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SCIENCE CHINA Information Sciences, Volume 61 , Issue 2 : 022303(2018) https://doi.org/10.1007/s11432-016-9040-x

Probabilistic-constrained robust secure transmission for energyharvesting over MISO channels

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  • ReceivedJan 10, 2017
  • AcceptedFeb 22, 2017
  • PublishedJul 28, 2017

Abstract


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61371075, 61421001) and 111 Project of China (Grant No. B14010).


References

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  • Figure 1

    (Color online) System model.

  • Figure 2

    (Color online) The harvested energy versus the transmission power constraint $P_{\textrm{th}}$ under $N_{\rm~t}=4$ and $K=2$.

  • Figure 3

    (Color online) The total transmission power $\mathrm{tr}({\boldsymbol~W}+{\boldsymbol~\varSigma})$ versus the harvested energy threshold $\varGamma_\mathrm{D}$ prescribed for each ER under $N_{\rm~t}=4$ and $K=\{2,4\}$.

  • Figure 4

    (Color online) The harvested energy versus the transmission power constraint $P_{\textrm{th}}$ for different $N_{\rm~t}$ and $p=q$.

  • Figure 5

    (Color online) The harvested energy versus the transmission power constraint $P_{\textrm{th}}$ for different $K$.

  • Table 1   Computational complexity analysis
    Methods Computation complexity order (ignoring $\ln(1/\epsilon)$ in $\mathcal{O}(\cdot)\ln(1/\epsilon)$, where $\epsilon$ denotes the
    accuracy requirement); $n=\mathcal{O}(KMN_{\rm~t}^2)$.
    Bernstein-type $\mathcal{O}\big(\sqrt{(K+M+4)N_{\rm~t}+2M+2K+6}\big[((K+M+2)N_{\rm~t}^3+2)+n((K+M+2)N_{\rm~t}^2+2)$
    $+(K+M+2)(N_{\rm~t}^2+N_{\rm~t}+1)^2+n^2~\big]\big)$
    Worst-case $\mathcal{O}\big(\sqrt{(K+M+4)N_{\rm~t}+2M+2K+4}\big[((K+M+2)(N_{\rm~t}+1)^3+2N_{\rm~t}^3+2)$
    $+n((K+M+2)(N_{\rm~t}+1)^2+2N_{\rm~t}^2+2)+n^2~\big]\big)$
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