MISO Broadcast Channel with Hybrid CSIT: Beyond Two Users

TL;DR

This paper characterizes the degrees-of-freedom region for the 3-user MISO broadcast channel with heterogeneous CSIT, introducing a novel interference bound and extending results to the general k-user case.

Contribution

It provides a complete DoF region characterization for all CSIT configurations in the 3-user case using linear strategies, and extends bounds to the k-user scenario.

Findings

Sum-DoF optimality of existing schemes under linear encoding.

Development of the Interference Decomposition Bound.

Approximate characterization of linear sum-DoF within 0.5 gap for general k-user case.

Abstract

We study the impact of heterogeneity of channel-state-information available at the transmitters (CSIT) on the capacity of broadcast channels with a multiple-antenna transmitter and $k$ single-antenna receivers (MISO BC). In particular, we consider the $k$-user MISO BC, where the CSIT with respect to each receiver can be either instantaneous/perfect, delayed, or not available; and we study the impact of this heterogeneity of CSIT on the degrees-of-freedom (DoF) of such network. We first focus on the $3$-user MISO BC; and we completely characterize the DoF region for all possible heterogeneous CSIT configurations, assuming linear encoding strategies at the transmitters. The result shows that the state-of-the-art achievable schemes in the literature are indeed sum-DoF optimal, when restricted to linear encoding schemes. To prove the result, we develop a novel bound, called Interference Decomposition Bound, which provides a lower bound on the interference dimension at a receiver which supplies delayed CSIT based on the average dimension of constituents of that interference, thereby decomposing the interference into its individual components. Furthermore, we extend our outer bound on the DoF region to the general $k$-user MISO BC, and demonstrate that it leads to an approximate characterization of linear sum-DoF to within an additive gap of $0.5$ for a broad range of CSIT configurations. Moreover, for the special case where only one receiver supplies delayed CSIT, we completely characterize the linear sum-DoF.