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SCIENTIA SINICA Informationis, Volume 49, Issue 10: 1353-1368(2019) https://doi.org/10.1360/N112018-00330

An online power-control algorithm for energy harvesting and secure transmission systems

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  • ReceivedDec 19, 2018
  • AcceptedApr 15, 2019
  • PublishedOct 15, 2019

Abstract

Here, we propose an online power-control strategy based on a Lyapunov optimization framework to optimize secrecy rate during the process of secure transmission in wireless communication systems with energy harvesting. We developed a system comprising one transmitter and two receivers that allow secure communication over a wireless fading channel. Additionally, this system includes an energy harvesting source node and two destination nodes that allow maintenance of information security between the two destination nodes. In each slot, the source node selects the destination node with the optimal channel state as the receiver of secret information, whereas the other destination node acts as an "eavesdropper." Transmission power and the rate of information transfer are established according to current battery power and channel status, with constraints related to battery power converted into a virtual queue and the optimization target converted into a penalty. By optimizing the transmission power to minimize the instantaneous drift plus penalty function, the long-term average secrecy rate is maximized under the constraint condition. Furthermore, the transmission fairness of the two destination nodes is evaluated during the optimization process. Simulation results show that the proposed scheme effectively improved the long-term average secrecy rate of the system.


Funded by

国家自然科学基金(61471076)

重庆市基础研究与前沿探索项目(cstc2018jcyjAX0432,cstc2017jcyjAX0204)


References

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  • Figure 1

    System model

  • Figure 2

    (Color online) Algorithm performance comparison

  • Figure 3

    (Color online) Battery power time track

  • Figure 4

    (Color online) Data queue backlog difference time track

  • Figure 5

    (Color online) Relationship between system performance and energy arrival rate. (a) Average security rate vs. energy arrival rate; (b) average battery power vs. energy arrival rate; (c) RMS value of data queue difference vs. energy arrival rate

  • Figure 6

    (Color online) The effect of $\delta~$ on system performance. (a) Average battery power vs. $\delta~$; (b) average security rate vs. $\delta~$; (c) RMS value of data queue difference vs. $\delta~$

  • Figure 7

    (Color online) Relationship between system performance and weight $U$ and $V$. (a) Average security rate vs. $U$ and $V$; (b) RMS value of data queue difference vs. $U$ and $V$

  • Figure 8

    (Color online) The influence of the upper and lower limits of weight on system performance. (a) Average security rate vs. ${{V}_{\max~}}$ and ${{V}_{\min~}}$; (b) RMS value of data queue difference vs. ${{V}_{\max~}}$ and ${{V}_{\min~}}$

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    Algorithm 1 Online power control algorithm based on Lyapunov

    Set weights $V$ $(V\!\ge\!~0)$, $U$ $(U\!\ge\!~0)$, weight limits ${{V}_{\max~}}$, ${{V}_{\min~}}$, initial battery energy ${{E}_{\text{b}}}(0)$, and time-independent constant $\delta~$.

    At time slot $t$:

    1: Observe system status ${{E}_{\text{a}}}(t)$, ${{h}_{1}}(t)$, ${{h}_{2}}(t)$, ${{Q}_{1}}(t)$, ${{Q}_{2}}(t)$, and $X(t)$.

    2: Observe channel states of two users:

    (1) if $|~{{h}_{1}}(t)~|>|~{{h}_{2}}(t)~|$, send confidential information to destination node 1.

    (i) if $X(t)\le~-\frac{\Delta~\gamma~(t)\tilde{V}(t)}{\ln~2\cdot~\Delta~t}$, the optimal transmission power is ${{P}^{\text{opt}}}(t)=0$.

    (ii) if $-\frac{\Delta~\gamma~(t)\widetilde{V}(t)}{\ln~2\cdot~\Delta~t}<X(t)<0$, the optimal transmission power is text ${{P}^{\text{opt}}}(t)=\min~({{P}^{*}}(t),{{P}_{\max~}},\frac{{{E}_{\text{b}}}(t)}{\Delta~t})$, ${{P}^{\text{*}}}(t)$ in it can be obtained by Eq. (37).

    (iii) if $X(t)\ge~0$, the optimal transmission power is ${{P}^{\text{opt}}}(t)=\min~({{P}_{\max~}},\frac{{{E}_{\text{b}}}(t)}{\Delta~t})$.

    (2) if $|~{{h}_{1}}(t)~|<|~{{h}_{2}}(t)~|$, send confidential information to destination node 2.

    (i) if $X(t)\le~-\frac{\Delta~\gamma~(t)\tilde{V}(t)}{\ln~2\cdot~\Delta~t}$, the optimal transmission power is ${{P}^{\text{opt}}}(t)=0$.

    (ii) if $-\frac{\Delta~\gamma~(t)\tilde{V}(t)}{\ln~2\cdot~\Delta~t}<X(t)<0$, the optimal transmission power is text ${{P}^{\text{opt}}}(t)=\min~({{P}^{*}}(t),{{P}_{\max~}},\frac{{{E}_{\text{b}}}(t)}{\Delta~t})$, ${{P}^{\text{*}}}(t)$ in it can obtain by Eq. (39).

    (iii) if $X(t)\ge~0$, the optimal transmission power is ${{P}^{\text{opt}}}(t)=\min~({{P}_{\max~}},\frac{{{E}_{\text{b}}}(t)}{\Delta~t})$. $\text{~}$3: Calculate the secrecy rate ${{R}_{\text{s}}}(t)$ according to Eq. (7)

    3: Calculate the secrecy rate ${{R}_{\text{s}}}(t)$ according to Eq. (7)

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