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Capacity regions of a MAC with a wireless-powered relay-to-destination link under different relay strategies

We consider a two-user multiple access channel (MAC) with a wireless-powered relay-to-destination (RD) link, where the relay harvests energy from a radio frequency (RF) signal sent by a dedicated Power Beacon (PB). Each frame is divided into three phases. In the first phase, the relay harvests energy from an RF signal sent by a dedicated PB. The relay then receives information from user nodes in the second phase and forwards it to the destination in the third phase using its harvested energy. We investigate the sum rate maximization problem and characterize the capacity region of such a channel with the relay's maximum transmit power constraint, under both the amplify-and-forward (AF) and decode-and-forward (DF) relay strategies. Optimal solutions are obtained for both cases. It is interesting to find that the shape of the capacity region is still pentagonal with the wireless-powered relay. Finally, simulation results demonstrate the correctness of our analysis.