Robust Energy-Efficient Analog Beamforming Under Short Packets and Per-Antenna Power Constraints

Designing energy-efficient beamformers is a major challenge to the deployment of battery-powered devices transmitting short data packets at millimeter-wave frequencies. In general, directly maximizing energy efficiency will not meet the stringent reliability requirements of certain Internet-of-Things applications. We focus on designing analog beamformers in a device-to-device setting under short packets, a finite encoder set, and imperfect channel knowledge. To guarantee the required error decoding performance, a two-step procedure is proposed such that beamformers are designed to minimize the power consumption subject to reliability constraints under worst-case channel estimation errors, and then the channel encoder maximizing the energy efficiency is selected. The proposed design enjoys a moderate loss under practical low-resolution phase shifters, and exhibits robustness to inaccurate channel estimators, which is crucial to the tradeoff between energy efficiency and error decoding performance.