  In this paper, a novel framework is proposed for optimizing the operation and
performance of a large-scale, multi-hop millimeter wave (mmW) backhaul within a
wireless small cell network (SCN) that encompasses multiple mobile network
operators (MNOs). The proposed framework enables the small base stations (SBSs)
to jointly decide on forming the multi-hop, mmW links over backhaul
infrastructure that belongs to multiple, independent MNOs, while properly
allocating resources across those links. In this regard, the problem is
addressed using a novel framework based on matching theory that is composed to
two, highly inter-related stages: a multi-hop network formation stage and a
resource management stage. One unique feature of this framework is that it
jointly accounts for both wireless channel characteristics and economic factors
during both network formation and resource management. The multi-hop network
formation stage is formulated as a one-to-many matching game which is solved
using a novel algorithm, that builds on the so-called deferred acceptance
algorithm and is shown to yield a stable and Pareto optimal multi-hop mmW
backhaul network. Then, a one-to-many matching game is formulated to enable
proper resource allocation across the formed multi-hop network. This game is
then shown to exhibit peer effects and, as such, a novel algorithm is developed
to find a stable and optimal resource management solution that can properly
cope with these peer effects. Simulation results show that the proposed
framework yields substantial gains, in terms of the average sum rate, reaching
up to 27% and 54%, respectively, compared to a non-cooperative scheme in which
inter-operator sharing is not allowed and a random allocation approach. The
results also show that our framework provides insights on how to manage pricing
and the cost of the cooperative mmW backhaul network for the MNOs.
