DoF analysis of the K-user MISO broadcast channel with hybrid CSIT

We consider a K-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user i(i = 1, 2, …, K) may be either instantaneously perfect (P), delayed (D) or not known (N) at the transmitter with probabilities λPⁱ, λDⁱ and λNⁱ, respectively. In this setting, according to the three possible CSIT for each user, knowledge of the joint CSIT of the K users could have at most 3^K states. Although the results by Tandon et al. show that for the symmetric two user MISO BC (i.e., λQⁱ = λQ, ∀i ∈ {1, 2}, Q ∈ {P, D, N}), the Degrees of Freedom (DoF) region depends only on the marginal probabilities, we show that this interesting result does not hold in general when K ≥ 3. In other words, the DoF region is a function of all the joint probabilities. In this paper, given the marginal probabilities of CSIT, we derive an outer bound for the DoF region of the K-user MISO BC. Subsequently, we investigate the achievability of the outer bound in some scenarios. Finally, we show the dependence of the DoF region on the joint probabilities.