On the Degrees-of-Freedom of the K-User Distributed Broadcast Channel

We study the Degrees-of-Freedom (DoF) in a wireless setting in which K Transmitters (TXs) aim at jointly serving K users. The performance is studied when the TXs are faced with a distributed Channel State Information (CSI) configuration in which each TX has access to its own multi-user imperfect channel estimate based on which it designs its transmit coefficients. The channel estimates are not only imperfectly acquired but they are also imperfectly shared between the TXs. Our first contribution consists of computing a genie-aided upper bound for the DoF of that setting. Our main contribution is then to develop a new robust transmission scheme that leverages the different qualities of CSI available at the TXs to improve the achieved DoF. We show the surprising result that there is a CSI regime, coined the Weak-CSIT regime, in which the genie-aided upper bound is achieved by the proposed transmission scheme. Interestingly, the optimal DoF in the Weak-CSIT regime only depends on the CSI quality at the best informed TX and not on the CSI quality at all other TXs.