On the secrecy capacity of the wiretap channel with imperfect main channel estimation
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Communication Theory Lab
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AbstractWe study the secrecy capacity of fast fading channels under imperfect main channel (between the transmitter and the legitimate receiver) estimation at the transmitter. Lower and upper bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate follows from a standard wiretap code in which a simple on-off power control is employed along with a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and eavesdropper channels and is the best known upper bound so far. The upper and lower bounds coincide with recently derived ones in case of perfect main CSI. Furthermore, the upper bound is tight in case of no main CSI, where the secrecy capacity is equal to zero. Asymptotic analysis at high and low signal-to-noise ratio (SNR) is also given. At high SNR, we show that the capacity is bounded by providing upper and lower bounds that depend on the channel estimation error. At low SNR, however, we prove that the secrecy capacity is asymptotically equal to the capacity of the main channel as if there were no secrecy constraint. Numerical results are provided for i.i.d. Rayleigh fading channels.
SponsorsThis work was supported in part by the Qatar National Research Fund (a member of Qatar Foundation) under NPRP Grant 5-603-2-243. This work was presented in part at the 2011 IEEE Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA. The editor coordinating the review of this paper and approving it for publication was A. Thangaraj.