In this paper, we analyze a backscatter network that implements simultaneous wireless information and power transfer. The backscatter devices (BDs) in the network work as relays that receive RF signals from the source, harvests the energy and uses it to reflect the signal to the receiver. We assume a non-linear energy harvesting (EH) circuit that takes into account the sensitivity and non-linearity of the electronic components. We formulate an optimization problem to maximize the achievable rate at the receiver of this network. By considering both amplify-and-forward and decode-and-forward modes, we propose algorithms to jointly optimize the power-splitting ratio and the reflection coefficient of the BDs. Simulation results demonstrate the effectiveness of the proposed algorithms with respect to baseline relay networks. In particular, the impact of the number of BDs, source transmit power, and distance of the BDs from the source and destination on the average rate and energy efficiency of the network are illustrated.INDEX TERMS Backscatter communications system, energy harvesting, relaying scheme, simultaneous wireless information power transfer.