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Dirty Paper Coding versus Linear GSVD-Based Precoding in MIMO Broadcast Channel with Confidential Messages

This paper studies linear beamforming based on the generalized singular value decomposition (GSVD) for the two-receiver multiple-input multiple-output (MIMO) Gaussian broadcast channel with confidential messages. The transmitter has two independent messages, each of which is intended for one of the receivers but needs to be kept as secret as possible from the other. Recently, it has been proved that, under an input power-covariance constraint, the secret dirty paper coding (S-DPC) scheme is optimal, but under the average power constraint, there is not a computable secrecy capacity expression for the general MIMO case. In fact, for this case, the secrecy capacity region must in general be found through an exhaustive search over the set of all possible matrix power constraints. Clearly, this exhaustive search, as well as the complexity of dirty-paper encoding and decoding, motivates us to consider low complexity linear beamforming technique whose performance is close to the optimal S-DPC scheme. In this paper, we propose a GSVD-based beamforming scheme for the general MIMO broadcast channel with confidential messages. Moreover, an optimal power allocation is obtained to maximize the sum-secrecy rates for the GSVD-based beamforming technique, under the average power constraint. Numerical results are presented to illustrate that the secrecy rate region of the linear precoding approach is nearly identical to that of the optimal S-DPC scheme.