Power Beacon-Based Wireless Power Transfer in MISO/SISO: An Application in Device-to-Device Networks

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Abstract

This paper considers device-to-device (D2D) together with single input single output and multiple input single output models in transmitting of nearby devices under help of wireless power transfer. To support more harvested energy, two modes are studied in which multiple-antenna/single antenna power beacons are proposed to robust D2D transmission network. Especially, enhanced successful communication is explored with short distance transmission. Accordingly, the alternative energy source can be used to maintain small devices which can operate at close position efficiently. In this paper, a model of radio frequency-assisted wireless energy transfer for D2D system with two realistic transmission schemes will be investigated, namely pure D2D and D2D with interference impact of conventional user equipment. As an important result, we derive analytical expressions for outage probability to achieve performance evaluation. This paper will analyze outage probability by matching Monte-Carlo and analytical simulations to corroborate the exactness of derived expressions.

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Correspondence to Dinh-Thuan Do.

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Appendix

Appendix

Proof of Proposition 2

We denote two new variables \(A = {{{{\left| g \right| }^2}} \over {{{\left| {g_c} \right| }^2} + {\varPsi _1}}}\) and \(B = {\left| {\left| {\mathbf{h}} \right| } \right| ^2}{P \over {{N_0}}}\). It can be shown the SINR as below

$${\gamma _I} = \Psi {}_2AB$$
(A.1)

We first examine the outage probability as following expression

$$\begin{aligned} {F_A}(x) = Pr\left( {{{{{\left| g \right| }^2}} \over {{{\left| {g_c} \right| }^2} + {\varPsi _1}}} \le x} \right) \end{aligned}$$
(A.2)

It can be shown the outage probability as [36]

$$\begin{aligned} {F_A}(x\left| {{{\left| {g_c} \right| }^2}} \right. ) = 1 - {e^{ - {\varPsi _1}x}}{e^{ - {{\left| {g_c} \right| }^2}x}} \end{aligned}$$
(A.3)

Such expression can be re-calculated as

$$\begin{aligned} {F_A}(x) = 1 - {e^{ - {\varPsi _1}x}}\int \limits _0^\infty {{e^{ - (1 + x)y}}dy} \end{aligned}$$
(A.4)

And then we obtain new expression as

$$\begin{aligned} {F_A}(x) = 1 - {{{e^{ - {\varPsi _1}x}}} \over {1 + x}} \end{aligned}$$
(A.5)

We only examine the special case of the PB where is equipped with large number of antenna which result in simple following result

$$\begin{aligned} {F_A}(x) = 1 - {{{e^{ - {\varPsi _1}\left( {{\gamma _{th}}{N_0}/\left( {{\varPsi _2}NP} \right) } \right) }}} \over {1 + {\gamma _{th}}{N_0}/\left( {{\varPsi _2}NP} \right) }} \end{aligned}$$
(A.6)

As a result, to clear evaluate outage performance, we can be obtain the closed-form expression as

$$\begin{aligned} P_{out,CDD}^{MISO} = 1 - {{{e^{ - {\varPsi _1}\left( {{\gamma _{th}}{N_0}/\left( {{b_2}NP} \right) } \right) }}} \over {1 + {\gamma _{th}}{N_0}/\left( {{\varPsi _2}NP} \right) }} \end{aligned}$$
(A.7)

This is end of proof.\(\square\)

Proof of Proposition 3

Having a look on the outage probability in CDD SISO mode, it can be given by

$$\begin{aligned} P_{out,CDD}^{SISO} = \Pr \left\{ {{\left| h \right| ^2}{\left| g \right| ^2} \le \frac{{{{\left| {g_c} \right| }^2}P + {N_0}}}{{\eta \varepsilon P}}{\gamma _{th}}} \right\} \end{aligned}$$
(B.1)

We first define new variables as \(x = {\left| h \right| ^2}{\left| g \right| ^2},y = {\left| {g_c} \right| ^2}\), conditioned on y, the outage probability can be computed as

$$\begin{aligned} P_{out,CDD}^{SISO} = \Pr \left\{ {x \le \frac{{yP + {N_0}}}{{\eta \varepsilon P}}{\gamma _{th}}} \right\} \end{aligned}$$
(B.2)

Utilizing the popular result in [1, 3], the CDF of x can be shown as

$$\begin{aligned} {F_x}\left( X \right) = 1 - 2\sqrt{\frac{X}{{{\lambda _h}{\lambda _g}}}} {K_1}\left( {2\sqrt{\frac{X}{{{\lambda _h}{\lambda _g}}}} } \right) \end{aligned}$$
(B.3)

To this end, averaging over y, the desired result can be obtained as in Proposition 3.

This completes the proof.\(\square\)

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Dang, HP., Le, CB., Do, DT. et al. Power Beacon-Based Wireless Power Transfer in MISO/SISO: An Application in Device-to-Device Networks. Wireless Pers Commun 110, 381–402 (2020). https://doi.org/10.1007/s11277-019-06733-z

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Keywords

  • Energy beamforming
  • Multiple input single output
  • D2D networks
  • Outage probability