Performance Evaluation of Relay Assisted Wireless Powered Network over Fluctuating Two Ray Fading Channel with Diversity Reception

Abstract

Recently wireless powered networks have emerged as cutting-edge technology for addressing the power constraint issue of wireless devices (WD’s). This technology enables wireless nodes to harness power from the ambient radio frequency (RF) signal thus enhances the energy efficiency of the communication network and also improves the network longevity. The underlying principle of energy harvesting (EH) by wireless power transfer (WPT) has implications on system performance due to link distance and channel fading. To address the impact of channel fading on energy constraints WD’s this work explores the maximal ratio combining (MRC) diversity at the receiver node for the presented simultaneous wireless information and power transfer (SWIPT) model considering the energy constraint unmanned aerial vehicle (UAV) mounted amplify and forward (AF) relay. Assuming fluctuating two ray (FTR) fading scenario a novel analytical expression for the outage probability (OP) and symbol error rate (SER) for the presented system has been derived. As the FTR fading channel provides a generalized fading model and can significantly model millimeter wave band signals. Based on derived performance metrics this paper investigates the impact of variation on node positioning and EH time allocation factor on system outage probability (OP) and symbol error rate (SER) performance. Finally, the derived expression has been validated by comparing the results obtained from the Monte Carlo simulation.

Appendices

Appendix 1

Proof of lemma 1

Expand lower incomplete gamma function in (9) using identity [21] we obtain following equivalent term

$$\frac{{G\left( {K + L,\mu \left( {\alpha \lambda + \frac{{\beta \lambda }}{\gamma }} \right)} \right)}}{{\Gamma \left( {K + L} \right)}} = 1 - e^{{ - \mu \left( {\alpha \lambda + \frac{{\beta \lambda }}{\gamma }} \right)}} \sum\limits_{{s = 0}}^{{K + L - 1}} {\frac{{\left( {\mu \left( {\alpha \lambda + \frac{{\beta \lambda }}{\gamma }} \right)} \right)^{s} }}{{s!}}} = 1 - e^{{ - \mu \left( {\alpha \lambda + \frac{{\beta \lambda }}{\gamma }} \right)}} \sum\limits_{{s = 0}}^{{K + L - 1}} {\sum\limits_{{t = 0}}^{s} {\left( \begin{gathered} s \hfill \\ t \hfill \\ \end{gathered} \right)} \frac{{\mu ^{s} }}{{s!}}\left( {\alpha \lambda } \right)^{{s - t}} \left( {\frac{{\beta \lambda }}{\gamma }} \right)^{t} }$$

(A.1)

From (9) and (A.1) we obtain

$$P_{{out}}^{{AF}} (C_{{th}} ) = \int\limits_{0}^{\infty } {\sum\limits_{{j_{1} ,..j_{L} = 0}}^{\infty } {\prod\limits_{{p = 1}}^{L} {C\left( {j_{p} } \right)} \sum\limits_{{k_{1} ,..k_{L} = 0}}^{\infty } {\prod\limits_{{q = 1}}^{L} {C\left( {k_{q} } \right)} } } \frac{{\mu ^{{J + L}} \gamma ^{{J + L - 1}} e^{{ - \mu \gamma }} }}{{\Gamma \left( {j + L} \right)}}} \left[ {1 - e^{{ - \mu \left( {\alpha \lambda + \frac{{\beta \lambda }}{\gamma }} \right)}} \sum\limits_{{s = 0}}^{{K + L - 1}} {\sum\limits_{{t = 0}}^{s} {\left( \begin{gathered} s \hfill \\ t \hfill \\ \end{gathered} \right)} \frac{{\mu ^{s} }}{{s!}}\left( {\alpha \lambda } \right)^{{s - t}} \left( {\frac{{\beta \lambda }}{\gamma }} \right)^{t} } } \right]d\gamma$$

(A.2)

Using identity (A.1) and properties of PDF the OP parameter can be equivalently expressed as,

$$P_{{out}}^{{AF}} (C_{{th}} ) = 1 - e^{{ - \mu \alpha \lambda }} \sum\limits_{{j_{1} ,..j_{L} = 0}}^{\infty } {\prod\limits_{{p = 1}}^{L} {C\left( {j_{p} } \right)} \sum\limits_{{k_{1} ,..k_{L} = 0}}^{\infty } {\prod\limits_{{q = 1}}^{L} {C\left( {k_{q} } \right)} } } \sum\limits_{{s = 0}}^{{K + L - 1}} {\sum\limits_{{t = 0}}^{s} {\left( \begin{gathered} s \hfill \\ t \hfill \\ \end{gathered} \right)} \frac{{\alpha ^{{s - t}} \lambda ^{s} \mu ^{{J + L + s}} \beta ^{t} }}{{s!\Gamma \left( {j + L} \right)}}} \int\limits_{0}^{\infty } {\gamma ^{{J + L - t - 1}} } e^{{ - \mu \gamma - \frac{{\mu \beta \lambda }}{\gamma }}} d\gamma$$

(A.3)

Again using identity (A.1), expression for OP with MRC diversity reception is given by (9).