Optimal Energy Harvesting Strategy in Relaying Networks: Dynamic Allocation Scheme and Performance Analysis

Abstract

This paper evaluates the performance of a wireless powered communications system, where an energy-aware relay can ability of controlling proper energy harvesting parameters for obtaining maximal throughput. Considering a power splitting approach, the relay first can calculate percentage of harvested wireless energy from power supply source, and then transmits information to the destination. This paper proposes the dynamic harvesting power allocation policy for energy harvesting and analytical expressions for the delay-limited and delay-tolerant throughput related to amplify-and-forward relaying mode. In particular, the optimal power coefficients can be derived in closed-form expressions, in which the maximal throughput can be obtained in special case, i.e., high transmit power regime. In addition, the impact of transmit power, power splitting fraction, the fixed rate factors, noise levels are well studied. Simulation results validate the theoretical expressions and show the effectiveness of the proposed policy.

Appendix

Proof of Proposition 2

The outage probability can be computed by

$$\begin{aligned} \Pr \left\{ {\frac{{\eta P^2 \left| h \right| ^4 \left| g \right| ^2 \beta \left( {1 - \beta } \right) }}{{P\left| h \right| ^2 L+ d_1^{2m} d_2^m \sigma _R^2 \sigma _D^2 }} < \gamma _0 } \right\} \end{aligned}$$

(23)

where $L={\beta \eta \left| g \right| ^2 d_1^m \sigma _R^2 + d_1^m d_2^m \sigma _D^2 \left( {1 - \beta } \right) }$. It can be re-expressed by

$$\begin{aligned} \Pr \left\{ {\left( {\left| h \right| ^2 - h_1 } \right) \left( {\left| h \right| ^2 - h_2 } \right) < 0} \right\} \end{aligned}$$

(24)

in which $h_1$ and $h_2$ are outcomes of the function below

$$\begin{aligned} \begin{array}{l} \eta P^2 \left| h \right| ^4 \left| g \right| ^2 \beta \left( {1 - \beta } \right) - d_1^{2m} d_2^m \sigma _R^2 \sigma _D^2 \gamma _0 \\ - P\left| h \right| ^2 \left( {\beta \eta \left| {g } \right| ^2 d_1^m \sigma _R^2 + d_1^m d_2^m \sigma _D^2 \left( {1 - \beta } \right) } \right) \gamma _0 = 0 \\ \end{array} \end{aligned}$$

(25)

and $h_1$ and $h_2$ are determined by

$$\begin{aligned} h_1& = {} (B - \sqrt{B^2 + 4AC} {/}(2A) \end{aligned}$$

(26)

$$\begin{aligned} h_2& = {} (B + \sqrt{B^2 + 4AC} {/}(2A) \end{aligned}$$

(27)

where

$$\begin{aligned} A& = {} \eta P^2 \left| g \right| ^2 \beta \left( {1 - \beta } \right) \end{aligned}$$

(28)

$$\begin{aligned} B& = {} P\left( {\beta \eta \left| g \right| ^2 d_1^m \sigma _R^2 + d_1^m d_2^m \sigma _D^2 \left( {1 - \beta } \right) } \right) \gamma _0 \end{aligned}$$

(29)

$$\begin{aligned} C& = {} d_1^{2m} d_2^m \sigma _R^2 \sigma _D^2 \gamma _0 \end{aligned}$$

(30)

Due to $h_1 <0$, the given outage probability can be rewritten as

$$\begin{aligned}&P_{out} = \Pr \left\{ {0< \left| {h_S } \right| ^2 < h_2 } \right\} = F_{\left| {h_S } \right| ^2 } \left( {h_2 } \right) \end{aligned}$$

(31)

$$\begin{aligned}&F_{\left| {h_S } \right| ^2 } \left( {h_2 } \right) = 1 - e^{ - \;\frac{{h_2 }}{{\varOmega _h }}} \end{aligned}$$

(32)

Thus, we obtain new expression as

$$\begin{aligned} F_{\left| {h_S } \right| ^2 } \left( {h_2 } \right) = 1 - e^{ - \;\frac{{P\left( {\beta \eta \left| {g } \right| ^2 d_1^m \sigma _R^2 + d_1^m d_2^m \sigma _D^2 \left( {1 - \beta } \right) } \right) \gamma _0 + \sqrt{\varDelta _2 } }}{{2\eta P^2 \left| {g } \right| ^2 \beta \left( {1 - \beta } \right) \varOmega _h }}} \end{aligned}$$

(33)

This is end of Proof of Proposition 2 by averaging value of channel gain of h.