Radar signal has been shown as a promising source for human identification. In daily home sleep-monitoring scenarios, large-scale motion features may not always be practical, and the heart motion or respiration data may not be as ideal as they are in a controlled laboratory setting. Human identification from radar sequences is still a challenging task. Furthermore, there is a need to address the open-set recognition problem for radar sequences, which has not been sufficiently studied. In this paper, we propose a deep learning-based approach for human identification using radar sequences captured during sleep in a daily home-monitoring setup. To enhance robustness, we preprocess the sequences to mitigate environmental interference before employing a deep convolution neural network for human identification. We introduce a Principal Component Space feature representation to detect unknown sequences. Our method is rigorously evaluated using both a public data set and a set of experimentally acquired radar sequences. We report a labeling accuracy of 98.2% and 96.8% on average for the two data sets, respectively, which outperforms the state-of-the-art techniques. Our method excels at accurately distinguishing unknown sequences from labeled ones, with nearly 100% detection of unknown samples and minimal misclassification of labeled samples as unknown.