Automatic modulation classification plays a key role in cognitive radio for recognizing the modulation scheme. In this paper, we propose a new classifier based on sparse signal decomposition using an overcomplete composite dictionary (constructed using cyclostationary coefficients) for the classification of modulation format of primary user or to identify noise. The basic principle of the classifier is to classify the received signal modulation format based on reconstructed sparse coefficients after solving l1 norm minimization using the overcomplete dictionary. Then, relative energies of reconstructed sparse coefficients are compared for recognition of modulation format of the received signal. It is a promising candidate for the cognitive radio due to its robust classification ability. The performance of the proposed classifier is compared with other well known classifiers available in literature. Results show the superiority of the proposed classifier over other classifiers. © 2017, Springer Science+Business Media New York.