Ergodic Secrecy Rate for Multiple-Antenna Wiretap Channels With Rician Fading

A Gaussian multiple-antenna wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver equipped with a single antenna, and an eavesdropper equipped with multiple antennas. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, assuming that full information on the legitimate channel is available to the transmitter, but only statistical information on the eavesdropper channel is known. More specifically, we investigate the case of MIMO Rician fading for the eavesdropper channel. We show that the optimal input covariance has rank one, which allows us to reduce the original optimization problem to a smooth one variable optimization problem. We propose a Newton-type method for a local maximizer, and Piyavskii's algorithm for the global maximizer. Numerical results are presented to illustrate the proposed algorithms.