Power control in spectrum overlay networks: How to cross a multi-lane highway

We consider power control in spectrum overlay networks (also referred to as opportunistic spectrum access) where secondary users identify and exploit instantaneous and local spectrum opportunities without causing unacceptable interference to primary users. We quantify the impact of the transmission power of secondary users on the occurrence of spectrum opportunities and the reliability of opportunity detection. We demonstrate that the probability of spectrum opportunity decreases exponentially with the transmission power and reliable opportunity detection is achieved in the two extreme regimes of the ratio between the transmission power of secondary users and that of primary users. Such analytical characterizations allow us to study power control for optimal transport throughput under constraints on the interference to primary users.