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Secrecy Performance in the Internet of Things: Optimal Energy Harvesting Time Under Constraints of Sensors and Eavesdroppers

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Abstract

In this paper, we investigate the physical layer security (PLS) performance for the Internet of Things (IoT), which is modeled as an IoT sensor network (ISN). The considered system consists of multiple power transfer stations (PTSs), multiple IoT sensor nodes (SNs), one legitimate fusion center (LFC) and multiple eavesdropping fusion centers (EFCs), which attempt to extract the transmitted information at SNs without an active attack. The SNs and the EFCs are equipped with a single antenna, while the LFC is equipped with multiple antennas. Specifically, the SNs harvest energy from the PTSs and then use the harvested energy to transmit the information to the LFC. In this research, the energy harvesting (EH) process is considered in the following two strategies: 1) the SN harvests energy from all PTSs, and 2) the SN harvests energy from the best PTS. To guarantee security for the considered system before the SN sends the packet, the SN’s power is controlled by a suitable power policy that is based on the channel state information (CSI), harvested energy, and security constraints. An algorithm for the nearly optimal EH time is implemented. Accordingly, the analytical expressions for the existence probability of secrecy capacity and secrecy outage probability (SOP) are derived by using the statistical characteristics of the signal-to-noise ratio (SNR). In addition, we analyze the secrecy performance for various system parameters, such as the location of system elements, the number of PTSs, and the number of EFCs. Finally, the results of Monte Carlo simulations are provided to confirm the correctness of our analysis and derivation.

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Acknowledgements

This work was supported in part by the Thailand Research Fund, Thai Network Information Center Foundation, under Grant RSA6180067, in part by Khon Kaen University, and in part by the SSF Framework Grant Serendipity.

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Authors and Affiliations

  1. International School, Duy Tan University, Danang, 550000, Vietnam

    Van Nhan Vo

  2. Applied Network Technology (ANT) Laboratory, Department of Computer Science, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

    Van Nhan Vo & Chakchai So-In

  3. Faculty of Information Technology, Duy Tan University, Danang, 550000, Vietnam

    Tri Gia Nguyen

  4. School of Innovation, Design and Engineering, Mälardalen University, Västerås, 72123, Sweden

    Hung Tran

  5. Faculty of Information Technology, Nguyen Tat Thanh University, Ho Chi Minh, 700000, Vietnam

    Hung Tran

  6. Department of Engineering, Faculty of Engineering, Kasetsart University, Bangkok, 10900, Thailand

    Surasak Sanguanpong

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  1. Van Nhan Vo
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Correspondence to Chakchai So-In.

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Appendix: Proofs for the PDF and the CDF of \(\gamma _{PS_{m}}\)

Appendix: Proofs for the PDF and the CDF of \(\gamma _{PS_{m}}\)

With the number of power transfer stations N = 2, we have

$$ {\gamma_{P{S_{m}}}} = {\gamma_{{P_{1}}{S_{m}}}} + {\gamma_{{P_{2}}{S_{m}}}}. $$
(62)

Accordingly, the PDF of \(\gamma _{P{S_{m}}}\) is formulated as follows:

$$\begin{array}{@{}rcl@{}} &&{\kern-16.4pt}{f_{{\gamma_{P{S_m}}}}}(z) = \int\limits_{- \infty }^{\infty} {\int\limits_{- \infty }^{z - y} {{f_{{\gamma_{{P_1}{S_m}}},{\gamma_{{P_2}{S_m}}}}}(x,y)\text{d}x\text{d}y} } \\ &=& \frac{1}{{{\lambda_{{P_1}{S_m}}} - {\lambda_{{P_2}{S_m}}}}}{e^{- \frac{z}{{{\lambda_{{P_1}{S_m}}}}}}} \left[ {{e^{\left( {\frac{{{\lambda_{{P_2}{S_m}}} - {\lambda_{{P_1}{S_m}}}}}{{{\lambda_{{P_2}{S_m}}}{\lambda_{{P_1}{S_m}}}}}} \right)z}} - 1} \right]\\ &=&\frac{{{\lambda_{{P_1}{S_m}}}}}{{{\lambda_{{P_1}{S_m}}} - {\lambda_{{P_2}{S_m}}}}}{f_{{\gamma_{{P_1}{S_m}}}}}(z) \\ &&+ \frac{{{\lambda_{{P_2}{S_m}}}}}{{{\lambda_{{P_2}{S_m}}} - {\lambda_{{P_1}{S_m}}}}}{f_{{\gamma_{{P_2}{S_m}}}}}(z) \end{array} $$
(63)
$$\begin{array}{@{}rcl@{}} &&\text{if}~\lambda_{{P_n}{S_m}} \neq \lambda_{{P_j}{S_m}}.\end{array} $$
(64)

Using the induction method [50], the PDF of \(\gamma _{P{S_{m}}}\) with N PTSs (i.e., the summary of N random variables having nonidentical exponential distributions) can be obtained as follows:

$$\begin{array}{@{}rcl@{}} &{f_{{\gamma_{P{S_{m}}}}}}\left( z \right) = \sum\limits_{n = 1}^{N} {\prod\limits_{\scriptstyle j = 1\hfill\atop \scriptstyle j \ne n\hfill}^{N} {\frac{{{\lambda_{{P_{n}}{S_{m}}}}}}{{{\lambda_{{P_{n}}{S_{m}}}} - {\lambda_{{P_{j}}{S_{m}}}}}}}} {f_{{\gamma_{{P_{n}}{S_{m}}}}}}\left( z \right)\\ &\text{ if } \lambda_{{P_{n}}{S_{m}}} \neq \lambda_{{P_{j}}{S_{m}}}. \end{array} $$
(65)

Similarly, the CDF of \(\gamma _{P{S_{m}}}\) with N PTSs can be derived:

$$\begin{array}{@{}rcl@{}} &{F_{{\gamma_{P{S_{m}}}}}}\left( z \right) = \sum\limits_{n = 1}^{N} {\prod\limits_{\scriptstyle j = 1\hfill\atop \scriptstyle j \ne n\hfill}^{N} {\frac{{{\lambda_{{P_{n}}{S_{m}}}}}}{{{\lambda_{{P_{n}}{S_{m}}}} - {\lambda_{{P_{j}}{S_{m}}}}}}}} {F_{{\gamma_{{P_{n}}{S_{m}}}}}}\left( z \right)\\ &\text{if } \lambda_{{P_{n}}{S_{m}}} \neq \lambda_{{P_{j}}{S_{m}}} \end{array} $$
(66)

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Vo, V.N., Nguyen, T.G., So-In, C. et al. Secrecy Performance in the Internet of Things: Optimal Energy Harvesting Time Under Constraints of Sensors and Eavesdroppers. Mobile Netw Appl 25, 193–210 (2020). https://doi.org/10.1007/s11036-019-01217-7

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