Abstract:
In this paper we consider a narrowband point-to-point
communication system with nt transmitters and nr receivers.
We assume the receiver has perfect knowledge of the channel while
the transmitter has no channel knowledge. We consider the case
where the receiving antenna array has uncorrelated elements while
the elements of the transmitting array are arbitrarily correlated.
Focusing on the case where nt=2 we derive simple analytic
expressions for the ergodic average and the cumulative
distribution function of the mutual information for arbitrary
input (transmission) signal covariance. We then determine the
ergodic and outage capacities and the associated optimal input
signal covariances. We thus show how a transmitter with covariance
knowledge should correlate its transmissions to maximize
throughput. These results allow us to derive an exact condition
(both necessary and sufficient) that determines when beamforming
is optimal for systems with arbitrary number of transmitters and
receivers.
Status:
Appears in IEEE JSAC 2003 Special Issue on MIMO Systems,
April 2003.
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