## 1 Introduction
In the rest of this paper, the terms identification and verification are used in a manner consistent with the sources in literature: Authentication is the process of confirming the claimed identity of a wireless device. In this case, the RF fingerprints of a wireless device, which claims to be the device A, are compared to the previously recorded (e.g., after the product phase and before marked deployment) fingerprints of the device A using the techniques described in this paper. Authentication (also called verification in other sources) is based on a binary classification. Identification is the process where the recognition system determines a wireless device's identity by comparing the device fingerprints with reference fingerprint templates for all known devices in the test set. Identification requires a one-to-many comparison and multi-classification algorithms. A potential application scenario is where a wirelessly-connected central node can accept data only from authenticated wireless devices, but the computing capabilities of the wireless devices are not sufficient to support cryptographic-based authentication or the cryptographic material (e.g., private keys) in the wireless device cannot be adequately protected for cost reasons [3]. In this scenario, before the deployment of the wireless device, its wireless signals are analyzed and recorded by the central node in order to compute the RF fingerprints [7; 8]. In a subsequent phase, the authentication is performed using the approach described in this paper. In this scenario, the authentication accuracy must be maximized to reduce the number of false alarms, and the processing time must be minimized. Another scenario is the fight against the distribution of counterfeit electronic products, where the RF fingerprints can be used to distinguish between counterfeit and proper products because the fingerprints will be different in counterfeit products of the same model [11]. A significant challenge for researchers both for identification and authentication is the definition of features or signal representations, which can be used to detect the differences and authenticate the wireless devices. A common strategy is to extract statistical features from the RF signal and then use a machine learning algorithm to classify the obtained set of features and correlate them to the identity of the wireless device. There is an extensive literature on the selection of different statistical features for RAI including variance, entropy, skewness, kurtosis and others [8; 12]. Our contribution: Following the recent trend of using 2D time frequency domain representations of the signal emitted by a wireless devices for the purpose of RAI, in this paper, we apply the SST algorithm to the problem of physical layer authentication and identification. In particular, we use a Wavelet Synchrosqueezed Transform (WSST) based on the Continuous Wavelet Transform (CWT). In the rest of this paper, such a transform will be called Wavelet Synchrosqueezed Transform (WSST). The WSST algorithm has been applied as a time frequency analysis tool for different kinds of nonlinear signals, such as the vibration signal in [13], for the detection of frequency shifting of earthquake damaged structures in [14] and to Time Frequency Domain (ECG) signal analysis in [15], but it has not been applied to the problem of physical layer authentication to the knowledge of the authors. In a similar way to the approach adopted by the other authors, this paper makes a comparison of the performance of WSST to methods based on the 1D time domain, 1D frequency domain and 2D Short Time Fourier Transform (STFT). The performance is evaluated on an experimental dataset of RF emissions transmitted by 12 wireless devices (i.e., GSM mobile phones) collected by the authors in a test bed environment. As mentioned before, this paper is an extended version of our paper published in the 2018 41 st International Conference on Telecommunications and Signal Processing (TSP) [2].