Cognitive Radio (CR) is an attractive technology to alleviate spectrum scarcity in wireless communications. It allows secondary users (SUs) to opportunistically access the licensed spectrum of primary users (PUs) so long as these users' communications are protected. Therefore, protection of the PUs is central to the adoption of this technology. In this paper, we consider an SU that must protect multiple non-interfering PUs simultaneously. These PUs may be heterogeneous in terms of their activity statistics and protection requirements. Assuming exponentially distributed idle times, we determine the limits on successful SU transmission time in such cases, and demonstrate the impact of these results on the channel selection problem. We also derive a time-threshold optimal policy for PUs with general idle time distributions and determine the conditions necessary for this policy to hold. We then discuss the implications of our results on related issues, in particular the information that the SU needs to determine transmission policies satisfy PU constraints.
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