Adaptive Underlay/Interweave Transmission Protocol for Cognitive Radio Networks

Abstract

In this paper, we suggest a new transmission technique for cognitive radio networks. The proposed adaptive underlay/interweave transmission technique is evaluated in the presence and absence of primary interference. The proposed adaptive underlay/interweave transmission technique offers 1–3 dB gains with respect to conventional cognitive radio networks (CRN) using either underlay or interweave. The proposed protocol is extended to CRN with energy harvesting using radio frequency (RF) signals. Our results are valid for any position of primary and secondary transmitter and receiver.

Appendices

Appendix 1: PDF of SINR for Underlay CRN Without Energy Harvesting

Let $\Gamma _{S_TS_R}^{underlay}$ be the SINR at $S_R$ defined in (9). The cumulative distribution function (CDF) of $\Gamma _{S_TS_R}^{underlay}$ can be evaluated as:

$$\begin{aligned}&P(\Gamma _{S_TS_R}^{underlay}<\gamma )\nonumber \\&\quad =P\left( \Gamma _{S_TS_R}^{underlay}<\gamma | \frac{T}{|g_{S_TP_R}|^2}<E_{\max }\right) \nonumber \\&\qquad P\left( \frac{T}{|g_{S_TP_R}|^2}<E_{\max }\right) \nonumber \\&\qquad +P\left( \Gamma _{S_TS_R}^{underlay}<\gamma |\frac{T}{|g_{S_TP_R}|^2}>E_{\max }\right) \nonumber \\&\qquad P\left( \frac{T}{|g_{S_TP_R}|^2}>E_{\max }\right). \end{aligned}$$

(32)

We have

$$\begin{aligned}&P\left( \frac{T}{|g_{S_TP_R}|^2}<E_{\max }\right) \nonumber \\&\quad =1-P\left( \frac{T}{|g_{S_TP_R}|^2}>E_{\max }\right) =e^{-\frac{T}{E_{\max }\lambda _{S_TP_R}}} \end{aligned}$$

(33)

where $\lambda _{S_TP_R}=E(|g_{S_TP_R}|^2)$ and E(.) is the expectation operator.

When $\frac{T}{|g_{S_TP_R}|^2}>E_{\max }$, $E_{S_T}=E_{\max }$ and we have

$$\begin{aligned}&P\left( \Gamma _{S_TS_R}^{underlay}<\gamma |\frac{T}{|g_{S_TP_R}|^2}>E_{\max }\right) \nonumber \\&\quad =P\left( \frac{E_{\max }|g_{S_TS_R}|^2}{N_0+E_{P_T}|g_{P_TS_R}|^2}<\gamma \right) \nonumber \\&\quad =\int _0^{+\infty }P(E_{\max }|g_{S_TS_R}|^2<\gamma (N_0+E_{P_T}y))\frac{e^{-\frac{y}{\lambda _{P_TS_R}}}}{\lambda _{P_TS_R}}dy \nonumber \\&\quad =\int _0^{+\infty }\left[ 1-e^{-\frac{\gamma (N_0+E_{P_T}y)}{E_{\max }\lambda _{S_TS_R}}}\right] \frac{e^{-\frac{y}{\lambda _{P_TS_R}}}}{\lambda _{P_TS_R}}dy\nonumber \\&\quad =1-\frac{E_{\max }\lambda _{S_TS_R}}{E_{\max }\lambda _{S_TS_R}+\gamma E_{P_T}\lambda _{P_TS_R}} \end{aligned}$$

(34)

where $\lambda _{S_TS_R}=E(|g_{S_TS_R}|^2).$

When $\frac{T}{|g_{S_TP_R}|^2}<E_{\max }$, $E_{S_T}=\frac{T}{|g_{S_TP_R}|^2}$ and we have

$$\begin{aligned}&P\left( \Gamma _{S_TS_R}^{underlay}<\gamma |\frac{T}{|g_{S_TP_R}|^2}<E_{\max }\right) \nonumber \\&\quad =P\left( \frac{T|g_{S_TS_R}|^2}{|g_{S_TP_R}|^2 (N_0+E_{P_T}|g_{P_TS_R}|^2)}<\gamma |\frac{T}{|g_{S_TP_R}|^2}<E_{\max }\right). \end{aligned}$$

(35)

We deduce

$$\begin{aligned}&P\left( \Gamma _{S_TS_R}^{underlay}<\gamma |\frac{T}{|g_{S_TP_R}|^2}<E_{\max }\right) \nonumber \\&\quad =\int _{\frac{T}{E_{\max }}}^{+\infty }\int _0^{+\infty } P\left( |g_{S_TS_R}|^2<\frac{\gamma x (N_0+E_{P_T}y)}{T}\right) \nonumber \\&\qquad \frac{e^{-\frac{y}{\lambda _{P_TS_R}}}e^{-\frac{x}{\lambda _{S_TP_R}}}}{\lambda _{S_TP_R}\lambda _{P_TS_R}}dxdy,\nonumber \\&\quad =\int _{\frac{T}{E_{\max }}}^{+\infty }\int _0^{+\infty }\left[ 1-e^{-\frac{\gamma x (N_0+E_{P_T}y)}{T\lambda _{S_TS_R}}}\right] \nonumber \\&\qquad \frac{e^{-\frac{y}{\lambda _{P_TS_R}}}e^{-\frac{x}{\lambda _{S_TP_R}}}}{\lambda _{S_TP_R}\lambda _{P_TS_R}}dxdy. \end{aligned}$$

(36)

After some calculation, we obtain

$$\begin{aligned}&P\left( \Gamma _{S_TS_R}^{underlay}<\gamma |\frac{T}{|g_{S_TP_R}|^2}<E_{\max }\right) \nonumber \\&\quad =1-\frac{e^{\frac{N_0}{E_{P_T}\lambda _{P_TS_R}}}}{E_{P_T}\lambda _{P_TS_R}} \times \frac{T\lambda _{S_TS_R}}{\gamma \lambda _{S_TP_R}} e^{\frac{\lambda _{S_TS_R}T}{\gamma E_{P_T}}\lambda _{P_TS_R}\lambda _{S_TP_R}}\nonumber \\&\qquad \times e^{\frac{T}{E_{\max }\lambda _{S_TS_R}}}E_i \left[ \left( N_0+\frac{\lambda _{S_TS_R}T}{\lambda _{S_TP_R}\gamma }\right) \right. \nonumber \\&\qquad \left. \left( \frac{1}{E_{P_T}\lambda _{P_TS_R}}+\frac{\gamma }{\lambda _{S_TS_R}E_{\max }}\right) \right] \end{aligned}$$

(37)

where

$$\begin{aligned} E_i(\gamma )=\int _{\gamma }^{+\infty }\frac{e^{-x}}{x}dx. \end{aligned}$$

(38)

Using (14–17) and by derivation, we deduce the PDF of SINR for underlay CRN

$$\begin{aligned}&f_{\Gamma ^{underlay}_{S_TS_R}}(\gamma )\nonumber \\&\quad =\frac{\left( 1-e^{-\frac{T}{E_{\max }\lambda _{S_TS_R}}}\right) e^{-\frac{N_0\gamma }{E_{\max }\lambda _{S_TS_R}}}}{\lambda _{S_TS_R}E_{\max }+\gamma \lambda _{P_TS_R}E_{P_T}} \nonumber \\&\qquad \times \left[ \frac{\lambda _{S_TS_R}E_{\max }\lambda _{P_TS_R}E_{P_T}}{\lambda _{S_TS_R}E_{\max }+\gamma \lambda _{P_TS_R}E_{P_T}}+\frac{N_0E_{P_T}\lambda _{P_TS_R}}{\lambda _{S_TS_R}E_{\max }}\right] \nonumber \\&\qquad +a(\gamma )e^{\frac{N_0}{E_{P_T}\lambda _{P_TS_R}}}\frac{T\lambda _{S_TS_R}}{\lambda _{S_TP_R}E_{P_T}\lambda _{P_TS_R}}e^{\frac{T\lambda _{S_TS_R}}{E_{P_T}\gamma \lambda _{P_TS_R}\lambda _{S_TP_R}}} \end{aligned}$$

(39)

where

$$\begin{aligned} a(\gamma )=\frac{E_i(b(\gamma ))}{\gamma ^2}+\frac{E_i(b(\gamma ))}{\gamma ^3}\frac{T\lambda _{S_TS_R}}{E_{P_T}\lambda _{P_TS_R}\lambda _{S_TP_R}}+\frac{e^{-b(\gamma )}}{\gamma b(\gamma )} \end{aligned}$$

(40)

and

$$\begin{aligned} b(\gamma )=\left( N_0+\frac{T\lambda _{S_TS_R}}{\gamma \lambda _{S_TP_R}}\right) \left( \frac{1}{E_{P_T}\lambda _{P_TS_R}}+\frac{\gamma }{E_{\max }\lambda _{S_TS_R}}\right) . \end{aligned}$$

(41)

Appendix 2

The CDF of $E_{S_T}$ is equal to

$$\begin{aligned}&F_{E_{S_T}}(x)\nonumber \\&\quad =P(E_{S_T}<x)=1-P\left( \min \left( \frac{\beta E_{H}\alpha |g_{HS_T}|^{2}}{1-\alpha },\frac{I}{|g_{S_TP_{R}}|^{2}}\right) >x\right). \end{aligned}$$

(42)

Using (42) and since $g_{HS_T}$ and $g_{S_TP_{R}}$ are independent, we deduce

$$\begin{aligned} F_{E_{S_T}}(x)= 1-P\left( \frac{\beta E_{H}\alpha |g_{HS_T}|^{2}}{1-\alpha }>x\right) \nonumber \\ P\left( \frac{I}{|g_{S_TP_{R}}|^{2}}>x\right)= 1-P(|g_{HS_T}|^2>\frac{(1-\alpha )x}{\beta E_{H}\alpha })P(|g_{S_TP_{R}}|^{2}<\frac{I}{x}), \end{aligned}$$

(43)

In fact, $P(min(X,Y)>x)=P(X>x)P(Y>x)$. We deduce

$$\begin{aligned} F_{E_{S_T}}(x)=1-e^{-\frac{x(1-\alpha )}{\lambda _{HS_T}\alpha E_H \beta }}[1-e^{-\frac{I}{x\lambda _{S_TP_R}}}]. \end{aligned}$$

(44)

Appendix 3

The SNR at $S_R$ is defined as

$$\begin{aligned} \Gamma ^{underlay} _{S_TS_R}=E_{S_T} \frac{|h_{S_TS_R}|^2}{N_0}. \end{aligned}$$

(45)

Using the expression of CDF of $E_{S_T}$ given in Appendix 2, we have

$$\begin{aligned} F_{\Gamma ^{underlay} _{S_TS_R}}(x) &= 1-\int _0^{+\infty }e^{-\frac{x(1-\alpha )}{v\lambda _{HS_T}\alpha E_H \beta }}\nonumber \\&\left[ 1-e^{-\frac{vI}{x\lambda _{S_TP_R}}}\right] \frac{N_0}{\lambda _{S_TS_R}} e^{\frac{-N_0v}{\lambda _{S_TS_R}}}dv. \end{aligned}$$

(46)

We use (Gradshteyn and Ryzhik 1994)

$$\begin{aligned} \int _0^{+\infty }e^{-Ax-\frac{B}{x}}dx=2\sqrt{\frac{B}{A}}K_1(2\sqrt{AB}), \forall A>0,B>0 \end{aligned}$$

(47)

to express the CDF of SNR as:

$$\begin{aligned} F_{\Gamma ^{underlay} _{S_TS_R}}(x) &= 1-2\sqrt{\frac{N_0(1-\alpha )x}{\alpha \beta E_H N_0\lambda _{S_TS_R}\lambda _{HS_T}}}\nonumber \\&K_1\left( 2\sqrt{\frac{N_0(1-\alpha )x}{\alpha \beta E_H\lambda _{S_TS_R}\lambda _{HS_T}}}\right) \nonumber \\&+\frac{2N_0}{\lambda _{S_TS_R}} \sqrt{\frac{(1-\alpha )x}{\lambda _{HS_T}\alpha \beta E_H\left( \frac{N_0}{\lambda {S_TS_R}}+\frac{I}{x\lambda _{S_TS_R}}\right) }}\nonumber \\&K_1\left( 2\sqrt{\frac{(1-\alpha )x}{\lambda _{HS_T}\alpha E_H \beta }\left( \frac{N_0}{\lambda _{S_TS_R}}+\frac{I}{x\lambda _{S_TP_R}}\right) }\right). \end{aligned}$$

(48)