflectors, a rotatable dihedral corner reflector is a suitable calibration object. It enables one to measure different scattering matrices with only one reflector. One alignment must be performed and the scattering matrices are measured at the same range. By measuring several scattering matrices, the accuracy of the calibration result can be estimated. A measurement campaign with a rotatable dihedral corner reflector was therefore performed. The experimental results and the calibration procedure are presented in this paper. >

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Calibration of a polarimetric radar using a rotatable dihedral corner reflector

After a brief review of discrete Fourier transformation (DFT) — and fast Fourier transformation (FFT) — properties, two representatives of partial (narrowband) spectrum computation methods, the zoom FFT and a specific type of zoom transform, are introduced. With respect to the FFT, only the zoom transform sufficiently fits demands concerning memory space and computional speed. Moreover, it offers improved accuracy and applicability relative to the existing type of zoom transform. The described transform method, a link between an FFT and a single DFT sum, is compared with the use of separate DFT sums.

Method for partial spectrum computation

The Delft FM-CW radar is used to characterise radar targets based on their polarisation parameters and Doppler velocity. Dedicated polarisers allow the radar system to have one receiver only. The domain of the polarisation information interferes with the domain of the Doppler-velocity information. To split these domains and to retrieve the target parameters, a specific processing approach has been developed. The method has been implemented to run on one or more array processors, which are used as preprocessing units on a host computer. Besides the mathematical outlines of the method, the structure and organisation of the processing units are discussed in the paper. Finally, some preliminary results of real-time performance measurements are shown. >

Multipolarisation FM-CW Doppler radar signal processing for nondistributed targets

An FM-CW Doppler-polarimetric radar is configured to measure the distance, radial velocity, and the complex scattering parameters of radar targets. The Doppler spectra are determined per range cell by applying an FFT to a series of range spectra. With a cyclic pattern of polarisation pairs in the transmitting and receiving channels, a Doppler spectrum is derived for each of the polarisation pairs. The complex scattering parameters are extracted using linear regression from these Doppler spectra. This approach results into the availability of the scattering parameters per range cell and per Doppler velocity cell. The processing algorithm has been implemented in the FM-CW Delft Atmospheric Research Radar (DARR). The paper discusses the processing algorithm with emphasis on real-time implementation.

Real-time Signal Processing in FM-CW Doppler-polarimetric Radar

The Delft Atmospheric Research Radar (DARR) is based on the FM-CW principle and operates at frequencies in the S-band. Both transmitting and receiving channels are linearly polarized and are equipped with a mechanical polarizer to change the angle of polarization. This paper describes the first measurement results obtained with DARR and its newly implemented real-time Doppler-Polarimetry computer programs. Measurements of a flat rotating plate and a tower, with emphasis on the possibilities of polarimetric target suppression, are shown. are denoted as arg(xy-xx) and arg(yy-xx),, which are the arguments of the complex ratios of Sxy/Sxx and Syy/Sxx respectively. The absolute phases of the scattering parameters are not calculated, because they do not necessarily represent: the target: they are easily affected by atmospheric disturbances. The emphasis of the target characterization in this paper lies in the! polarization domain, since the targets observed do not have a significant Doppler behavior. Target characterization is complete, when the Doppler characteristics are taken into account. Coherency of the DARR radar is only used to calculate the

J.S. van Sinttruyen

Papers

Calibration of a polarimetric radar using a rotatable dihedral corner reflector

Method for partial spectrum computation

Multipolarisation FM-CW Doppler radar signal processing for nondistributed targets

Real-time Signal Processing in FM-CW Doppler-polarimetric Radar

Real-time Determination Of Doppler And Polarization Parameters Using An FM-CW Radar