Statistical distributions that arise in constrained beamforming with incomplete channel information

We examine the statistical distribution of received power when a subscriber terminal with multiple transmit antennas beamforms on the uplink of a wireless orthogonal frequency-division multiplexing system to a base station with multiple receive antennas. We assume that a time-division duplex terminal has incomplete uplink channel knowledge obtained by measuring the downlink channel during base station transmissions. The base station transmissions employ cyclic delay diversity, of which the terminal is unaware. The distribution of uplink power received at the base station, with and without downlink cyclic delay diversity and with various types of power constraints at the terminal, allow us to make some surprising conclusions about how the power constraints and cyclic delay influence the performance of beamforming. We show that beamforming gains need to be examined critically beyond simple average performance metrics to conclude that they are superior to simpler channel-unaware methods. We also conclude that cyclic delay on the downlink is very beneficial to beamforming on the uplink, even with restrictive types of power constraints.