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The two-user multiple-input multiple-output (MIMO) Gaussian broadcast channel(BC) with common, private and confidential messages is considered. Thetransmitter sends a common message to both users, a confidential message toUser 1 and a private (non-confidential) message to User 2. The secrecy-capacityregion is characterized by showing that certain inner and outer bounds coincideand that the boundary points are achieved by Gaussian inputs, which enables thedevelopment of a tight converse. The proof relies on factorization of upperconcave envelopes and a variant of dirty-paper coding (DPC). It is shown thatthe entire region is exhausted by using DPC to cancel out the signal of thenon-confidential message at Receiver 1, thus making DPC against the signal ofthe confidential message unnecessary. A numerical example illustrates thesecrecy-capacity results.

MIMO Gaussian Broadcast Channels with Common, Private and Confidential Messages