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Specific emitter identification (SEI) plays an increasingly crucial and potential role in both military and civilian scenarios. It refers to a process to discriminate individual emitters from each other by analyzing extracted characteristics from given radio signals. Deep learning (DL) and deep neural networks (DNNs) can learn the hidden features of data and build the classifier automatically for decision making, which have been widely used in the SEI research. Considering the insufficiently labeled training samples and large unlabeled training samples, semi-supervised learning-based SEI (SS-SEI) methods have been proposed. However, there are few SS-SEI methods focusing on extracting the discriminative and generalized semantic features of radio signals. In this paper, we propose an SS-SEI method using metric-adversarial training (MAT). Specifically, pseudo labels are innovatively introduced into metric learning to enable semi-supervised metric learning (SSML), and an objective function alternatively regularized by SSML and virtual adversarial training (VAT) is designed to extract discriminative and generalized semantic features of radio signals. The proposed MAT-based SS-SEI method is evaluated on an open-source large-scale real-world automatic-dependent surveillance-broadcast (ADS-B) dataset and WiFi dataset and is compared with state-of-the-art methods. The simulation results show that the proposed method achieves better identification performance than existing state-of-the-art methods. Specifically, when the ratio of the number of labeled training samples to the number of all training samples is 10\%, the identification accuracy is 84.80\% under the ADS-B dataset and 80.70\% under the WiFi dataset. Our code can be downloaded from https://github.com/lovelymimola/MAT-based-SS-SEI.