On the Effect of Feedback Delay on Limited-Rate Beamforming Systems

The use of beamforming to enable higher data rates in telecommunications is widely appreciated, but performance gains are typically calculated assuming delay-free feedback from the receiver and neglecting processing time. This paper introduces a mathematical framework based on outage probability that measures the extent to which current channel state information is accurate. Performance gains from beamforming can then be evaluated as a function of the currency of system state. Results are provided for Multiple Input Single Output (MISO) and for Multiuser Multiple Input Multiple Output (MU-MIMO) systems. Outage probabilities and effective diversity orders are calculated for widely used methods of beamforming such as Transmit Antenna Selection as a function of the speed of channel variation.