Grassmannian Frames, the Heisenberg Group, and Wireless Communications

Prof. Thomas Strohmer

Department of Mathematics
University of California, Davis, USA

Friday, April 4th, 3:00 PM, ENS 637

strohmer@math.ucdavis.edu

Abstract

Frames - a generalization of orthonormal bases - have emerged as powerful tool in signal processing and communications. Especially attractive are so-called Grassmannian frames, which are frames of fixed redundancy that minimize the mutual correlation between frame elements. I will show how one can design Grassmannian frames via the Heisenberg group over Galois fields by a construction proposed by Calderbank et al. This construction turns out to be a goldmine for wireless communications. For instance it leads to a flexible method for designing spreading sequences for CDMA (which includes an interesting method by Kumar et al. as special case). Furthermore I will demonstrate that the very same Grassmannian frames also yield good codes with low peak-to-average ratio for OFDM modulation. Finally, as a byproduct, we will recover a class of space-time codes, known as orthogonal designs, proposed by Tarokh et al.. Part of this talk is joint work with Robert Heath.

Biography

Thomas Strohmer got his M.S. and Ph.D. in Mathematics in 1991 and 1993 respectively from the University of Vienna, Austria. He spent one year at the Department of Statistics at the Stanford University and is now Associate Professor at the Department of Mathematics at the University of California, Davis, USA. His research interests are in applied harmonic analysis, numerical analysis, digital signal processing and communications.

A list of Wireless Networking and Communications Seminars is available at from the ECE department Web pages under "Seminars". The Web address for the Wireless Networking and Communications Seminars is http://signal.ece.utexas.edu/seminars