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In this paper, to maximize the energy efficiency (EE) in the two-hop multi-relay cooperative decoding and forwarding (DF) system for simultaneous wireless information and power transmission (SWIPT), an optimal power allocation algorithm is proposed, in which the relay energy harvesting (EH) adopts a nonlinear model. Under the constraints, including energy causality, the minimum transmission quality of information and the total transmission power at the relays, an optimization problem is constructed to jointly optimize the transmit power and power-splitting (PS) ratios of multiple relays. Although this problem is a nonlinear fractional programming problem, an iterative algorithm is developed to obtain the optimal power allocation. In particular, the joint power allocation at multiple relays is first decoupled into a single relay power allocation, and then single-relay power allocation is performed by the Dinkelbach iteration algorithm, which can be proven that it is a convex programming problem. Its closed form solutions for different polylines of EH models are obtained by using mathematical methods, such as monotonicity, Lagrange multipliers, the KKT condition and the Cardan formula. The simulation results show the superiority of the power allocation algorithm proposed in this paper in terms of EE.

This paper analyzes outage probability and reliable throughput performance of a multi-user wireless-powered communication network-simultaneous wireless information and power transfer (WPCN-SWIPT) network with the logistic function-based (LG) nonlinear energy-harvesting (EH) model in Nakagami-m fading. Power-splitting (PS) receiver architecture is considered. The closed-form expressions of the system outage probability and the system reliable throughput are derived, and then the corresponding asymptotic expressions are also provided to achieve simpler calculation in the high-transmit power scenarios. Simulation results demonstrate the correctness of our derived analytical results and show that the systems under the LG nonlinear and linear EH models have very different performance behaviors. Moreover, since the LG nonlinear EH model is closer to the features of practical EH circuit than the linear one, using the LG nonlinear EH model can avoid the false output results of the system performance evaluation.