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In this paper, we investigate a communication system comprised of an energyharvesting (EH) source which harvests radio frequency (RF) energy from anout-of-band full-duplex relay node and exploits this energy to transmit data toa destination node via the relay node. We assume two scenarios for the batteryof the EH source. In the first scenario, we assume that the EH source is notequipped with a battery and thereby cannot store energy. As a result, the RFenergy harvested during one symbol interval can only be used in the followingsymbol interval. In the second scenario, we assume that the EH source isequipped with a battery having unlimited storage capacity in which it can storethe harvested RF energy. As a result, the RF energy harvested during one symbolinterval can be used in any of the following symbol intervals. For both systemmodels, we derive the channel capacity subject to an average power constraintat the relay and an additional energy transmission cost at the EH source. Wecompare the derived capacities to the achievable rates of several benchmarkschemes. Our results show that using the optimal input distributions at boththe EH source and the relay is essential for high performance. Moreover, wedemonstrate that neglecting the energy transmission cost at the source canresult in a severe overestimation of the achievable performance.

Capacity of the Two-Hop Relay Channel with Wireless Energy Transfer from Relay to Source and Energy Transmission Cost