On Secure Degrees of Freedom for K-User MISO Broadcast Channel With Alternating CSIT

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 alternating CSIT. Alternating CSIT 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 <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</inf> = (2K − 1)/2. Interestingly, this SDoF <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sum</inf> 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. The proof for the case K = 3 is discussed in detail.