Achievable Rate-Energy Region in Two-Way Decode-and-Forward Energy Harvesting Relay Systems

At an energy harvesting relay, securing residual harvested energy, net remaining energy after each receiving and forwarding cycle, is of importance for sustainable operation. However, there exists a tradeoff between achievable rate and residual harvested energy whereby understanding this tradeoff concretely is crucial for energy harvesting relay system design. This paper analyzes rate-energy (R-E) region for achievable rate and residual harvested energy in two-way decode-and-forward (DF) relay systems with a power splitting (PS) based energy harvesting relay. In particular, we characterize R-E regions for multiple access broadcast (MABC) and time division broadcast (TDBC) protocols. Moreover, we propose a new energy harvesting relaying protocol, namely, information and energy signals multiple access broadcast (IEBC), to improve achievable R-E region. The boundary of the R-E regions is obtained by optimizing a power split factor in each protocol. Moreover, to have better analytic comparisons and useful insights on performance, we derive approximated R-E regions of all protocols for high and low signal-to-noise ratio (SNR) cases. Based on the approximated R-E region, it is shown that if the required residual energy is large, the IEBC outperforms the others, but if the required residual energy is small, either the IEBC or MABC is preferred.