Power scaling for cognitive radio

In this paper we explore the idea of using cognitive radios to reuse locally unused spectrum for their own transmissions. We impose the constraint that they cannot general e unacceptable levels of interference to licensed systems on the same frequency. Using received SNR as a proxy for distance, we prove that a cognitive radio can vary its transmit power while maintaining a guarantee of service to primary users. We consider the aggregate interference caused by multiple cognitive radios and show that aggregation causes a change in the effective decay rate of the interference. We examine the effects of heterogeneous propagation path loss functions and justify the feasibility of multiple secondary users with dynamic transmit powers. Finally, we prove the fundamental constraint on a cognitive radio's transmit power is the minimum SNR it can detect and explore the effect of this power cap.