### Motivation and Related Literature  
PHY layer authentication techniques are gaining a lot of interest. These can be distinguished between those that are key based or keyless, depending on whether a shared secrecy key is used by the transmitter and receiver or not [12]. Different key-based authentication approaches have been proposed. The main idea is superimposing an authentication or a noise-like signal to the message, or introducing a certain level of randomness in the signal [13; 14; 15]. This in general requires additional computational complexity to recover the signal through demodulation and decoding and to generate the keys. Differently, keyless PHY layer authentication methods exploit the properties of the wireless link (_wireless fingerprint_--WF) to identify the legitimate node: specific characteristics of the transmitter or of its communication channel are extracted from the received signal and compared with those of previous authenticated messages (this can be provided, for example, using an initial higher layer authentication procedure) to identify a claimed source. In this way, the receiver can continuously authenticate the transmitting node, and being that the channel properties are location dependent, these are difficult to be obtained by a malicious user if it is not very close to the legitimate one. Several PHY layer authentication methods have been proposed, under different assumptions of the available channel information and system models. These methods exploit channel state information and spatial domain measurements, such as channel gains, path delay profile, carrier frequency offset, power spectra density, and received signal strength as, for example, in refs. [16; 17; 18; 19]. In general, such methods compare a specific PHY layer feature of the received signal with a test threshold that influences the authentication accuracy. However, choosing the appropriate threshold can be challenging due to the characteristics of the propagation environment and the unknown spoofing model. Additionally, in ref. [20], it is shown that under a low-SNR regime, the authentication based on a binary hypothesis testing cannot guarantee robust performance; thus an adaptive threshold is proposed. In ref. [21], a Q-learning method is used to select the optimal test threshold based on the received signal strength indicator (RSSI). Another problem of many of existing PHY layer authentication methods is that they use only one channel attribute that might be inaccurate and not enough to provide sufficient differentiation among transmitters. Indeed, channel attributes are time varying and must be estimated; hence, they can be affected by errors. Analyzing multiple PHY layer attributes improves the authentication robustness. In fact, it is more difficult for a malicious user to predict all attributes from the signal received on a different location: the legitimate user has high-dimensional protection. Toward this goal, ML has emerged as a viable solution for security and in particular for authentication [1; 2]. It allows considering multiple parameters; moreover, it can provide a model-free authentication, also under dynamic network conditions. Differently, most of the existing approaches are model based, thus requiring a lot of data for achieving an accurate model that in complex environments may be difficult to obtain with a consequent performance degradation. ML was applied to PHY layer authentication only very recently, in general not considering time-varying channels and in simple network models, where a single node communicates with an authorizing entity that has to distinguish between the authorized node and a potential malicious user. In ref. [22], an extreme learning machine is used, exploiting multi-dimensional attributes and using the training data generated from a spoofing model. Attributes must have the same statistical distribution (Gaussian), and the spoofing model is needed, so its applicability is limited. In ref.