## 6 Conclusions  
This paper has presented the novel application of WSST to the physical layer authentication and identification of wireless devices for an experimental dataset based on the collection of RF emissions of 12 wireless devices (e.g., GSM mobile phones). The dataset is particularly challenging because the RF emissions has been collected with a low sample rate (1 MHz). This paper has performed an analysis on the application of WSST both for the problem of identification and authentication. The analysis includes the evaluation of the performance in the presence of AWGN. In both cases, the application of WSST  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Technique** & \begin{tabular}{l} **Predicted Percentage** \\ **for the Three Models** \\ \end{tabular} & \
\begin{tabular}{l} **Predicted Percentage** \\ **for iPhone 1** \\ \end{tabular} &
\begin{tabular}{l} **Predicted Percentage** \\ **for iPhone 2** \\ \end{tabular} \\ \hline \hline
**SNR = 100** & === & === & === \\ \hline WSST & 0 & 0.51 & 0.49 \\ \hline STFT & 0 & 0.72 & 0.28 \\ \hline FFT & 0 & 0.57 & 0.43 \\ \hline TIME & 0 & 0.77 & 0.23 \\ \hline
**SNR = 10** & === & === & === \\ \hline WSST & 0.45 & 0.18 & 0.37 \\ \hline STFT & 0.3 & 0.21 & 0.49 \\ \hline FFT & 0.44 & 0.18 & 0.38 \\ \hline TIME & 0.26 & 0.26 & 0.48 \\ \hline
**SNR = 0** & === & === & === \\ \hline WSST & 0.8 & 0.09 & 0.11 \\ \hline STFT & 0.71 & 0.1 & 0.19 \\ \hline FFT & 0.77 & 0.1 & 0.13 \\ \hline TIME & 0.69 & 0.15 & 0.16 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Predicted percentage with an unknown device.  
outperforms STFT and the time domain and the frequency domain representation for medium and high SNR values. The results are consistent for different machine learning algorithms. An extensive analysis of the hyperparameters for the application of WSST has been implemented.  
Conceptualization, G.B., R.G. and G.S. Methodology, G.B. Software, G.B., G.S. Validation, G.S. Resources, R.G. Data curation, R.G. Writing, original draft preparation, G.B. Writing, review and editing, G.B., R.G. and G.S. Project administration, G.B. Funding acquisition, G.B.  
This research has been supported by the EC H2020-IOT-2016-2017 (H2020-IOT-2017) Program under Grant Agreement 780139 for the SEcuRe and safe Internet Of Things (SerIoT) Research and Innovation Action.  
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses or interpretation of the data; in the writing of the manuscript; nor in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} AWGN & Additive White Gaussian Noise \\ CMOS & Complementary Metal Oxide Semiconductor \\ CWT & Continuous Wavelet Transform \\ DDC & Digital Down Converter \\ ECG & Electro-CardioGram \\ EER & Equal Error Rate \\ EMD & Empirical Mode Decomposition \\ FAR & False Accept Rate \\ FN & False Negatives \\ FP & False Positives \\ FRR & False Reject Rate \\ GNSS & Global Navigation Satellite System \\ GSM & Global System for Mobile Communications \\ GT & Gabor Transform \\ GWT & Gabor-Wigner Transform \\ HHT & Hilbert-Huang Transform \\ ISM & Industrial, Scientific and Medical \\ ISO & International Organization for Standardization \\ JPEG & Joint Photographic Experts Group \\ KNN & K Nearest Neighbor \\ PNU & Pixel Non-Uniformity \\ PRNU & Photo-Response Non-Uniformity noise \\ PUF & Physical Unclonable Functions \\ RAI & Radiometric Identification \\ RF & Radio Frequency \\ RF-DNA & Radio Frequency DNA \\ ROC & Receiver Operative Characteristics \\ SDR & Software-Defined Radio \\ SNR & Signal to Noise Ratio \\ SST & Synchrosqueezing Transform \\ STFT & Short Time Fourier Transform \\ SVM & Support Vector Machine \\ TAR & True Accept Rate \\ TD & Time Domain \\ TFD & Time Frequency Domain \\ TN & True Negatives \\ TP & True Positives \\ UMTS & Universal Mobile Telecommunications System \\ \end{tabular}