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 λ_Pⁱ, λ_Dⁱ and λ_Nⁱ, 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., λ_Qⁱ = λ_Q, ∀_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.