Secrecy Analysis of Wireless-Powered Multi-Antenna Relaying System With Nonlinear Energy Harvesters and Imperfect CSI

Abstract

In this paper, the secrecy performance of a wireless-powered multi-antenna relaying system, which consists of a source <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {(S)}$ </tex-math></inline-formula> , a destination <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {(D)}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {N (N&gt;1)}$ </tex-math></inline-formula> relays (Rs), a power beacon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {(B)}$ </tex-math></inline-formula> , and an eavesdropper <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {(E)}$ </tex-math></inline-formula> , is studied in the presence of imperfect channel state information at Rs. Both S and Rs are assumed to be with nonlinear energy harvesters, and harvest energy from radio-frequency signals from B through a time-switching harvesting scheme. Assuming Rs deploy decode-and-forward scheme, a general <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {K}$ </tex-math></inline-formula> th best relay in terms of instantaneous secrecy capacity for S-R-D link is selected for information transmission. An analytical expression for secrecy outage probability (SOP), validated via Monte Carlo simulation, is derived when all channels experience independent Rayleigh fading. Numerical results show that a higher correlation coefficient between the estimated and real channel values leads to better SOP performance when the ratio of the channel gains of R-D and R-E links is in the high region for the first hop or in the low-to-medium region for the second hop. Furthermore, there exists a special value of the saturation threshold of the energy harvester at S or R, and SOP performance cannot be improved when the saturation threshold is beyond that value.