A Gaussian multiple-input multiple-output wiretap channel in which the eavesdropper and legitimate receiver are equipped with arbitrary numbers of antennas and the transmitter has two antennas is studied in this paper. It is shown that the secrecy capacity of this channel can be achieved by linear precoding. The optimal precoding and power allocation schemes achieving the secrecy capacity are developed subsequently, and the secrecy capacity is compared with the generalized singular value decomposition (GSVD)-based precoding, which is the best previously proposed precoding for this problem. Numerical results show that substantial gain can be obtained in secrecy rate between the proposed and GSVD-based precodings.
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