  In this work, we consider a wireless network with K cooperating transmitters
(TXs) serving jointly K receivers (RXs). Due to the practical limitations of
the backhaul network, it is relevant to consider a setting where each TX
receives its own imperfect estimate of the multi-user channel state, denoted as
the distributed channel state information (CSI) setting. We focus in this work
on a particular distributed CSI configuration called hierarchical CSI
configuration in which the TXs can be ordered by increasing level of CSI. This
scenario is particularly relevant for future networks with heterogeneous
backhaul where the TXs connected with a weak backhaul link will receive only a
coarse estimate while the TXs with a stronger backhaul will have a more
accurate CSI. In that scenario, we formulate the optimal precoding as a team
decision problem. Solving optimally this problem is extremely challenging such
that we propose a heuristic approach allowing to obtain a simple, yet efficient
and practical, precoding algorithm. The proposed precoding algorithm exploits
the hierarchical structure of the CSI to make the transmission more robust to
the imperfect CSI knowledge at the TXs.
