Discrete time analysis of cognitive radio networks with imperfect sensing and saturated source of secondary users

Sensing is one of the most challenging issues in cognitive radio networks. Selection of sensing parameters raises several tradeoffs between spectral efficiency, energy efficiency and interference caused to primary users (PUs). In this paper we provide representative mathematical models that can be used to analyze sensing strategies under a wide range of conditions. The activity of PUs in a licensed channel is modeled as a sequence of busy and idle periods, which is represented as an alternating Markov phase renewal process. The representation of the secondary users (SUs) behavior is also largely general: the duration of transmissions, sensing periods and the intervals between consecutive sensing periods are modeled by phase type distributions, which constitute a very versatile class of distributions. Expressions for several key performance measures in cognitive radio networks are obtained from the analysis of the model. Most notably, we derive 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, through several transmission epochs uninterruptedly; and the goodput when an interrupted SU transmission has to be restarted from the beginning due to the presence of a PU.