## EECS CSPL SEMINAR SERIES

WINTER TERM 2000

Alfred O. Hero
### EECS Department

### University of Michigan

### hero@eecs.umich.edu

Thursday, April 20

4:00 - 5:00 P.M.

Room 1311 EECS

###
Cut-off Rate and Signal Design for the Rayleigh Fading
Space-Time Channel

Abstract-

We consider the computational cut-off rate and its implications on
signal
design for the complex Rayleigh flat fading
spatio-temporal
(multiple-antenna) communications channel under a peak
power constraint.
Different characterizations of the optimal rate-achieving
signal
constellation are obtained. For arbitrary finite
dimension, the optimal
constellation must admit an equalizer distribution, i.e.,
a positive set of
signal probabilities which equalizes the conditional
decoding error
probabilities. When the number of signal matrices in the
constellation is
less than the ratio of the number of time samples to the
number of transmit
antennas, the optimal cut-off rate attaining constellation
is a set of
equiprobable mutually-orthogonal unitary matrices. When
the SNR is below a
specified threshold the matrices in the constellation are
rank one and the
cutoff rate is achieved by applying all transmit power to
a single antenna
and using orthogonal signaling. Implications on the
achievable rate region
for space-time coding in diffuse vs. specular multi-path
channels will be
discussed.

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