  This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap
channel model, where there exists a transmitter, a legitimate receiver and an
eavesdropper, each equipped with multiple antennas. Perfect secrecy is achieved
when the transmitter and the legitimate receiver can communicate at some
positive rate, while ensuring that the eavesdropper gets zero bits of
information. In this paper, the perfect secrecy capacity of the multiple
antenna MIMO wiretap channel is found for aribtrary numbers of antennas under
the assumption that the transmitter performs beamforming based on the
generalized singular value decomposition (GSVD). More precisely, the optimal
allocation of power for the GSVD-based precoder that achieves the secrecy
capacity is derived. This solution is shown to have several advantages over
prior work that considered secrecy capacity for the general MIMO Gaussian
wiretap channel under a high SNR assumption. Numerical results are presented to
illustrate the proposed theoretical findings.
