In this paper, we investigate the simultaneous wireless information and power transfer (SWIPT) for the two-hop Multiple-Input Multiple-Output (MIMO) Amplify-and-Forward (AF) relay communication systems with the multi-antenna energy harvesting relay. We derive the optimal source and relay co-variance matrices to characterize the achievable region between the source-destination rate and the harvested energy at the relay, namely Rate-Energy (R-E) region. In this context, we consider the ideal

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... rio where the energy harvester (EH) receiver and the information decoder (ID) receiver at the relay can simultaneously decode the information and harvest the energy at the relay. Then, we consider more practical schemes which are the power splitting (PS) and the time switching (TS) which separate the EH and ID transfer over the power domain and the time domain, respectively. Figure 1: Sources of energy harvesting and applications of wireless power transfer. • Harvesting energy from the environment provides a promising future for wireless networks: self-sustainability and virtually perpetual operation. • Solar, wind and vibration are known to be the classical sources for energy harvesting (EH) at the transmit nodes. • Radio frequency (RF) signals from ambient transmitters have recently been considered as a possible source of wireless energy transfer (WET). RF signals are known to be used for wireless information transfer (WIT). =⇒ It is interesting to study the simultaneous wireless information and power transfer (SWIPT) when RF signals are simultaneously used to transmit information and scavenge energy.