6. Conclusion
In this paper we have developed mathematical models for the study of sensing strategies in Cognitive Radio networks. The models developed here are largely general. The channel busy and idle periods are described as alternating Markov phase renewal process, which allows the busy and idle times durations to assume a wide variety of distributions and also captures broad correlation aspects of the two intervals. As regards the secondary user (SU) behavior, the duration of transmissions, sensing periods and the intervals between consecutive sensing periods (sleeping) are modeled by general phase type distributions. Furthermore, imperfect sensing has been considered by modeling two types of misdetections and false alarms, which also allowed us to cover a wide range of situations. Several key performance measures in Cognitive Radio network have been obtained from the analysis of our model. Most notably, we derived the distribution of the length of an effective white space, the distributions of the waiting times until the SU transmits a given amount of data in total (through several transmissions separated by interruptions, or uninterruptedly), and the SU goodput when an interrupted SU transmission has to be started over from the beginning. We also obtained expressions for the probabilities of global misdetection and global false alarm, which have a more general meaning that the probabilities of misdetection and false alarm referred to measurements taken during a single time slot.
