  We investigate the secrecy capacity of an ergodic fading wiretap channel in
which the main channel is correlated with the eavesdropper channel. In this
study, the full Channel State Information (CSI) is assumed, and thus the
transmitter knows the channel gains of the legitimate receiver and the
eavesdropper. By analyzing the resulting secrecy capacity we quantify the loss
of the secrecy capacity due to the correlation. In addition, we study the
asymptotic behavior of the secrecy capacity as Signal-to-Noise Ratio (SNR)
tends to infinity. The capacity of an ordinary fading channel logarithmically
increases with SNR. On the contrary, the secrecy capacity converges into a
limit which can be an upper bound on the secrecy capacity over the fading
wiretap channel. We find a closed form of the upper bound for the correlated
Rayleigh wiretap channel which also includes the independent case as a special
one. Our work shows that the upper bound is determined by only two channel
parameters; the correlation coefficient and the ratio of the main to the
eavesdropper channel gains that will be called PCC and CGR respectively. The
analysis of the upper bound tells how the two channel parameters affect the
secrecy capacity and leads to the conclusion that the excessively large signal
power does not provide any advantage in the secrecy capacity, and the loss due
to the correlation is especially serious in low CGR regime.
