  We study the transmission capacities of two coexisting wireless networks (a
primary network vs. a secondary network) that operate in the same geographic
region and share the same spectrum. We define transmission capacity as the
product among the density of transmissions, the transmission rate, and the
successful transmission probability (1 minus the outage probability). The
primary (PR) network has a higher priority to access the spectrum without
particular considerations for the secondary (SR) network, where the SR network
limits its interference to the PR network by carefully controlling the density
of its transmitters. Assuming that the nodes are distributed according to
Poisson point processes and the two networks use different transmission ranges,
we quantify the transmission capacities for both of these two networks and
discuss their tradeoff based on asymptotic analyses. Our results show that if
the PR network permits a small increase of its outage probability, the sum
transmission capacity of the two networks (i.e., the overall spectrum
efficiency per unit area) will be boosted significantly over that of a single
network.
