IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 42, NO. 5, MAY 2004 941 Pseudowhitening of Weather Radar Signals to Improve Spectral Moment and Polarimetric Variable Estimates at Low Signal-to-Noise Ratios Sebastián M. Torres, Member, IEEE, Christopher D. Curtis, and J. R. Cruz, Fellow, IEEE Abstract—Pseudowhitening of oversampled signals in range is proposed as a method to improve the performance of spectral moment and polarimetric variable estimators on weather surveil- lance radars. In an attempt to overcome the noise sensitivity of the whitening transformation, a solution based on the minimum mean-square-error criterion is considered first; however, this transformation is less practical than whitening because it requires knowledge of the signal-to-noise ratio at every range location. Pseudowhitening techniques are introduced as practical solutions that achieve a suboptimal compromise between variance reduc- tion and noise sensitivity. Based on regularization methods for the solution of ill-conditioned problems, two pseudowhitening schemes are proposed: the clipped singular value decomposition transformation and the sharpening filter. By comparing their sta- tistical performance with theoretical minimum bounds, it is shown that pseudowhitening-based estimators are almost optimal under practical conditions. Estimators based on pseudowhitening tech- niques avoid the pitfalls of their whitening-transformation-based counterparts and lead to more accurate radar products and/or rapid data acquisition for a much wider range of signal-to-noise ratios. Index Terms—Meteorological radar, oversampled signals, pulse Doppler radar, radar polarimetry, radar signal processing, spec- tral moment estimation, variance reduction, whitening transfor- mation. I. INTRODUCTION R ADAR meteorology applications rely on pulsed weather radars that survey the atmosphere and estimate a set of me- teorological variables for each resolution volume. Because the usefulness of these applications depends on the quality of the supplied data, weather radars average signals from many pulses to reduce the statistical uncertainty of estimates. The variance reduction of estimates is inversely proportional to the equiva- lent number of independent samples [1], and the total number of samples available for averaging is determined by the pulse repetition time and the dwell time, which are constrained by the required azimuthal resolution. Manuscript received October 22, 2003; revised December 18, 2003. This work was supported in part by the National Weather Service, the Federal Aviation Administration, and the Air Force Weather Agency through the NEXRAD Product Improvement Program, and in part by the National Oceanic and Atmospheric Administration under NOAA–OU Cooperative Agreement NA17RJ1227. S. M. Torres and C. D. Curtis are with the Cooperative Institute for Mesoscale Meteorological Studies, The University of Oklahoma, Norman, OK 73069 USA (e-mail: Sebastian.Torres@noaa.gov; Chris.Curtis@noaa.gov). J. R. Cruz is with the School of Electrical and Computer Engineering, The University of Oklahoma, Norman, OK 73019 USA (e-mail: jcruz@ou.edu). Digital Object Identifier 10.1109/TGRS.2004.825579 Rapid acquisition of volumetric radar data has significant sci- entific and practical ramifications. For example, observations at few-minute intervals are required to understand the details of vortex formation and demise near the ground. Even faster rates of volumetric data are needed to determine the presence of transverse winds [2]. Fast update rates would also yield more timely warnings of impending severe weather phenomena such as tornadoes and strong winds. Hence, from an operational point of view, users are faced with conflicting requirements. On one hand, rapid updates between volume scans require faster an- tenna rotation rates, limiting the number of samples available for each resolution volume. On the other hand, a large number of samples is needed to attain acceptable errors of estimates and efficiently exploit weather surveillance radars for precise iden- tification and quantification of weather phenomena. Torres and Zrnic ´ [3], [4] recently proposed a solution to this long-standing dilemma; they suggested application of a whitening transformation to oversampled data along range time for estimating Doppler spectral moments and polarimetric variables. The application of this technique on radars that do not have a pulse compression capability effectively increases the equivalent number of independent samples while keeping the dwell time constant and without significantly degrading the range resolution. The scheme operates on oversampled echoes in range, i.e., samples of in-phase and quadrature-phase components that are taken at a rate times larger than the reciprocal of the transmitted pulse length. Each set of corre- lated samples is then transformed into a set of decorrelated samples using a whitening transformation. Covariances are estimated in the usual way along sample time resulting in values for each of these estimated quantities. For each quantity, the values are averaged, and classical algorithms are used to compute the spectral moments and polarimetric variables. Because covariances are derived from a set of decorrelated samples, the variance of estimates decreases significantly. This technique’s substantial improvement is only achievable at large SNRs (approximately greater than 20 dB) due to the noise introduced by the whitening transformation, usually referred to as noise enhancement [3]. Although most severe weather phenomena produce signals several tens of decibels above the noise level, operational radars such as the Weather Surveillance Radar 1988 Doppler (WSR-88D) generate prod- ucts that are derived from signals exhibiting as little as 2-dB SNR. Hence, it is of practical importance to extend the benefits of whitening to lower SNRs. By relaxing the requirements of perfect whitening, it is possible to derive transformations that 0196-2892/04$20.00 © 2004 IEEE