How to reduce complexity of the practical automatic modulation classification systems is a very active research area. Moreover, keeping the classification accuracy to a near optimal level is an added challenge. Recently, three new classifiers have been proposed with reduced complexity, mainly: linear support vector machine classifier, approximate maximum likelihood classifier, and backpropogation neural networks classifier. However, these methods include the sorting process of the features $z$ to form an ordered vector $\vec {z}$ employing $K$ log $(K)$ comparison operations. Here, we propose a ${k}$ -sparse autoencoder-based classifer, with unsorted input data features and called it unsorted deep neural network (UDNN). Thus, we strive to omit the $K$ log $(K)$ comparison operations. The results obtained using the UDNN classifier show improved performance when compared with the above three methods. Moreover, using ${k}$ highest hidden units to reconstruct input data further reduces the overall complexity of the AMC system.