Abstract:
In this paper we consider a narrowband point-to-point
communication system with many (input) transmitters and a single
(output) receiver (i.e., a "MISO" system). We assume the
receiver has perfect knowledge of the channel but the transmitter
has only limited information of the channel. We focus on two
canonical classes of channel models: (a) the channel has zero mean
with a fixed covariance matrix and (b) the channel has nonzero
mean with covariance matrix proportional to unity. In both cases
we are able to derive simple analytic expressions for the ergodic
average and the cumulative distribution function of the mutual
information for arbitrary input (transmission) signal covariance.
With minimal numerical effort, we then determine the ergodic and
outage capacities and the input signal covariances which achieve
these maximal capacities. We thus show how a transmitter with
partial channel knowledge (either knowing the mean channel or the
signal covariance) should correlate its transmissions to maximize
throughput.
Status:
Appears in IEEE Transactions on Information Theory,
pp. 2770-2780, Oct. 2003
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