On the Synergistic Benefits of Alternating CSIT for the MISO BC

TL;DR

This paper characterizes the degrees of freedom (DoF) region for a two-user MISO broadcast channel with alternating channel state information at the transmitter (CSIT), revealing that the DoF depends only on marginal CSIT probabilities and demonstrating the benefits of alternating CSIT.

Contribution

It provides a complete characterization of the DoF region under symmetric alternating CSIT states, showing dependence only on marginal probabilities and highlighting synergistic benefits.

Findings

DoF region depends solely on marginal CSIT probabilities

The DoF region with all 9 CSIT states equals that with only 3 states under same marginals

Alternating CSIT offers significant synergistic benefits

Abstract

The degrees of freedom (DoF) of the two-user multiple-input single-output (MISO) broadcast channel (BC) are studied under the assumption that the form, I_i, i=1,2, of the channel state information at the transmitter (CSIT) for each user's channel can be either perfect (P), delayed (D) or not available (N), i.e., I_1 and I_2 can take values of either P, D or N, and therefore the overall CSIT can alternate between the 9 resulting states, each state denoted as I_1I_2. The fraction of time associated with CSIT state I_1I_2 is denoted by the parameter \lambda_{I_1I_2} and it is assumed throughout that \lambda_{I_1I_2}=\lambda_{I_2I_1}, i.e., \lambda_{PN}=\lambda_{NP}, \lambda_{PD}=\lambda_{DP}, \lambda_{DN}=\lambda_{ND}. Under this assumption of symmetry, the main contribution of this paper is a complete characterization of the DoF region of the two user MISO BC with alternating CSIT. Surprisingly, the DoF region is found to depend only on the marginal probabilities (\lambda_P, \lambda_D,\lambda_N)=(\sum_{I_2}\lambda_{PI_2},\sum_{I_2}\lambda_{DI_2}, \sum_{I_2}\lambda_{NI_2}), I_2\in {P,D,N}, which represent the fraction of time that any given user (e.g., user 1) is associated with perfect, delayed, or no CSIT, respectively. As a consequence, the DoF region with all 9 CSIT states, \mathcal{D}(\lambda_{I_1I_2}:I_1,I_2\in{P,D,N}), is the same as the DoF region with only 3 CSIT states \mathcal{D}(\lambda_{PP}, \lambda_{DD}, \lambda_{NN}), under the same marginal distribution of CSIT states, i.e., (\lambda_{PP}, \lambda_{DD},\lambda_{NN})=(\lambda_P,\lambda_D,\lambda_N). The results highlight the synergistic benefits of alternating CSIT and the tradeoffs between various forms of CSIT for any given DoF value.