Optimizing multiantenna systems with partial channel knowledge

In this paper we consider a narrowband point-to-point communication system with multiple transmitters with the receiver having perfect channel knowledge and the transmitter having only limited channel information. We focus on two canonical classes of channel models: (a) the channel has zero mean with an arbitrary covariance matrix and (b) the channel has nonzero mean with covariance matrix proportional to unity. In both cases we present 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.