Rezki, Zouheir; Alomair, Basel; Alouini, Mohamed-Slim(2014 IEEE Global Communications Conference, Institute of Electrical and Electronics Engineers (IEEE), 2014-12)[Conference Paper]
We consider a wiretap channel consisting of a source with multiple antennas, a legitimate receiver and an eavesdropper with a single antenna each. The channels between the source and the receivers undergo fast fading. We assume that the transmitter, in addition to the statistics of both channels, is only aware of a noisy version of the CSI to the legitimate receiver referred to as main channel. The legitimate receiver is aware of both its instantaneous channel gain and the transmitter's estimate of the main channel. On the other hand, the eavesdropper's receiver, in addition to its instantaneous channel realization, is aware of the actual main CSI and the transmitter's estimate as well. While the capacity of this channel is still open even with perfect CSI at the transmitter, we provide in this paper upper and lower bounds on the secrecy capacity. The upper bound is tighter than the one corresponding to perfect main CSI and the gap between the two upper bounds is characterized in function of the channel estimation error variance, at high-SNR. Furthermore, we show that our upper and lower bounds coincide in the case of no main CSI providing a trivial secrecy capacity.
Rezki, Zouheir; Khisti, Ashish J.; Alouini, Mohamed-Slim(IEEE Transactions on Communications, Institute of Electrical and Electronics Engineers (IEEE), 2014-10)[Article]
We 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.
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