  This paper analyzes the performance of the primary and secondary users (SUs)
in an arbitrarily-shaped underlay cognitive network. In order to meet the
interference threshold requirement for a primary receiver (PU-Rx) at an
arbitrary location, we consider different SU activity protocols which limit the
number of active SUs. We propose a framework, based on the moment generating
function (MGF) of the interference due to a random SU, to analytically compute
the outage probability in the primary network, as well as the average number of
active SUs in the secondary network. We also propose a cooperation-based SU
activity protocol in the underlay cognitive network which includes the existing
threshold-based protocol as a special case. We study the average number of
active SUs for the different SU activity protocols, subject to a given outage
probability constraint at the PU and we employ it as an analytical approach to
compare the effect of different SU activity protocols on the performance of the
primary and secondary networks.
