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This paper investigates the performance of incremental relaying (IR) in a two-hop network with a battery-assisted EH relay. Assuming nonlinear energy harvesting (EH) and time-switching protocol at relay, expressions are derived for outage probability and throughput in closed-form to show that augmenting the harvested energy by a small amount of battery energy significantly enhances the throughput. We demonstrate that unlike linear EH, nonlinear EH causes loss of diversity, making use of the direct link very important. Further, using the asymptotic expression for the outage probability, we establish concavity of throughput with respect to EH parameter and demonstrate that a judicious choice of the TS parameter is essential in order to maximize the throughput when fixed battery energy is available per signalling interval. Judicious choice of target rate is important to minimize battery energy consumption at the relay …