Precoding Design of MIMO Amplify-and-Forward Communication System With an Energy Harvesting Relay and Possibly Imperfect CSI

In this paper, we investigate the simultaneous wireless information and power transfer (SWIPT) in a Multiple-Input Multiple-Output (MIMO) Amplify-and-Forward (AF) relay communication system where the relay is an energy harvesting (EH) node and harvests the energy the signals transmitted from the source. The harvested energy is partially used to forward signals from the source to the destination, and the remaining energy is stored for other usages. The SWIPT in relay-assisted communication is interesting as long as the relay stores energy from the source and the destination receives successfully the data from the source. In this context, we propose to investigate the source and relay precoders that characterize the relationship between the achievable stored energy at the relay and the achievable sourceto- destination rate, namely the rate-stored energy (R-E) tradeo region. First, we consider the ideal scheme where there is the simultaneous operation of the EH and ID receivers at the relay. Then, we consider practical schemes such as the power splitting (PS) and the time switching (TS) that separate the operation of EH and information decoding (ID) receivers over power domain or time domain, respectively. Moreover, we study the case of imperfect channel state information (CSI) at the relay and the destination and characterize its impact on the achievable R-E region. Through the simulation results, we show the eect of the position of the relay and the channel uncertainty on the achievable R-E regions of all the schemes when the used energy at the relay is constant or variable. We also show that, although it provides an outer bound on the achievable rate-energy region in one-hop MIMO systems, the ideal scheme provides only an upper bound on the maximum achievable end-to-end rate and not an outer bound on the R-E region.