Secure SWIPT-powered UAV communication against full-duplex active eavesdropper

Abstract

To further address the energy constraint problem and improve the secrecy performance of unmanned aerial vehicle (UAV) systems in the fifth generation (5G)-enabled Internet of Things, we consider a secure UAV system with simultaneous wireless information and power transfer in the presence of a full-duplex active eavesdropper, which eavesdrops on confidential information and transmits malicious jamming signals simultaneously. In particular, the UAV is powered by a constrained onboard battery that can harvest energy from the ambient radio frequency signals. The trajectory of the UAV, power splitting ratio, and transmitting power are jointly optimized to maximize the secrecy rate of the system. Owing to the non-convexity of the problem, we propose an alternative optimization algorithm by applying successive convex approximation and block coordinate descent methods. The simulation results show the proposed joint optimization algorithm can promote the average secrecy rate of the system as compared with other benchmark schemes.

Appendix 1: Proof of the Theorem 1

It is obvious to find that if $a_n \le b$, the information sent to U is eavesdropped by E. In this case, optimal transmitting power $P_s[n]=0$. For the case of $a_n > b$, we can see that the objective function (9a) is concave with respect to $P_s$. The Lagrangian of Problem (9) can be given as follows

$$\begin{aligned} \begin{aligned} L(P_s[n],\lambda _1,\lambda _2)=&\sum _{n=1}^{N}\left( \log _2(1+a_nP_s[n])-\log _2(1+bP_s[n])\right) \\&+\lambda _1\left( \frac{1}{N}\sum _{n=1}^Nc_nP_s[n]-\phi ^{EH}+d_n\right) \\&+\lambda _2\left( P_{\text {mean}}-\frac{1}{N}\sum _{n=1}^{N}P_s[n]\right) ,\\ \end{aligned} \end{aligned}$$

(22)

where $\lambda _1, \lambda _2 \ge 0$. Thus, the Lagrangian dual function of Problem (9) be reexpressed as

$$\begin{aligned} \begin{aligned} g(\lambda _1,\lambda _2)= \mathop {\max }_{0 \le P_s[n] \le P_{\max }}L(P_s[n],\lambda _1,\lambda _2), \end{aligned} \end{aligned}$$

(23)

It can be concluded that solving Problem (9) is equivalent to its dual problem, which is expressed as

$$\begin{aligned} \begin{aligned} \mathop {\min }_{\lambda _1,\lambda _2}g(\lambda _1,\lambda _2). \end{aligned} \end{aligned}$$

(24)

Note that the dual problem can be divided into N subproblems, as follows

$$\begin{aligned} \begin{aligned}&L(P_s[n],\lambda _1,\lambda _2)\\&=\sum _{n=1}^{N}L_n(P_s[n],\lambda _1,\lambda _2)-\lambda _1(\phi ^{EH}-d_n)+\lambda _2P_{\text {mean}}, \end{aligned} \end{aligned}$$

(25)

where

$$\begin{aligned} \begin{aligned} L_n(P_s[n],\lambda _1,\lambda _2)=&\log _2(1+a_nP_s[n])-\log _2(1+bP_s[n])\\&+\frac{\lambda _1c_n}{N}P_s[n]-\frac{\lambda _2}{N}P_s[n]. \end{aligned} \end{aligned}$$

(26)

As such, the derivation of the Lagrangian of Problem (9) can be obtained as

$$\begin{aligned} \begin{aligned} \frac{\partial L(P_s[n],\lambda _1,\lambda _2)}{\partial P_s[n]}=&\frac{a_n}{\ln 2(1+a_nP_s[n])}-\frac{b}{\ln 2(1+bP_s[n])}\\&+\frac{\lambda _1c_n}{N}-\frac{\lambda _2}{N}. \end{aligned} \end{aligned}$$

(27)

By setting the derivative to 0, we can obtain the optimal transmitted power $\hat{P}_s[n]$. The proof is completed.