On beamforming solution for secrecy capacity of MIMO wiretap channels

A Gaussian multiple-input multiple-output (MIMO) wiretap channel model is considered, where there exists a transmitter, a legitimate receiver and an eavesdropper each equipped with multiple antennas. The problem of finding the optimal input covariance matrix that achieves secrecy capacity subject to a power constraint is studied. In particular, it is shown that when the difference between the Grams of legitimate and eavesdropper channel matrices has all negative eigenvalues except one positive eigenvalue, beamforming is optimal. For that case, the secrecy capacity is obtained.