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Due to imperfections in transmitters' hardware, wireless signals can be used to verify their identity in an authorization system. While deep learning was proposed for transmitter identification, the majority of the work has focused on classification among a closed set of transmitters. Malicious transmitters outside this closed set will be misclassified, jeopardizing the authorization system. In this paper, we consider the problem of recognizing authorized transmitters and rejecting new transmitters. To address this problem, we adapt the most prominent approaches from the open set recognition and anomaly detection literature to the problem. We study how these approaches scale with the required number of authorized transmitters. We propose using a known set of unauthorized transmitters to assist the training and study its impact. The evaluation procedure takes into consideration that some transmitters might be more similar than others and nuances these effects. The robustness of the RF authorization with respect to temporal changes in fingerprints is also considered in the evaluation. When using 10 authorized and 50 known unauthorized WiFi transmitters from a publicly accessible testbed, we were able to achieve an outlier detection accuracy of 98% on the same day test set and 80% on the different day test set.