Optimizing Multi-Transmitter–Single-Receiver (MISO) Antenna Systems With Partial Channel Knowledge

In this paper we consider a narrowband point-to-point communication system with many (input) transmitters and a single (output) receiver (ie, a “MISO” system). We assume the receiver has perfect knowledge of the channel but the transmitter has only limited channel information. 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.