Secure Degrees of Freedom Region of the Two-User MISO Broadcast Channel with Alternating CSIT

TL;DR

This paper characterizes the secure degrees of freedom region for a two-user MISO broadcast channel with confidential messages under varying types of channel state information, revealing how different CSIT states affect secrecy capacity.

Contribution

It establishes the s.d.o.f. region for the MISO BCCM with alternating CSIT, introducing novel coding schemes and converse proofs that account for security constraints and CSIT variability.

Findings

Derived the s.d.o.f. region under symmetric CSIT state probabilities.

Developed new achievable schemes leveraging inter-state coding for secrecy.

Provided converse proofs using local statistical equivalence and channel enhancement techniques.

Abstract

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 $I_{i}$, $i=1,2$ where $I_{1}, I_{2}\in \{\mathsf{P}, \mathsf{D}, \mathsf{N}\}$, and the forms $\mathsf{P}$, $\mathsf{D}$ and $\mathsf{N}$ correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between $9$ possible states corresponding to all possible values of $I_{1}I_{2}$, with each state occurring for $\lambda_{I_{1}I_{2}}$ fraction of the total duration. 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 $\lambda_{I_{1} I_{2}}=\lambda_{I_{2}I_{1}}$. The main technical contributions include developing a) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints which also highlight the synergistic benefits of inter-state coding for secrecy, b) new converse proofs via local statistical equivalence and channel enhancement; and c) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f.