Beamforming capacity and SNR maximization for multiple antenna systems

We explore the optimal input distributions to maximize average received SNR and to achieve beamforming capacity on the downlink for two different channel models. First we model a scenario where the mobile unit is surrounded by local scatterers while the base station (BS) is relatively un-obstructed, so that the channel matrix consists of i.i.d. rows and correlated columns. For this model we show that the average SNR maximizing input distribution also achieves the beamforming capacity. Then we model a scenario where the transmit antennas at the BS are placed significantly far apart, so that the fades are independent but not identically distributed. For this model we obtain necessary and sufficient conditions under which the average SNR maximizing solution also achieves beamforming capacity. We find that for typical mobile unit antenna spacings, increasing the BS antenna spacing not only improves the capacity but achieves this higher capacity using just one transmit antenna at a time, thus saving significantly on the cost of power amplifiers at the BS.