Sensitivity of the secrecy capacity of a wiretap channel to the channel gains with imperfect channel information

In this paper, the impact of a small variations in the channel gains on the secrecy rate of the wiretap channel is studied, in which it is assumed that the imperfect channel knowledge is available at the transmitter. First, we consider general additive noise model for both legitimate and eavesdropper channels in the wiretap channel, and compute the variation of the secrecy rate resulting from the small variations in the channel gains. Then, we focus on the Gaussian wiretap channel, as a special case and calculate the sensitivity of the secrecy capacity to the channel gains with imperfect channel knowledge. Interestingly, it is shown that in some situations the effect of the channel variation on the secrecy capacity can be canceled out.