Power-Splitting Scheme for Nonlinear Energy Harvesting AF Relaying with Direct Link

Simultaneous wireless information and power transfer (SWIPT) is a promising technique to prolong the lifetime of energy-constrained relay systems. Most previous works optimize power-splitting (PS) scheme based on a linear or a simple two-piecewise linear energy harvesting (EH) model, while the employed EH model may not characterize the properties of practical EH harvesters well. This leads to a mismatch between the existing PS scheme and the practical EH harvester available for relay systems. Motivated by this, this paper is devoted to the design of PS scheme in a nonlinear EH amplify-and-forward energy-constrained relay system in the presence of a direct link between the source and the destination. In particular, we formulate an optimization problem to maximize the system capacity according to the instantaneous channel state information, subject to a nonlinear EH model based on the logistic function. The objective function of the formulated problem is proven to be unimodal and there is no closed-form expression for the optimal PS ratio due to the complexity of logistic function. In order to reduce overhead cost of optimizing PS ratio, a simpler nonlinear EH model based on the inverse proportional function is employed to replace the nonlinear EH model based on the logistic function and we further derive the closed-form expression for the optimal PS ratio. Simulation results reveal that a higher system capacity can be achieved when the PS scheme is optimized based on nonlinear EH models instead of the linear EH model, and that there is only a marginal difference between the capacity under the two optimal PS schemes optimized for two different nonlinear EH models.