Quality of Protection in Cloud-Assisted Cognitive Machine-to-Machine Communications for Industrial Systems

Abstract

Cloud-assisted cognitive machine-to-machine co- mmunications (CM2M) is a new paradigm to improve the mobile services, which have drawn considerable attention in industry and academia. In this paper, we consider the quality of protection (QoP) of information transmission in cloud-assisted CM2M communications. In such an environment, the secondary M2M system intends to share the primary spectrum on the condition that the secondary transmitter (ST) has to relay the primary message. However, the ST is a low-energy device which adopts the energy harvesting technique to power itself. In particular, we focus on secure information transmission for the primary system when the secondary users (SUs) are the potential eavesdroppers. We aim to jointly design power splitting and secure beamforming to maximize the secondary M2M system data rate subject to the secrecy requirement of the primary system and the ST power constraint. To solve this non-convex problem, we propose a computationally efficient two-stage optimization approach. Simulation results demonstrate that our proposed scheme achieves a significant transmission rate of the secondary M2M system while provides a high secrecy rate for the primary system compared to the scheme without energy harvesting.

Appendix A Proof of Proposition 3.1

The Karush-Kuhn-Tucker (KKT) conditions of problem (P3) are expressed as

$$ A_{1}^{*}\textbf{W}_{s}^{*} = 0, ~B_{1}^{*}\textbf{W}_{p}^{*} = 0, $$

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First, we show that $\text {rank}\left ({\textbf {W}_{p}^{*}} \right )=1$. The ST power constraint in (P3) is active with equality, it follows that the optimal dual variable 𝜃 ^∗>0. Since ${\textbf {H}_{ss}}\underset {\smash {\scriptscriptstyle -}}{\succ } 0$ and ${\textbf {H}_{ss_{k}}}\underset {\smash {\scriptscriptstyle -}}{\succ } 0$, we obtain $\text {rank}\left ({ - {\lambda ^{*}}{\textbf {H}_{ss}} - {\partial _{k}^{*}}{\textbf {H}_{ss_{k}}} - {\theta ^{*}}\textbf {I}} \right )=N$. Moreover, since rank(H _sp )≤1, it follows from Eq. 18 that $\text {rank}\left ({B_{1}^{*}} \right ) \geqslant N - 1$. According to Eq. 22, we have $\text {rank}\left ({\textbf {W}_{p}^{*}} \right )=1$.

Next, we prove the second part of Proposition 3.1. Define

$$ C_{1}^{*} = - {\lambda^{*}}{\textbf{H}_{ss}} - {\beta^{*}}{\tilde {\Gamma}_{p}}{\textbf{H}_{sp}} + \sum\limits_{k = 1}^{K} {\partial_{k}^{*}} {\tilde {\Gamma}_{{e_{k}}}}{\textbf{H}_{s{s_{k}}}} - {\theta^{*}}\textbf{I}, $$

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Then we have

$$ A_{1}^{*} = C_{1}^{*} + \left( {{\lambda^{*}} + 1} \right){\textbf{H}_{ss}}, $$

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since 𝜃 ^∗>0, $\textbf {H}_{ss}\underset {\smash {\scriptscriptstyle -}}{ \succ } 0$, $\textbf {H}_{ss_{k}}\underset {\smash {\scriptscriptstyle -}}{ \succ } 0$ and ${\textbf { H}_{sp}}\underset {\smash {\scriptscriptstyle -}}{ \succ } 0$, we have $\text {rank}\left ({ - {\lambda ^{*}}{\textbf {H}_{ss}} - {\beta ^{*}}{{{\tilde {\Gamma } }_{p}}}{\textbf {H}_{sp}} - {\theta ^{*}}\textbf {I}} \right )=N$ . Without loss of generality, we define $r = {\text { }}\text {rank}\left ({C_{1}^{*}} \right )$ and the orthonormal basis of the null space of $C_{1}^{*}$ as ${\Upsilon } \in {\mathbb {C}^{N \times (N - r)}}$ such that $C_{1}^{*}{\Upsilon } = 0$ and rank(Υ) = N−r. Let ${\pi _{t}} \in {\mathbb {C}^{N \times 1}}$, 1 ≤ t ≤ N−r, denote the tth column of Υ. We can express the optimal solution of $W_{s}^{*}$ as

$$ \textbf{W}_{s}^{*} = \sum\limits_{t = 1}^{N - r} {{a_{t}}} {\pi_{t}}\pi_{t}^{\dag} + bu{u^{\dag} }, $$

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where ${a_{t}} \geqslant 0$, ∀t, b>0 and $u \in {\mathbb {C}^{N \times 1}}$, ∥u∥=1, u ^†Υ=0.

Last, we prove the third part. For $\text {rank}\left ({\textbf {W}_{s}^{*}} \right ) > 1$, we construct another solution of the relaxed version of (P3), $\tilde {\textbf {W}}_{s}^{*} = \textbf {W}_{s}^{*} - \sum \limits _{t = 1}^{N - r} {{a_{t}}} {\pi _{t}}\pi _{t}^{\dag }$, $\tilde {\textbf {W}}_{p}^{*} = \textbf {W}_{p}^{*}$, ${\tilde {\tau }^{*}} = {\tau ^{*}}$. Then substituting them into the objective function and constraints in (P3) which achieves the same optimal value as the optimal solution and satisfies all the constrains. Thus, $\left (\tilde {\mathbf {W}}_{s}^{*}, \tilde {\textbf {W}}_{p}^{*},{{\tilde {\tau }^{*}}} \right )$ is also an optimal solution to (P3) but with $\text {rank}\left ({\textbf {W}_{s}^{*}} \right )=1$.