Secrecy capacity over correlated log-normal fading channel

This paper is concerned with the study of secrecy capacity for the log-normal fading channel in which the main channel is correlated with the eavesdropper channel. Perfect secrecy is achieved when the transmitter and legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. We consider the full channel state information (CSI) case, where the transmitter has access to both the main channel and eavesdropper channel gains. Under this assumption, we define the secrecy capacity of single-input single-output (SISO) log-normal fading channel and find the optimal power allocation at the transmitter that achieves the secrecy capacity. By analyzing the resulting secrecy capacity, we quantify the loss of secrecy capacity due to the correlation. We also find the closed-form analytical expression for the upper bound of secrecy capacity in terms of correlation coefficient which includes the independent case as a special one. The analysis of upper bound tells how the correlation coefficient and the ratio of main and eavesdropper channel gains affect the secrecy capacity.