MIT Electrical Engineering and Computer Science EECS Event

Communicating on the Grassmann Manifold: A Geometric Approach to Non-coherent Multi-Antenna Channels

Prof. David Tse
Univ. of California, Berkeley (Visiting LIDS Fall 2000)

Tuesday, October 17, 2000
4:00 PM (reception following)
Room 35-225
LIDS Colloquium

Abstract

In this talk, we study the capacity of multiple antenna fading channels. We focus on non-coherent communications where the fading coefficients vary quickly and an accurate estimation of the coefficients is not available to either the transmitter or the receiver. Using a block fading model, we compute the capacity at high SNR in terms of the coherence time T, the number of transmit antennas M and the number of receive antennas N. A fundamental measure of performance at high SNR is the number of degrees of freedom. While the number of degrees of freedom in the coherent multi-antenna channel is min{M,N} per second per Hz, the corresponding quantity for the non-coherent channel turns out to be M*(1-M*/T), where M* = min{M, N, T/2}. The capacity expression has a geometric interpretation of sphere packing in the Grassmann manifold.

This is joint work with Lizhong Zheng at U.C. Berkeley.