Coding Requirements for Multiple-Antenna Channels
with Unknown Rayleigh Fading
Ibrahim Abou-Faycal
Bertrand M. Hochwald
Abstract:
Multiple transmitter and receiver antennas can boost the reliability
and capacity of wireless fading channels. When the channel is
unknown to the transmitter and receiver, it is known that the fading
coherence time in a piecewise-constant fading channel ultimately
limits the channel capacity. In this work, we examine coding
requirements for the unknown fading channel by computing the random
coding error exponent. We show that the fading coherence time also
plays a fundamental role in the error exponent, by proving that the
error exponent is not increased by having more transmitter antennas
than the number of samples in the coherence time. The signal
structure that maximizes the exponent is computed and is shown to be
very similar to the signal structure that achieves capacity. We
calculate the minimum coding block length requirements as a function
of probability of error for various fading coherence times. We
conclude that coding over a certain number of independent fades is
always needed to guarantee low probabilities of error, regardless of
the coherence time.
Status:
Bell Labs Technical Memorandum, 1999. Submitted to IEEE Transactions on
Information Theory.
Files:
Compressed PostScript (.ps.gz) (144K),
PostScript (.ps) (876K),
PDF v3.0 (.pdf) (279K).
Bert Hochwald <hochwald@bell-labs.com>