Degrees-of-Freedom Regions for $K$-User MISO Time-Correlated Broadcast Channel

In this paper, we study the achievable degrees-of-freedom (DoF) regions of the $K$-user multiple-input-single-output (MISO) time correlated broadcast channel (BC). The time correlation induces knowledge of the current channel state information at transmitter (CSIT) with an estimation error $P^{-α}$, where $P$ is the signal-to-noise ratio (SNR). We consider the following two scenarios: $(i)$ $K$-user with $K$-antenna base station (BS) and $(ii)$ $3$-user with $2$-antenna BS. In case of symmetric DoF tuples, where all the users obtain the same DoF, we derive the total DoF equal to $\frac{K(1-α)}{1+\frac{1}{2}+\cdots+\frac{1}{K}}+Kα$ for the first scenario and $\frac{3+α}{2}$ for the second one. In particular, we provide the achievability schemes for these two DoF tuples. Nevertheless, we also consider the asymmetric case where one of the users is guaranteed {\it one} DoF, and provide the achievability scheme. Notably, the consistency of the proposed DoF regions with an already published outer bound , as well as with the Maddah-Ali-Tse (MAT), which assumes only perfect delayed CSIT, and the ZF beamforming schemes (perfect current CSIT) consents to the optimality of the proposed achievability schemes.

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