Leakage-probability-constrained secrecy capacity of a fading channel

Secure transmission of information over wireless channels in the presence of an eavesdropper has attracted much attention recently. Previous work assumes that a transmitter has perfect knowledge of the channel side information (CSI) of the legitimate channel and the eavesdropper's channel. To loosen this strong requirement, this paper considers the case where a transmitter has perfect knowledge of the CSI of the legitimate channel and only the average channel gain of the eavesdropper's channel. In this case, some information may be leaked to the eavesdropper because the eavesdropper's channel may have a higher gain than the legitimate channel. Hence, we propose, for the first time, to study leakage-probability-constrained secrecy capacity of a fading channel, that is, secrecy capacity under the constraint on leakage probability. We also propose an optimal power allocation strategy that maximizes leakage-probability-constrained secrecy capacity under average power constraint. Moreover, we study the impact of the bias of the average gain estimate of the eavesdropper's channel on leakage-probability-constrained secrecy capacity.