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Solving the Matched Filter Detector in Linear Time

Shamgar Gurevich (UW Madison)

Wed. Mar 7, 2:00pm. EEB 248

Abstract: We will explain the mathematical model of a wireless communication. One of the main problems is finding (time,frequency) shift of a signal in a noisy environment which is caused by time asynchronization of a sender with a receiver and by a non-zero speed of a sender with respect to a receiver.

A classical solution (Matched Filter Algorithm) of a discrete analog of the problem uses a pseudo-random waveform S(t) of the length p and gives rise to the complexity p^2 log(p) operations (using fast Fourier transform). We will explain how to use techniques from group representation theory to construct waveforms S(t) which enable us to introduce a fast matched filter algorithm, called the “flag algorithm”, which solves (time,frequency) shift problem in O(p*log (p)) operations. We will discuss applications to radars, GPS system, and Mobile Communication.

This is a joint work with A. Fish (Mathematics, Madison), R. Hadani (Mathematics, Austin), A. Sayeed (Electrical Engineering, Madison), and O. Schwartz (Computer Science, Berkeley).

Bio: Shamgar Gurevich is assistant prof. of mathematics at UW Madison, he obtained his Ph.D. Degree in pure math from Tel-Aviv University, Israel, under the directions of Joseph Bernstein. He likes to collaborate with researchers and students outside of mathematics, especially around applied problems. In particular, he is working on developing new tools for efficient wireless communication.

Host: Alex Dimakis, dimakis [at]

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