Throughput analysis and optimization of cognitive radio networks using incremental relaying

Abstract

In this paper, we derive the throughput and Bit Error Probability of incremental relaying for cognitive radio networks. Relaying in the secondary network is performed only when the SNR of the direct link is lower than a predefined threshold $\beta$. Also, all relays must verify interference constraints: the generated interference to primary receiver must be below a chosen threshold (T) so that the primary throughput is larger than a predefined value. The analysis is valid for different relay selection techniques: Opportunistic amplify and forward, opportunistic decode and forward, partial and reactive AF relay selection. We also consider multihop relaying with single and multiple branches. For multiple branches, two scenarios are considered: all branches are maximum ratio combined or the best branch is activated. We also take into account the interference from primary to secondary nodes. The parameter $\beta$ of incremental relaying is also numerically optimized to achieve the highest secondary throughput.

Appendix A

PDF of $Z^{up}=\Gamma _{SD}+\Gamma _{SRD}^{up}|\Gamma _{SD}<\beta$.

$$\begin{aligned} f_{Z}(z)=\int _{0}^{\beta }f_{\Gamma _{SD}|\Gamma _{SD}<\beta }(x)f_{\Gamma _{SRD}^{up}}(z-x)dx \end{aligned}$$

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Notice that $\Gamma _{SRD}^{up}$ is exponentially distributed. If $z<\beta ,$ the previous integral becomes

$$\begin{aligned} f_{Z}(z)= & {} \int _{0}^{z}\frac{e^{-\frac{x}{\overline{\Gamma }_{SD}}}}{ {\overline{\Gamma }}_{SD}\left[ 1-e^{-\frac{\beta }{{\overline{\Gamma }}_{SD}}} \right] }\frac{e^{-\frac{\left( z-x\right) }{{\overline{\Gamma }}_{SRD}^{up}}} }{{\overline{\Gamma }}_{SRD}^{up}}dx \nonumber \\= & {} \frac{e^{-\frac{z}{\overline{\Gamma }_{SD}}}-e^{-\frac{z}{{\overline{\Gamma }}_{SRD}^{up}}}}{\left( {\overline{\Gamma }}_{SD}-{\overline{\Gamma }} _{SRD}^{up}\right) \left[ 1-e^{-\frac{\beta }{{\overline{\Gamma }}_{SD}}} \right] } \end{aligned}$$

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When $z>\beta$,

$$\begin{aligned} f_{Z}(z)= & {} \int _{0}^{\beta }\frac{e^{-\frac{x}{\overline{\Gamma }_{SD}}}}{ {\overline{\Gamma }}_{SD}\left[ 1-e^{-\frac{\beta }{{\overline{\Gamma }}_{SD}}} \right] }\frac{e^{-\frac{\left( z-x\right) }{{\overline{\Gamma }}_{SRD}^{up}}} }{{\overline{\Gamma }}_{SRD}^{up}}dx \nonumber \\= & {} \frac{e^{-\frac{z}{{\overline{\Gamma }}_{SRD}^{up}}}\left[ e^{\beta \left( \frac{1}{\overline{\Gamma }_{SRD}^{up}}-\frac{1}{{\overline{\Gamma }}_{SD}} \right) }-1\right] }{\left( {\overline{\Gamma }}_{SD}-{\overline{\Gamma }} _{SRD}^{up}\right) \left[ 1-e^{-\frac{\beta }{\overline{\Gamma }_{SD}}} \right] } \end{aligned}$$

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