Eigenvalue Beamforming: Beamforming is a an approach to the filtering of spatial fields that is entirely analogous to FIR digital filtering of time series. In this paper we review various applications of beamforming in medicine, communications, and radar/sonar. Then we address the problem of phase front mismatch in beamforming. Our idea is to construct matched subspace and matched direction beamformers (to be defined) for radiating phase fronts that are wrinkled and which may wiggle from snapshot to snapshot. In the construction of these beamformers, a Slepian subspace is steered around in space, and eigenvalues of a corresponding beamformer matrix are used to map out the spatial location of radiating sources.
Louis Scharf received his Ph.D. in Electrical Engineering from the University of Washington, Seattle in 1969. From 1969 to 1971 he was a member of the Technical Staff at Honeywell’s Marine Systems Center, Seattle. He served as Professor of Electrical Engineering and Statistics at Colorado State University from 1971 to 1981. From 1982 to 1985 he was Professor and Chair of Electrical and Computer Engineering at the University of Rhode Island. From 1985 to 2001 he was Professor of Electrical and Computer Engineering at the University of Colorado, Boulder. He is currently Professor of Electrical and Computer Engineering and Statistics at Colorado State University, Ft. Collins. He has held Visiting Professorships at Duke University, University of Wisconsin, Universite de Paris Sud, University of La Plata, Ecole Nationale Superiere d’Electricite, EURECOM (Sophia-Antipolis), and University of Tromso.
Prof. Scharf’s research interests are in statistical signal processing, applied to radar, sonar, and communication. His current interests are subspace methods for adapting space-time and frequency-time transceivers. His recent contributions are to matched and adaptive subspace detectors; adaptive multi-access communication; reduced rank Wiener filters for efficient coding and filtering; canonical decompositions for reduced dimensional filtering; and time-varying spectrum estimators for experimental times series modeling.
Prof. Scharf was Technical Program Chair for the IEEE International Conference on Acoustics, Speech, and Signal Processing in 1980, and Tutorials Chair for the same conference in 2001. He was Technical Program Chair for Asilomar 2002. He has delivered plenary addresses at many IEEE Workshops on Statistical Signal and Array Processing and on Sensor Arrays and Multichannel Filtering. In 1994, he served as a Distinguished Lecturer for the IEEE Signal Processing Society. In 1995 he received the Society’s Technical Achievement Award, and in 2005 its Society Award. In 2000 he received an IEEE Third Millennium Medal, and in 2007 he was elevated to Life Fellow of IEEE.