  We consider collocated primary and secondary networks that have simultaneous
access to the same frequency bands. Particularly, we examine three different
levels at which primary and secondary networks may coexist: pure interference,
asymmetric co-existence, and symmetric co-existence. At the asymmetric
co-existence level, the secondary network selectively deactivates its users
based on knowledge of the interference and channel gains, whereas at the
symmetric level, the primary network also schedules its users in the same way.
Our aim is to derive optimal sum-rates (i.e., throughputs)of both networks at
each co-existence level as the number of users grows asymptotically and
evaluate how the sum-rates scale with network size. In order to find the
asymptotic throughput results, we derive a key lemma on extreme order
statistics and a proposition on the sum of lower order statistics. As a
baseline comparison, we calculate the sum-rates for channel sharing via
time-division (TD). We compare the asymptotic secondary sum-rate in TD with
that under simultaneous transmission, while ensuring the primary network
maintains the same throughput in both cases. The results indicate that
simultaneous transmission at both asymmetric and symmetric co-existence levels
can outperform TD. Furthermore, this enhancement is achievable when uplink
activation or deactivation of users is based only on the interference gains to
the opposite network and not on a network's own channel gains.
