On spectrally-efficient device-to-device communication with wireless information and power transfer

Abstract

In this paper, the model of cooperative cognitive radio network is used to explore the two-way communications between a pair of unlicensed users by sharing the spectrum of any existing pair of licensed users. The licensed users of the spectrum are considered as primary users (PUs) and the unlicensed users of the spectrum are considered as secondary users (SUs). SUs are able to access the PUs spectrum by serving the relaying action between PU-to-PU communications. SUs are enabled by harvesting the energy from radio frequency signal following the principle of power splitting (PS) scheme of simultaneous wireless information and power transfer protocol. The closed form outage expressions of both PU and SU systems are derived. Analytical results validated through the simulations results. The results are also compared with existing work on two-way SU communications in presence of two-way PU communications. Based on the comparison, it is found that about ${\sim 191\%}$ and ${\sim 656\%}$ performance gains are possible to achieve by using proposed PS protocol in terms of spectrum efficiency and energy efficiency, respectively as compared to similar system using time switching protocol.

Appendices

Appendix - A

1.1 Derivation of (24)

$$\begin{aligned}&\mathscr {P}\Bigg ( X_{i2}\le \dfrac{k^{1t} }{b_{si} X_{i1}}-\dfrac{a_{si} X_{i1}}{b_{si}}\Bigg )\\&\quad =\int \limits _0^{\sqrt{\dfrac{k^{1t}}{a_{si}}}} {\exp }(-{x_{i1}}) \Big \{\int \limits _{0}^{\dfrac{k^{1t}}{b_{si} x_{i1}}-\dfrac{a_{si} x_{i1}}{b_{si}}} {\exp }(-{x_{i2}})dx_{i2}\Big \}dx_{i1}\\&\quad = \int \limits _0^{\sqrt{\dfrac{k^{1t}}{a_{si}}}} {\exp }(-{x_{i1}}) \Big (1- \exp \Big [-\dfrac{k^{1t}}{b_{si} x_{i1}}+\dfrac{a_{si} x_{i1}}{b_{si}}\Big ]\Big )dx_{11} \end{aligned}$$

By using Taylor Series Expansion, it can be written as follows,

$$\begin{aligned}&=1-\exp \bigg (-\sqrt{\dfrac{k^{1t} }{a_{si}}}\bigg )\nonumber \\&\quad -\sum _{l=0}^{\infty } \dfrac{(-1)^l}{l! (2t_l-l+1)} \sum _{t_l=0}^{l}{{l}\atopwithdelims (){t_l}} {\Big (\dfrac{k^{1t}}{b_{si}}\Big )}^{l-t_l}\nonumber \\&\quad \Bigg ({1-\dfrac{a_{si}}{b_{si}}}\Bigg )^{t_l} \Bigg (\sqrt{\dfrac{k^{1t} }{a_{si}}}\Bigg )^{2t_l-l+1} \end{aligned}$$

(A.1)

Appendix - B

1.1 Derivation of (28)

$$\begin{aligned} \mathscr {P}( R_{SU_p}^{(t)}\ge R_{ts})=\mathscr {P}\Big ( Z\ge \dfrac{u_3}{c_s (a_{si} X_{i1} +b_{si} X_{i2})}\Big ) \end{aligned}$$

(B.1)

Let, $X_u = (a_{si} X_{i1} +b_{si} X_{i2})$. Then the PDF of $X_u$ is given by [24],

$$\begin{aligned} f_{X_u}(x_u) = {\left\{ \begin{array}{ll} \frac{1}{a_{si}-b_{si}}\Big [\exp \Big ({-\frac{x_u}{a_{si}}}\Big )-\exp \Big ({-\frac{x_u}{b_{si}}}\Big )\Big ],\quad a_{si} \ne b_{si}\\ \frac{x_u}{a_{si} b_{si}}\exp \Big (-\frac{x_u}{a_{si}}\Big ), \quad a_{si} = b_{si} .\\ \end{array}\right. } \end{aligned}$$

(B.2)

The solution of product of two random variables can be obtained as follows [23, Sec. 3.324.1, 3.471.9].

$$\begin{aligned}&\mathscr {P}\bigg \lbrace Z \ge \frac{u_3}{c_s X_u} \bigg \rbrace = 1 - \mathscr {P}\bigg \lbrace Z < \frac{u_3}{c_s X_u} \bigg \rbrace \nonumber \\&\quad = \int _{0}^{\infty }\exp \bigg ({-\frac{u_3}{c_s x_u}}\bigg )f_{X_u}(x_u)dx_u\nonumber \\&\quad ={\left\{ \begin{array}{ll} \frac{1}{a_{si}-b_{si}}\int _{0}^{\infty }\exp \Big ({-\frac{u_3}{c_s x_u}}\Big )\Big [\exp \Big ({-\frac{x_u}{a_{si}}}\Big )-\exp \Big ({-\frac{x_u}{b_{si}}}\Big )\Big ] dx_u ;\\ { \quad \text {for},} \quad a_{si}\ne b_{si} \\ \int _{0}^{\infty }\exp \Big ({-\frac{u_3}{c_s x_u}}\Big )\frac{x_u}{a_{si} b_{si}}\exp \Big (-\frac{x_u}{a_{si}}\Big ) dx_u ;{\text {for},} a_{si} = b_{si}\\ \end{array}\right. }\nonumber \\&\quad ={\left\{ \begin{array}{ll}\dfrac{2 \frac{\sqrt{u_3}}{\sqrt{c_s}} }{(a_{si}-b_{si})}\Bigg \{\sqrt{{a_{si}}} \mathscr {K}_1\bigg (2\sqrt{\frac{u_3}{c_s a_{si}}}\bigg )-\sqrt{{ b_{si}}} \mathscr {K}_1\bigg (2\sqrt{\frac{u_3}{c_s b_{si}}}\bigg )\Bigg \};\\ { \quad \text {for},} \quad a_{si}\ne b_{si} \\ \dfrac{2 u_3}{c_s a_{si}}\mathscr {K}_2\bigg (2\sqrt{\frac{u_3}{c_s b_{si}}}\bigg ); {\text {for},} \quad a_{si} = b_{si}\\ \end{array}\right. }\nonumber \\ \end{aligned}$$

(B.3)