Multi-antenna beamforming: Feedback or no feedback?

Transmit beamforming increases throughput and transmission range of a wireless communication system. However, the required feedback of channel state information (CSI) consumes radio resources that otherwise can be used for data transmission. This makes "Feedback or no feedback?" a relevant question to ask. This paper answers this question by proposing intelligent feedback control using a Markov decision process. The feedback controller turns feedback on/off according to the channel state and the criterion of maximum net throughput, namely throughput minus average feedback cost. Assuming channel isotropicity and Markovity, the state of the feedback controller reduces to two channel parameters. This allows the optimal control policy to be efficiently computed using dynamic programming. The optimal control policy is proved to be of the threshold type. Under this policy, feedback is performed whenever a channel parameter indicating the accuracy of transmit CSI is below a threshold, which varies with channel power. The above result holds regardless of whether the controller's state space is discretized or continuous. Simulation shows that feedback control increases net throughput by up to 0.5 bit/s/Hz without requiring additional bandwidth or antennas.