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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.

The aim of Internet of Things (IoT) is to enable people and things to be connected anytime, anyplace, with anything and anyone, ideally using any path/network and any service [

Until now, there have been many reports [

These works [

Motivated by this observation, this paper is devoted to the design of PS schemes for an AF relay system with direct link in terms of system capacity, where the nonlinear EH models proposed in [

We optimize the PS scheme to maximize the system capacity under the nonlinear EH model based on a logistic function. We prove that the objective function is unimodal and the optimal solution is obtained by the golden section search method.

Employing the nonlinear EH model based on an inverse proportional function instead of the logistic function, a closed-form expression for the optimal PS ratio is derived to maximize the system capacity. Compared with the PS scheme optimized for the nonlinear EH model based on the logistic function, the PS scheme optimized for the nonlinear EH model based on the inverse proportional enjoys a lower computational complexity with the near-optimal performance.

It is worth pointing out that energy efficiency (EE) is also an important performance metric. Since the EE is defined as the ratio of system capacity to power consumption [

As shown in Figure

An illustration of PS scheme.

Since the conventional linear EH model may not be accurate for modelling the practical energy harvester due to the nonlinearity of the diodes, inductors, and capacitors, by fitting over real measurement data based on the logistic function, the authors of [

Recently, using the inverse proportional function instead of the logistic function to fit over real measurement data, Chen et al. in [

In the first time slot,

For the destination

For the relay

If the energy harvesting is completed, the total harvested energy is given by

In the second time slot,

Then the received SNR from

By implementing the maximal ratio combining (MRC) scheme at the destination

In this subsection, we design an optimal PS scheme to maximize the overall system capacity for an AF relay system with SWIPT based on the nonlinear EH model in [

Substituting (

Then the system capacity in this case can be computed as

Based on (

By taking the first-order derivative of the objective function

Let

Let

In this subsection, we design an optimal PS scheme to maximize the overall system capacity for an AF relay system with SWIPT based on the nonlinear EH model in [

Then the optimization problem can be formulated as

According to (

Based on (

Let

According to the expression of

Based on

Let

When

For the case with

For the case with

Thus, the optimal solution to

The optimal PS ratio for

In this section, we evaluate the performance of the designed PS schemes based on two nonlinear EH models: the nonlinear EH model based on the logistic function and the nonlinear EH model based on the inverse proportional function, respectively. The basic parameters throughout the simulations, unless otherwise specified, are as follows. We consider the path model to be

Figure

Comparison between the harvested powers among the nonlinear EH models in [

Figure

Convergence of Algorithm

The PS schemes used for comparing are as follows:

Figure

System capacity versus the transmit power

In this paper, we have developed the optimal PS schemes for an AF relay system with direct link to maximize the system capacity, where both the nonlinear EH model based on the logistic function and the nonlinear EH model based on the inverse proportional function are employed to model the practical energy harvester. Through simulations, three insights were obtained as follows:

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was supported by the Research Program of Education Bureau of Shaanxi Province (17JK0699), Shaanxi Industrial Science and Technology Key Project (2017GY-039), and 2017 China Textile Industry Federation Science and Technology Guidance Project (2017067).