Grassmannian Frames, the Heisenberg Group, and Wireless Communications

Prof. Thomas Strohmer

Department of Mathematics
University of California, Davis, USA

Thursday, April 3rd, 3:30 PM, ACES 6.304

strohmer@math.ucdavis.edu

Abstract

In this talk I will show how recent methods from applied harmonic analysis can play a key role in modern wireless communications. I will first briefly describe Orthogonal Frequency Division Multiplexing (OFDM), which is one of the most promising transmission schemes for wireless communications. An important problem in OFDM is the design of transmission pulses that are robust against interference caused by time-varying channels. By exploiting the connection between Weyl-Heisenberg systems (a family of functions that consists of translations and modulations of some ``nice'' function), Banach algebras and OFDM I will construct a theoretical framework for the construction of orthogonal transmission functions that are optimally localized in the phase space. This localization property is crucial in order to mitigate the distortions caused by time-frequency dispersive channels. Some nice properties of Weyl-Heisenberg systems enable us to compute the aforementioned optimal pulses by a fast numerical algorithm, which is suitable for real-time applications. I will derive convergence rates for this algorithm and discuss some open problems. The proposed algorithm, which takes into account various practical constraints, has been recently used in the design of a modem for short-radio wave communications.

Biography

Dr. 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