On ergodic secrecy capacity of fast fading MIMOME wiretap channel with statistical CSIT

In this paper, we consider the secure transmission in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When legitimate receiver has more (or equal) antennas than the eavesdropper, we prove the first MIMOME secrecy capacity result with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is forming an MIMOME degraded channel by dividing the legitimate receiver´s channel matrix into two submatrices, and setting one of which the same as the eavesdropper´s channel matrix. Next, subject to the total power constraint overall transmit antennas, we solve the channel-input covariance matrix optimization problem to fully characterize the MIMOME secrecy capacity. Typically, the MIMOME optimization problems are non-concave. However, with aids of the proposed degraded channel, we show that the stochastic MIMOME optimization problem can be transformed to be a Schur-concave problem to find its optimal solution. Finally, we find that the MIMOME secrecy capacities scale with the signal-to-noise ratios with large enough numbers of antennas at legitimate receiver. However, as shown in previous works, such a scaling does not exist for wiretap channels with single antenna at legitimate receiver and eavesdropper each.