Diversity-Multiplexing Tradeoff for the Multiple-Antenna Wire-tap Channel

In this paper the fading multiple antenna (MIMO) wire-tap channel is investigated under short term power constraints. The secret diversity gain and the secret multiplexing gain are defined. Using these definitions, the secret diversity-multiplexing tradeoff (DMT) is calculated analytically for no transmitter side channel state information (CSI) and for full CSI. When there is no CSI at the transmitter, under the assumption of Gaussian codebooks, it is shown that the eavesdropper steals both transmitter and receiver antennas, and the secret DMT depends on the remaining degrees of freedom. When CSI is available at the transmitter (CSIT), the eavesdropper steals only transmitter antennas. This dependence on the availability of CSI is unlike the DMT results without secrecy constraints, where the DMT remains the same for no CSI and full CSI at the transmitter under short term power constraints. A zero-forcing type scheme is shown to achieve the secret DMT when CSIT is available.