On Ergodic Secrecy Capacity of Multiple Input Wiretap Channel with Statistical CSIT

We consider the secure transmission in ergodic fast-Rayleigh fading multiple-input single-output single-antennaeavesdropper (MISOSE) wiretap channels. We assume that the statistics of both the legitimate and eavesdropper channel s is the only available channel state information at the transmi tter (CSIT). By introducing a new secrecy capacity upper bound, we prove that the secrecy capacity is achieved by Gaussian input without prefixing. To attain this, we form another MISO SE channel for upper-bounding, and tighten the bound by finding the worst correlations between the legitimate and eavesdro pper channel coefficients. The resulting upper bound is tighter t han the others in the literature which are based on modifying the correlation between the noises at the legitimate receiver a nd eavesdropper. Next, we fully characterize the ergodic secr ecy capacity by showing that the optimal channel input covariance matrix is a scaled identity matrix, with the transmit power allocated uniformly among the antennas. The key to solve suc h a complicated stochastic optimization problem is by exploitng the completely monotone property of the ergodic secrecy capaci ty to use the stochastic ordering theory. Finally, our simulat ion results show that for the considered channel setting, the se crecy capacity is bounded in both the high signal-to-noise ratio a nd large number of transmit antenna regimes.