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For a cognitive radio (CR) system, we investigate the estimation problem in which a secondary user (SU) estimates the channel parameters such as the sojourn times on the active and the inactive states of the primary user (PU) as well as the PU signal strength on the basis of the sequence of the sensing results. By modeling the CR system as a hidden Markov model (HMM), the channel parameters are estimated by the standard expectation-maximization (EM) algorithm. We focus on mathematically analyzing the condition under which the EM algorithm can find the true channel parameters. For this, we apply the theory of the equivalence and the identifiability to the proposed HMM model for a CR system. Based on the identifiability analysis, we propose a parameter estimation algorithm for our problem by extending the EM algorithm. The numerical results show that the proposed algorithm successfully estimates the true channel parameters as long as the condition for finding the channel parameters is satisfied.