Markov chain existence and Hidden Markov models in spectrum sensing

The primary function of a cognitive radio is to detect idle frequencies or sub-bands, not used by the primary users (PUs), and allocate these frequencies to secondary users. The state of the sub-band at any time point is either free (unoccupied by a PU) or busy (occupied by a PU). The states of a sub-band are monitored over L consecutive time periods, where each period is of a given time interval. Existing research assume the presence of a Markov chain for sub-band utilization by PUs over time, but this assumption has not been validated. Therefore, in this paper we validate existence of a Markov chain for sub-band utilization using real-time measurements collected in the paging band (928-948 MHz). Furthermore, since the detection of idle sub-bands by a cognitive radio is prone to errors, we probabilistically model the errors and then formulate a spectrum sensing paradigm as a hidden Markov model that predicts the true states of a sub-band. The accuracy of our proposed method in predicting the true states of the sub-band is substantiated using extensive simulations.