In this paper, we present a framework for distributively optimizing thetransmission strategies of secondary users in an ad hoc cognitive radionetwork. In particular, the proposed approach allows secondary users to settheir transmit powers and channel access probabilities such that, on average,the quality of service of both the primary and secondary networks aresatisfied. The system under consideration assumes several primary and secondarytransceiver pairs and assumes no cooperation or information exchange betweenneither primary and secondary users nor among secondary users. The outageprobability, and consequently the connection probability, is derived for thesystem and is used in defining a new performance metric in the optimizationproblem using tools from stochastic geometry. We refer to this metric as thespatial density of successful transmission. We corroborate our derivationsthrough numerical evaluations. We further demonstrate that even in the absenceof any form of cooperation, an acceptable quality of service can be attained inthe cognitive radio environment.
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