On Sum Secure Degrees of Freedom for K-User MISO Broadcast Channel With Alternating CSIT (2011.00889v2)

Abstract: In this paper, the sum secure degrees of freedom (SDoF) of the $K$-user Multiple Input/Single Output (MISO) Broadcast Channel with Confidential Messages (BCCM) and alternating Channel State Information at the Transmitter (CSIT) is investigated. In the MISO BCCM, a $K$-antenna transmitter (TX) communicates toward $K$ single-antenna receivers (RXs), so that message for RX $k$ is kept secret from RX $j$ with $j<k$. For this model, we consider the scenario in which the CSI of the RXs from $2$ to $K$ is instantaneously known at the transmitter while CSI of RX $1$ is known at the transmitter (i) instantaneously for half of the time and (ii) with a unit delay for the remainder of the time. We refer to this CSIT availability as \emph{alternating} CSIT. Alternating CIST has been shown to provide synergistic gains in terms of SDoF and is thus of a viable strategy to ensure secure communication by simply relying on the CSI feedback strategy. Our main contribution is the characterization of sum SDoF for this model as $SDoF_{\rm sum}= (2K-1)/2$. Interestingly, this $SDoF_{\rm sum}$ is attained by a rather simple achievability in which the TX uses artificial noise to prevent the decoding of the message of the unintended receivers at RX $1$. For simplicity first, the proof for the case $K=3$ is discussed in detail and after that, we have presented the results for any number of RXs.