  We consider a heterogeneous network (HetNet) of base stations (BSs) connected
via a backhaul network of routers and wired/wireless links with limited
capacity. The optimal provision of such networks requires proper resource
allocation across the radio access links in conjunction with appropriate
traffic engineering within the backhaul network. In this paper we propose an
efficient algorithm for joint resource allocation across the wireless links and
the flow control within the backhaul network. The proposed algorithm, which
maximizes the minimum rate among all the users and/or flows, is based on a
decomposition approach that leverages both the Alternating Direction Method of
Multipliers (ADMM) and the weighted-MMSE (WMMSE) algorithm. We show that this
algorithm is easily parallelizable and converges globally to a stationary
solution of the joint optimization problem. The proposed algorithm can also be
extended to deal with per-flow quality of service constraint, or to networks
with multi-antenna nodes.
