On the Synergistic Benefits of Alternating CSIT for the MISO BC

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.