  We consider a cooperative Gaussian interference channel in which each
receiver must decode its intended message locally, with the help of cooperation
either at the receivers side or at the transmitter side. In the case of
receiver cooperation, the receivers can process and share information through
limited capacity backhaul links. In contrast to various previously considered
distributed antenna architectures, where processing is utterly performed in a
centralized fashion, the model considered in this paper aims to capture the
essence of decentralized processing, allowing for a more general class of
"interactive" interference management strategies. Focusing on the three-user
case, we characterize the fundamental tradeoff between the achievable
communication rates and the corresponding backhaul cooperation rate, in terms
of degrees of freedom (DoF). Surprisingly, we show that the optimum
communication-cooperation tradeoff per user remains the same when we move from
two-user to three-user interference channels. In the absence of cooperation,
this is due to interference alignment, which keeps the fraction of
communication dimensions wasted for interference unchanged. When backhaul
cooperation is available, we develop a new idea that we call cooperation
alignment, which guarantees that the average (per user) backhaul load remains
the same as we increase the number of users. In the case of transmitter
cooperation, the transmitters can form their jointly precoded signals through
an interactive protocol over the backhaul. In this case, we show that the
optimal (per user) tradeoff between the achievable communication rates and the
corresponding backhaul cooperation rate in the three-user case is the same as
for receiver cooperation.
