  Spectrum sharing between wireless networks improves the efficiency of
spectrum usage, and thereby alleviates spectrum scarcity due to growing demands
for wireless broadband access. To improve the usual underutilization of the
cellular uplink spectrum, this paper studies spectrum sharing between a
cellular uplink and a mobile ad hoc networks. These networks access either all
frequency sub-channels or their disjoint sub-sets, called spectrum underlay and
spectrum overlay, respectively. Given these spectrum sharing methods, the
capacity trade-off between the coexisting networks is analyzed based on the
transmission capacity of a network with Poisson distributed transmitters. This
metric is defined as the maximum density of transmitters subject to an outage
constraint for a given signal-to-interference ratio (SIR). Using tools from
stochastic geometry, the transmission-capacity trade-off between the coexisting
networks is analyzed, where both spectrum overlay and underlay as well as
successive interference cancelation (SIC) are considered. In particular, for
small target outage probability, the transmission capacities of the coexisting
networks are proved to satisfy a linear equation, whose coefficients depend on
the spectrum sharing method and whether SIC is applied. This linear equation
shows that spectrum overlay is more efficient than spectrum underlay.
Furthermore, this result also provides insight into the effects of different
network parameters on transmission capacities, including link diversity gains,
transmission distances, and the base station density. In particular, SIC is
shown to increase transmission capacities of both coexisting networks by a
linear factor, which depends on the interference-power threshold for qualifying
canceled interferers.
