Radar-based activity recognition is a problem that has been of great interest due to applications such as border control and security, pedestrian identification for automotive safety, and remote health monitoring. This work seeks to show the efficacy of micro-Doppler analysis to distinguish even those gaits whose micro-Doppler signatures are not visually distinguishable. Moreover, a 3-layer, deep convolutional autoencoder (CAE) is proposed, which utilizes unsupervised pre-training to initialize the weights in the subsequent convolutional layers. This architecture is shown to be more effective than other deep learning architectures, such as convolutional neural networks (CNN) and autoencoders (AE), as well as conventional classifiers employing pre-defined features, such as support vector machines (SVM), random forest (RF) and extreme gradient boosting (Xgboost). Results show the performance of the proposed deep CAE yields a correct classification rate of 94.2% for micro-Doppler signatures of 12 different human activities measured indoors using a 4 GHz continuous wave radar - 17.3% improvement over SVM.