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arXiv:2011.00889

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

Leyla Sadighi, Sadaf Salehkalaibar, Stefano Rini

Published Nov 2, 2020• 0 citations
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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

DOI
10.48550/arxiv.2011.00889

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We study a three-user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM). We have three messages where each of them is intended to the corresponding receiver. We impose confidentiality constraints for two of the messages at the receiving terminals. Half of the time, the channel state information (CSI) of all receivers are known perfectly at the transmitter. At the other half, the CSI of one of the receivers is available with some delay. The main contribution of this paper is to find the sum secure degrees of freedom (SDoF) of the proposed channel. We utilize the alternating CSIT scheme to design the precoding matrices. The proof of the converse is challenging for this model. The idea of the converse proof is to adapt the well known statistical equivalent property (SEP) lemma for our model.
The two user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied, in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1, I2∈ {P, D, N}, and the forms P, D, and N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between nine possible states corresponding to all possible values of I1I2, with each state occurring for λI1I2fraction of the total duration. We assume that perfect and instantaneous CSI is available at the all receivers. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where λI1I2= λI2I1. The main technical contributions include developing 1) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints, which also highlight the synergistic benefits of inter-state coding for secrecy; 2) new converse proofs via local statistical equivalence and channel enhancement; and 3) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f.
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We consider the two-user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM), in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form P, D and N, corresponding to perfect and instantaneous, completely delayed, and no CSIT, respectively. We focus on the cases with heterogeneous CSIT from the users, that is, the states PD, PN and DN. The main contribution of this paper is to establish the exact secure degrees of freedom (s.d.o.f.) regions of the MISO BCCM in all of these three heterogeneous states. The results highlight the impact of availability of CSIT on the s.d.o.f. region.