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A Gaussian multiple-input multiple-output wiretap channel in which theeavesdropper and legitimate receiver are equipped with arbitrary numbers ofantennas and the transmitter has two antennas is studied in this paper. Underan average power constraint, the optimal input covariance to obtain the secrecycapacity of this channel is unknown, in general. In this paper, the inputcovariance matrix required to achieve the capacity is determined. It is shownthat the secrecy capacity of this channel can be achieved by linear precoding.The optimal precoding and power allocation schemes that maximize the achievablesecrecy rate, and thus achieve the capacity, are developed subsequently. Thesecrecy capacity is then compared with the achievable secrecy rate ofgeneralized singular value decomposition (GSVD)-based precoding, which is thebest previously proposed technique for this problem. Numerical resultsdemonstrate that substantial gain can be obtained in secrecy rate between theproposed and GSVD-based precodings.

Optimal Beamforming for Gaussian MIMO Wiretap Channels with Two Transmit Antennas