Optimal Beamforming for Gaussian MIMO Wiretap Channels with Two Transmit\n Antennas

A Gaussian multiple-input multiple-output wiretap channel in which the\neavesdropper and legitimate receiver are equipped with arbitrary numbers of\nantennas and the transmitter has two antennas is studied in this paper. Under\nan average power constraint, the optimal input covariance to obtain the secrecy\ncapacity of this channel is unknown, in general. In this paper, the input\ncovariance matrix required to achieve the capacity is determined. It is shown\nthat the secrecy capacity of this channel can be achieved by linear precoding.\nThe optimal precoding and power allocation schemes that maximize the achievable\nsecrecy rate, and thus achieve the capacity, are developed subsequently. The\nsecrecy capacity is then compared with the achievable secrecy rate of\ngeneralized singular value decomposition (GSVD)-based precoding, which is the\nbest previously proposed technique for this problem. Numerical results\ndemonstrate that substantial gain can be obtained in secrecy rate between the\nproposed and GSVD-based precodings.\n