Secure communication in K-user multi-antenna broadcast channel with state feedback

In this paper, we consider the secure communication in a K-user multi-antenna broadcast channel (BC) with state feedback. We characterize the optimal secure degrees of freedom (SDoF) region of multiple-input single-output (MISO) channel. The SDoF region is achievable by a secret key based linear scheme, which generates analog secret keys by sending artificial noise and then performs space-time alignment scheme secured by these secret keys. The optimality is proved by deriving a new outer bound on the capacity region in a systematic way. Interestingly, the proposed outer bounding technique also applies to the erasure broadcast channel and provides a simpler proof as compared to the existing one. Finally, an explicit connection between the multi-antenna BC and the erasure BC is revealed. We show that, with a large number of users, secrecy cannot be guaranteed in the erasure BC, while it comes almost 'for free' in the multi-antenna BC when the number of transmit antennas grows accordingly.