Capacity of the Two-Hop Full-Duplex Relay Channel with Wireless Power Transfer from Relay to Battery-less Source

In this paper, we investigate a communication system comprised of a wireless sensor which harvests radio frequency (RF) energy from a full-duplex relay node and exploits this energy to transmit data to a destination node via the relay node. Thereby, the relay has two functions. Namely, it transfers RF energy to the sensor via wireless power transfer and relays the information received from the sensor to the destination. Moreover, we assume that the sensor is too small to be equipped with a battery. As a result, the energy of each symbol transmitted by the sensor is limited by the energy harvested during the previous symbol interval. For this system model, we derive the capacity for an average power constraint at the relay. Thereby, we show that in order to achieve the capacity, the sensor has to harvest the RF energy that reaches the sensor when the relay transmits information to the destination. As a result, the relay does not need to dedicate energy strictly for energy harvesting since the energy spent by the relay for information transfer can also be used by the sensor to harvest energy. In a numerical example, we compare the derived capacity to the rates of two benchmark schemes. Our results show that using the optimal input distributions at both the sensor and the relay is essential for high performance.