Spectral windows for satellite radar altimeters

Abstract

A satellite altimeter’s waveform is a power spectral density (PSD) estimate that displays backscattered power as a function of range, and in the Delay/Doppler or multi-looked SAR (D/D-SAR) algorithm, also of along-track position. Earth surfaces reflect radar power at a continuum of ranges and along-track positions, and so waveforms inevitably suffer from spectral leakage. Leakage may be mitigated, and the PSD resolution (“point target response”, PTR) shaped, by employing a spectral window, in either or both of the range and along-track dimensions. This paper demonstrates the sampling, symmetry and zero-padding required to ensure that the window does not introduce any distortion of the waveform. Because the PTR shapes the waveform through convolution, this paper characterizes waveform resolution in terms of PTR integrals. Expressing these as matrix-vector quadratic forms shows that ideal windows may be built from eigenvectors of appropriate matrices. A new approach taken here is to seek windows that make the PTR as nearly Gaussian as possible, since a Gaussian PTR is assumed in theoretical models for the statistical expectation of waveforms from uniformly rough surfaces. Up to now, altimeters have used either rectangular or Hamming windows, but this paper proposes other windows that provide a narrower and more Gaussian PTR with adequate leakage suppression. CryoSat-2 SAR mode data over transponders and leads in sea ice are processed with various windows to demonstrate applications and results.