Event-Driven Optimal Feedback Control for Multi-Antenna Beamforming

TL;DR

This paper develops an optimal feedback control strategy for multi-antenna beamforming that adaptively manages CSI feedback to maximize net throughput, effectively balancing feedback costs and system performance.

Contribution

It introduces a threshold-based feedback control policy for beamforming that is optimal under certain channel assumptions and extends to practical quantized feedback scenarios.

Findings

Feedback control can increase net throughput by up to 0.5 bit/s/Hz.

Optimal policies are of threshold type regardless of state space discretization.

Quantization effects are equivalent to an increased feedback cost.

Abstract

Transmit beamforming is a simple multi-antenna technique for increasing throughput and the transmission range of a wireless communication system. The required feedback of channel state information (CSI) can potentially result in excessive overhead especially for high mobility or many antennas. This work concerns efficient feedback for transmit beamforming and establishes a new approach of controlling feedback for maximizing net throughput, defined as throughput minus average feedback cost. The feedback controller using a stationary policy turns CSI feedback on/off according to the system state that comprises the channel state and transmit beamformer. Assuming channel isotropy and Markovity, the controller's state reduces to two scalars. This allows the optimal control policy to be efficiently computed using dynamic programming. Consider the perfect feedback channel free of error, where each feedback instant pays a fixed price. The corresponding optimal feedback control policy is proved to be of the threshold type. This result holds regardless of whether the controller's state space is discretized or continuous. Under the threshold-type policy, feedback is performed whenever a state variable indicating the accuracy of transmit CSI is below a threshold, which varies with channel power. The practical finite-rate feedback channel is also considered. The optimal policy for quantized feedback is proved to be also of the threshold type. The effect of CSI quantization is shown to be equivalent to an increment on the feedback price. Moreover, the increment is upper bounded by the expected logarithm of one minus the quantization error. Finally, simulation shows that feedback control increases net throughput of the conventional periodic feedback by up to 0.5 bit/s/Hz without requiring additional bandwidth or antennas.