  In this paper, we present a framework for distributively optimizing the
transmission strategies of secondary users in an ad hoc cognitive radio
network. In particular, the proposed approach allows secondary users to set
their transmit powers and channel access probabilities such that, on average,
the quality of service of both the primary and secondary networks are
satisfied. The system under consideration assumes several primary and secondary
transceiver pairs and assumes no cooperation or information exchange between
neither primary and secondary users nor among secondary users. The outage
probability, and consequently the connection probability, is derived for the
system and is used in defining a new performance metric in the optimization
problem using tools from stochastic geometry. We refer to this metric as the
spatial density of successful transmission. We corroborate our derivations
through numerical evaluations. We further demonstrate that even in the absence
of any form of cooperation, an acceptable quality of service can be attained in
the cognitive radio environment.
