  Heterogeneous base stations (e.g. picocells, microcells, femtocells and
distributed antennas) will become increasingly essential for cellular network
capacity and coverage. Up until now, little basic research has been done on the
fundamentals of managing so much infrastructure -- much of it unplanned --
together with the carefully planned macro-cellular network. Inter-cell
coordination is in principle an effective way of ensuring different
infrastructure components behave in a way that increases, rather than
decreases, the key quality of service (QoS) metrics. The success of such
coordination depends heavily on how the overhead is shared, and the rate and
delay of the overhead sharing. We develop a novel framework to quantify
overhead signaling for inter-cell coordination, which is usually ignored in
traditional 1-tier networks, and assumes even more importance in multi-tier
heterogeneous cellular networks (HCNs). We derive the overhead quality contour
for general K-tier HCNs -- the achievable set of overhead packet rate, size,
delay and outage probability -- in closed-form expressions or computable
integrals under general assumptions on overhead arrivals and different overhead
signaling methods (backhaul and/or wireless). The overhead quality contour is
further simplified for two widely used models of overhead arrivals: Poisson and
deterministic arrival process. This framework can be used in the design and
evaluation of any inter-cell coordination scheme. It also provides design
insights on backhaul and wireless overhead channels to handle specific overhead
signaling requirements.
