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Security-embedded opportunistic user cooperation with full diversity

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Abstract

As a promising technique for wireless networks, cooperative communications is coming to maturity in both theory and practice. The main merit of the cooperation technique is its capability in providing additional transmission links to harvest the spatial diversity gain at the physical layer. However, due to the broadcast nature of wireless medium, the diversity gain can be also freely achieved at the potential eavesdropper if the cooperation is performed blindly. To solve this problem, we propose a security-embedded opportunistic user cooperation scheme (OUCS) in this paper. The OUCS first defines a concept called secrecy-providing capability (SPC) for both the source and the cooperative relays. By comparing the values of SPC of these nodes, the OUCS jointly decides whether to cooperate and with whom to cooperate from the perspective of physical layer security. The secrecy outage performance of the OUCS is then derived. From the results we prove that full diversity can be achieved (i.e., the diversity order is N + 1 for N cooperative relays), which outperforms existing alternatives. Finally, numerical results are provided to validate the theoretical analysis.

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Notes

  1. There are examples of real-world systems corresponding to the three cases: (A) the eavesdropper performs strict passive eavesdropping; (B) the location of the eavesdropper can be determined to analyze its average channel conditions; (C) the eavesdropper is also a legitimate node which transmits its own signals but is prohibited from obtaining the confidential messages [24].

  2. The achievable secrecy rate can be further increased if the source continues to transmit in Phase II. For a simple comparison between the OUCS and alternatives, this manner is not considered in this paper.

  3. The results with a shared frequency resource (i.e., an identical \(\gamma _{SE}\)) are also simulated in the next section, which show a similar outage performance and a same diversity order as the orthogonal scenario.

  4. In [22], only the eavesdropper exploits the direct link.

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Correspondence to Hao Niu.

Appendix: Diversity order analysis of \(P_{out}^{A{\text{-}}up}\)

Appendix: Diversity order analysis of \(P_{out}^{A{\text{-}}up}\)

Equation (9) can be divided into different parts based on “+” and “−” operations,

$$\begin{aligned} &P_{out}^{A {\text{-}} up1}\\&=\int _0^\infty {\prod \limits _{n = 1}^N {\left[ {({\lambda _{Sn}} + {\lambda _{nD}})x} \right] {\lambda _{SD}}{e^{ - {\lambda _{SD}}x}}{e^{ - {\lambda _{SE}}\frac{x}{{{2^{2{R_s}}}}}}}dx} }\\&=\prod \limits _{n = 1}^N {\left[ { \left( {{\lambda _{Sn}} + {\lambda _{nD}}} \right) } \right] } {\lambda _{SD}}\frac{{\varGamma (N + 1)}}{{{{\left( {{\lambda _{SD}} + \frac{{{\lambda _{SE}}}}{{{2^{2{R_s}}}}}} \right) }^{N + 1}}}} \\&= \prod \limits _{n = 1}^N {\left( {\frac{1}{{{c_{Sn}}\sigma _{SD}^2}} + \frac{1}{{{c_{nD}}\sigma _{SD}^2}}} \right) }\\&\quad \frac{1}{{\sigma _{SD}^2}}\frac{{\varGamma (N + 1)}}{{{{\left( {\frac{1}{{\sigma _{SD}^2}} + \frac{1}{{{2^{2{R_s}}}\sigma _{SE}^2}}} \right) }^{N + 1}}}}\\&= {\left( {\frac{1}{{{\delta _{de}}}}} \right) ^{N + 1}}\prod \limits _{n = 1}^N {\left( {\frac{1}{{{c_{Sn}}}} + \frac{1}{{{c_{nD}}}}} \right) } \frac{{\varGamma (N + 1)}}{{{{\left( {\delta _{de}^{ - 1} + a} \right) }^{N + 1}}}} \end{aligned}$$
$$\begin{aligned} P_{out}^{A {\text{-}} up2}&= \sum \limits _{n = 1}^N {\int _0^\infty {{\lambda _{SD}}x {\mathop{\mathop{\prod}\limits_{m = 1}^N}\limits_{m \ne n}} {\left[ {({\lambda _{Sm}} + {\lambda _{mD}})x} \right] } } }\\&\quad {\lambda _{Sn}}{e^{ - {\lambda _{Sn}}x}}{e^{ - {\lambda _{SE}}\frac{{x}}{{{2^{2{R_s}}}}}}}{e^{ - {\lambda _{nD}}x}} dx\\&= {\left( {\frac{1}{{{\delta _{de}}}}} \right) ^{N + 1}} \sum \limits _{n = 1}^N\frac{1}{{{c_{Sn}}}} {\mathop{\mathop{\prod}\limits_{m = 1}^N}\limits_{m \ne n}} {\left( {\frac{1}{{{c_{Sm}}}} + \frac{1}{{{c_{mD}}}}} \right) }\\&\quad \frac{{\varGamma (N + 1)}}{{{{\left[ {\left( {\frac{1}{{{c_{Sn}}}} + \frac{1}{{{c_{nD}}}}} \right) \delta _{de}^{ - 1} + a} \right] }^{N + 1}}}} \end{aligned}$$
$$\begin{aligned} P_{out}^{A {\text{-}} up3}&=\sum \limits _{n = 1}^N {\int _0^\infty {{\lambda _{SD}}x {\mathop{\mathop{\prod}\limits_{m = 1}^N}\limits_{m \ne n}} {\left[ {({\lambda _{Sm}} + {\lambda _{mD}})x} \right] } } } {\lambda _{Sn}}{e^{ - {\lambda _{Sn}}x}}\\&\quad \int _x^\infty {{\lambda _{nD}}{e^{ - {\lambda _{nD}}y}}{e^{ -{\lambda _{nE}} \frac{{y}}{{{2^{2{R_s}}}}}}}dy} dx\\&= {\left( {\frac{1}{{{\delta _{de}}}}} \right) ^{N + 2}}\sum \limits _{n = 1}^N\frac{1}{{{c_{Sn}}{c_{nD}}}} {\mathop{\mathop{\prod}\limits_{m = 1}^N}\limits_{m \ne n}} {\left( {\frac{1}{{{c_{Sm}}}} + \frac{1}{{{c_{mD}}}}} \right) }\\&\quad \frac{{\varGamma (N + 1)}}{{\left( {\frac{1}{{{c_{nD}}}}\delta _{de}^{ - 1} + \frac{a}{{{c_{nE}}}}} \right) {{\left[ {\left( {\frac{1}{{{c_{Sn}}}} + \frac{1}{{{c_{nD}}}}} \right) \delta _{de}^{ - 1} + \frac{a}{{{c_{nE}}}}} \right] }^{N + 1}}}} \end{aligned}$$
$$\begin{aligned} P_{out}^{A {\text{-}} up4}&=\sum \limits _{n = 1}^N {\int _0^\infty {{\lambda _{SD}}x {\mathop{\mathop{\prod}\limits_{m = 1}^N}\limits_{m \ne n}}{\left[ {({\lambda _{Sm}} + {\lambda _{mD}})x} \right] } } } {\lambda _{Sn}}{e^{ - {\lambda _{Sn}}x}}\\&\quad {e^{ - {\lambda _{SE}}\frac{{x}}{{{2^{2{R_s}}}}}}}\int _x^\infty {{\lambda _{nD}}{e^{ - {\lambda _{nD}}y}}{e^{ - {\lambda _{nE}}\frac{{y}}{{{2^{2{R_s}}}}}}}dy} dx \\&= {\left( {\frac{1}{{{\delta _{de}}}}} \right) ^{N + 2}}\sum \limits _{n = 1}^N\frac{1}{{{c_{Sn}}{c_{nD}}}} {\mathop{\mathop{\prod}\limits_{m = 1}^N}\limits_{m \ne n}} {\left( {\frac{1}{{{c_{Sm}}}} + \frac{1}{{{c_{mD}}}}} \right) } \\&\quad \frac{{\varGamma (N + 1)}}{{\left( {\frac{1}{{{c_{nD}}}}\delta _{de}^{ - 1} + \frac{a}{{{c_{nE}}}}} \right) {{\left[ {\left( {\frac{1}{{{c_{Sn}}}} + \frac{1}{{{c_{nD}}}}} \right) \delta _{de}^{ - 1} + \left( {1 + \frac{1}{{{c_{nE}}}}} \right) a} \right] }^{N + 1}}}} \end{aligned}$$

where, \(a = \frac{1}{{{2^{2{R_s}}}}}\). The results of the last three parts of Eq. (9) are similar to \(P_{out}^{A-up2}\), \(P_{out}^{A - up3}\) and \(P_{out}^{A - up4}\) respectively. Therefore,

$$\begin{aligned} d_{secrery}^{A{\text{-}}up}&\,=\,\min \left\{ {- \mathop {\lim }\limits _{{\delta _{de}} \rightarrow \infty } \frac{{\log (P_{out}^{A - up1})}}{{\log ({\delta _{de}})}}, -\mathop {\lim }\limits _{{\delta _{de}} \rightarrow \infty } \frac{{\log (P_{out}^{A {\text{-}} up2})}}{{\log ({\delta _{de}})}},\ldots }\right\} \\&=\,N+1 \end{aligned}$$

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Niu, H., Zhu, N., Sun, L. et al. Security-embedded opportunistic user cooperation with full diversity. Wireless Netw 22, 1513–1522 (2016). https://doi.org/10.1007/s11276-015-1044-7

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