How Often and How Long Should a Cognitive Radio Sense the Spectrum?

This paper presents a Bayesian framework and a pricing structure for a secondary wireless user that opportunistically uses a RF channel licensed to a network of N primary users. The secondary user operates in a time-slotted fashion, where each time slot consists of observing the channel for D seconds followed by possibly using it for W seconds depending on the decision the user makes after observing the channel. The paper assumes the secondary user observes the on-off Markov process modeling the primary user activity corrupted by additive white Gaussian noise, and it employs a decision rule that is a time-averager followed by a threshold device. The pricing structure includes rewards for the secondary user when it uses the channel without interfering with the primary users and penalties when it does so and it interferes. The paper derives a formula for the average per unit time net profit of the secondary user. Numerical results are presented that show the behavior of the maximum profit of the secondary user, its throughput, and the resulting level of interference to the primary users as functions of various network parameters.