Abstract:
Multiple-antenna wireless communication links promise very high data rates
with low error probabilities, especially when the wireless channel response
is known at the receiver. In practice, knowledge of the channel is often
obtained by sending known training symbols to the receiver. We show how
training affects the capacity of a fading channel---too little training and
the channel is improperly learned, too much training and there is no time
left for data transmission before the channel changes. We use an
information-theoretic approach to compute the optimal amount of training as
a function of the received signal-to-noise ratio, fading coherence time,
and number of transmitter antennas. When the training and data powers
are allowed to vary, we show that the optimal number of training symbols is
equal to the number of transmit antennas---this number is also the smallest
training interval length that guarantees meaningful estimates of the
channel matrix. When the training and data powers are instead required to
be equal, the optimal number of symbols may be larger than the number of
antennas. As side results, we obtain the worst-case power-constrained
additive noise in a matrix-valued additive noise channel, and show that
training-based schemes are highly suboptimal at low SNR.
Status:
Technical Memorandum, Bell Laboratories, Lucent Technologies,
April 2000. Submitted to IEEE Trans. Info. Theory
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