Incremental Expectation Maximization for Estimating Dynamic Primary User Activity in Cognitive Radio

In this paper we consider a cognitive radio (CR) scenario with a dynamic primary user (PU) that switches between active and idle transmission modes at random time instances, and a secondary user (SU) that is unaware of the PU activity and employs an energy detector to seek transmission opportunities. A two-state Markov chain is used to model the dynamic activity of the PU and establish a chi-squared mixture model for the energy detector output that allows accurate calculation of the probabilities of detection (Pd) and false alarm (Pf) for the SU in the context of the dynamic PU activity. The chi-squared mixture parameters are estimated from a set of observations using an incremental expectation maximization (EM) algorithm. The proposed approach is illustrated with numerical results obtained from simulations showing receiver operating characteristic (ROC) curves corresponding to the SU energy detector with dynamic PU in various scenarios.