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Spectrum sensing with multihop distributed switch and stay combining

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Abstract

In this paper, we derive the detection probability of cooperative spectrum sensing with multihop relaying and Distributed Switch and Stay Combining (DSSC). The primary user signal is amplified by relay nodes using Amplify and Forward multihop relaying to reach the fusion node where spectrum sensing is performed. A given branch is used when its end-to-end Signal to Noise Ratio is larger than a predefined threshold T. Otherwise, the second branch will be activated. We show that the proposed sensing with DSSC offers similar performance as All Participating (AP) relaying where both branches are active. Besides, DSSC offers close performance to Selection Combining (SC) where the branch with largest SNR is activated. We also optimize threshold T to maximize the detection probability. Spectrum sensing with DSCC is less complex than SC since no signalization is required to select the best branch.

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Authors and Affiliations

  1. King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia

    Ghassan Alnwaimi

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  1. Ghassan Alnwaimi
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Correspondence to Ghassan Alnwaimi.

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Appendix A

Appendix A

When there are two branches without a direct link, we have:

$$\begin{aligned} \frac{\partial P_d^{up}(T)}{\partial T}=[f_{\varGamma _1^{up}}(T)F_{\varGamma _2^{up}}(T)^2+f_{\varGamma _2^{up}}(T)F_{\varGamma _1^{up}}(T)^2] \end{aligned}$$
$$\begin{aligned}&\times \frac{a(\overline{\varGamma _1}^{up})+a(\overline{\varGamma _2}^{up})+b(\overline{\varGamma _1}^{up})+b(\overline{\varGamma _2}^{up})-2}{[F_{\varGamma _1^{up}}(T)+F_{\varGamma _2^{up}}(T)]^2}\\&+\frac{[f_{\varGamma _2^{up}}(T)F_{\varGamma _1^{up}}(T)-f_{\varGamma _1^{up}}(T)F_{\varGamma _2^{up}}(T)]}{[F_{\varGamma _1^{up}}(T)+F_{\varGamma _2^{up}}(T)]^2} \end{aligned}$$
$$\begin{aligned} \quad \times [b(\overline{\varGamma _1}^{up})-b(\overline{\varGamma _2}^{up})] \end{aligned}$$
(33)

When there is a direct link, the derivative of detection probability is expressed similarly to (33).

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Alnwaimi, G. Spectrum sensing with multihop distributed switch and stay combining. SIViP 16, 515–522 (2022). https://doi.org/10.1007/s11760-021-01994-3

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