DoF Region of the Decentralized MIMO Broadcast Channel -- How many informed antennas do we need?

Abstract: In this work, we study the impact of imperfect sharing of the Channel State Information (CSI) available at the transmitters on a Network MIMO setting in which a set of $M$ transmit antennas, possibly not co-located, jointly serve two multi-antenna users endowed with $N_1$ and $N_2$ antennas, respectively. We consider the case where only a subset of $k$ transmit antennas have access to perfect CSI, whereas the other $M-k$ transmit antennas have only access to finite precision CSI. The analysis of this configuration aims to answer the question of how much an extra informed antenna can help. We model this scenario as a Decentralized MIMO Broadcast Channel (BC) and characterize the Degrees-of-Freedom (DoF) region, showing that only $k=\max(N_1,N_2)$ antennas with perfect CSI are needed to achieve the DoF of the conventional BC with ubiquitous perfect CSI. Furthermore, we identify the increase of DoF obtained by providing CSI to an extra transmit antenna.