  This paper studies the opportunistic spectrum access (OSA) of the secondary
users in a large-scale overlay cognitive radio (CR) network. Two
threshold-based OSA schemes, namely the primary receiver assisted (PRA)
protocol and the primary transmitter assisted (PTA) protocol, are investigated.
Under the PRA/PTA protocol, a secondary transmitter (ST) is allowed to access
the spectrum only when the maximum signal power of the received beacons/pilots
sent from the active primary receivers/transmitters (PRs/PTs) is lower than a
certain threshold. To measure the resulting transmission opportunity for the
secondary users by the proposed OSA protocols, the concept of spatial
opportunity, which is defined as the probability that an arbitrary location in
the primary network is detected as a spatial spectrum hole, is introduced and
then evaluated by applying tools from stochastic geometry. Based on spatial
opportunity, the coverage (non-outage transmission) performance in the overlay
CR network is analyzed. With the obtained results of spatial opportunity and
coverage probability, we finally characterize the spatial throughput, which is
defined as the average spatial density of successful transmissions in the
primary/secondary network, under the PRA and PTA protocols, respectively.
