Optimal Scheduling and Beamforming in Relay Networks with Energy Harvesting Constraints

In this paper, multiple relays capable of harvesting energy from radio-frequency (RF) signals are employed to collaboratively forward data from a source transmitter to its destined receiver. Due to the relays' inability to harvest energy and transmit data simultaneously, the source needs to optimally schedule the relays' energy harvesting (EH) and data transmission. Considering different channel conditions and energy constraints, the relays need to optimally design a beamforming vector that specifies each relay a power amplifier coefficient to forward the source signal and suppress the noise. By joint EH scheduling and beamforming, we maximize the overall throughput formulated in a nonconvex problem. We first propose a centralized scheme that achieves the optimal throughput by exploiting the monotonicity in the problem structure. We further propose a distributed suboptimal scheme in a game theoretic approach, which requires the source and the relays to iteratively update EH scheduling and beamforming vector, respectively. We show that the suboptimal scheme has a threshold-based structure for the relays' power control depending on the source-relay channel conditions. Numerical results show near-optimal performance of the distributed scheme compared with the centralized optimal scheme.