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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

In this paper, we consider a system supporting simultaneous wireless information and power transfer (SWIPT),where the transmitter delivers private message to a destination receiver (DR) and powers to multipleenergy receivers (ERs) with multiple single-antenna external eavesdroppers (Eves). We study secure robust beamformer and powersplitting (PS) design under imperfect channel state information (CSI).The artificial noise (AN) scheme is further utilized at the transmitter to provide strong wireless security.We aim at maximizing the energy harvested by ERs subject to the transmission power constraint, a range of outageconstraints concerning the signal-to-interference-plus-noise ratio (SINR) recorded at the DR and the Eves, as well as concerningthe energy harvested at the DR. The energy harvesting maximization (EHM) problem is challenging to directly solve,we resort to Bernstein-type inequality restriction technique to reformulatethe original problem as a tractable approximated version. Numerical results show that our robust beamforming schemeoutperforms the beamforming scheme relying on the worst-case design philosophy.


Acknowledgment

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


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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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