## 1 Introduction  
The authentication of wireless devices can be implemented using various approaches. Historically, authentication has been implemented using information known by the device (cryptographic information) or owned by the device (a SIM card). Another form of authentication is based on what a device is (i.e., the physical properties). A well-known example is biometric authentication such as scanning of the human eye iris used to prove the authenticity of a person. This approach has disadvantages and advantages, which are well known in literature [1]. A known advantage is that the intrinsic information of a device is difficult to clone, to steal or remove from a device. The disadvantages are that the extraction of the information can be more difficult to achieve or it can provide a statistical-only confirmation of authenticity (e.g., biometrics matching to a certain level of accuracy), rather than a precise confirmation as it is obtained with cryptographic means (e.g., the signing of a message with a key). In this paper, we investigate the identification and authentication of wireless devices using the physical properties (physical layer authentication) in their transmission components, which generate specific analogical artifacts in their RF emissions. This paper is an extended version of our paper published in the 2018 41 st International Conference on Telecommunications and Signal Processing (TSP) [2]. Physical layer authentication is relevant when the authentication based on cryptographic means is difficult to achieve, either due to the limitations of IoT devices or because the context does not support an efficient distribution of cryptographic materials (e.g., keys and certificates). In the case of the Internet of Things, the authors in [3] highlighted that, although the design of authentication mechanisms based on cryptography is always desirable, it may not be applicable to several IoT scenarios because it may imply high computational cost and/or always connected trusted entities. We propose an authentication mechanism for wireless devices, which can be an alternative to cryptography or can complement and strengthen it (i.e., multi-factor authentication). The effectiveness of this identification and authentication technique has been demonstrated in the literature in various settings and propagation conditions, and it has different names: Radiometric Identification (RAI) [4], Special Emitter Identification (SEI) [5] or Radio Frequency DNA (RF-DNA) [6], because RF fingerprints resemble the DNA of human beings. It is due to small differences in the material and the composition of the electronic circuits used for wireless transmission, which are represented in the RF signal over the air. These differences are usually not relevant to hamper the correct functioning of wireless services, but they are significant enough to identify the model or the electronic device itself uniquely [7]. The differences in the wireless transmission components, which become embedded in the RF signal, are usually stable during the transmission time (even if environment and aging effects have been reported), and they are not strongly related to the transmitted content. In many cases, RF fingerprinting in ideal wireless propagation conditions (i.e., high signal to noise radio or low fading effects) can provide a very high authentication accuracy of wireless devices. This technique requires the selection of features and classification algorithms, which are both accurate and time effective. This is often a design trade-off, because the application of sophisticated features and algorithms may require a longer processing time than the application of simple features and algorithms, even if the former provide a better identification accuracy. RAI has been applied to a large variety of electronic devices and wireless standards including WiFi [8], ZigBee [9], WiMAX [6] and Global System for Mobile Communications (GSM) in [10]. An analysis of existing literature in this area is reported in Section 2.