Automatic Modulation Classification (AMC), as a crucial technique in modern non-cooperative communication networks, plays a key role in various civil and military applications. However, existing AMC methods based on deep learning are often excessively complex and restricted to batch-mode processing due to their high computational overhead. Furthermore, they usually rely on indirect signal representations that can compromise performance. To address these issues, this paper introduces a new online AMC scheme based on a direct and lossless distributional representation of signals. It works well in online settings under realistic time-varying channel conditions. Through extensive experiments in online settings, we demonstrate the effectiveness of the proposed classifier. Our results indicate that the proposed approach outperforms existing baseline models, including two advanced deep learning classifiers. Moreover, it distinguishes itself as the first online classifier for AMC with linear time complexity, which marks a significant efficiency boost for real-time applications.