## 9 Qualitative Discussion and Open Challenges  
Based on our literature research and the preliminary theoretical analysis, Table 3 shows a suitability analysis of various combinations of feature-extraction transforms and classifiers for four selected classifiers and five selected feature-extraction transforms. The suitability analysis took into account both the expected performance and the complexity of the algorithm.  
The most promising combinations, based on our preliminary analysis, are the kurtosis and thresholding combination, and the spectrogram and SVM combination. Potential good results may also be expected, based on a current literature search and theoretical analysis, from kurtosis and SVM combination, as shown in Table 3. Further simulation-based and measurement-based analysis is necessary to validate these findings and this remains a topic of future research. The methodology presented in this paper can serve as a basis for also studying other possible combinations of feature-extraction transforms and classifiers.  
Table 4 also discusses the expected impact of various features of the transmitter HW on the accuracy of the results. The analysis is based on the theoretical insights from the mathematical models presented in Section 3. It is expected that the PA non-linearity, the phase noises and the I/Q imbalances are the strongest differentiating features of the transmitter HW impairments, while the DAC non-linearities are expected to have little or no impact upon the classification performance (as differences between the GNSS and spoofer DAC non-linearities are not expected to be high). The band-pass filter (BPF) at the end of the transmission chain is, however, expected to have a negative impact upon the ability to differentiate among various features, because it is acting as a smoother (or high-frequency removing unit). In practice, an RFF algorithm would, most likely, not be able to distinguish between each individual transmitter feature and would treat all effects jointly. Based on sufficiently large databases, it is expected that the positive-impact effects from Table 4 will be predominant compared to the zero- and negative-impact effects.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Transmitter Features**} \\ \cline{2-6}
**Phase Noise** & \begin{tabular}{c} **I/Q** \\ **Imbalance** \\ \end{tabular} & \
\begin{tabular}{c} **DAC** \\ **Non-Linearity** \\ \end{tabular} &
\begin{tabular}{c} **PA** \\ **Non-Linearity** \\ \end{tabular} & **BPF** \\ \hline
**Impact** & 0 & + & 0 & + & + \\ \hline \hline \end{tabular}
\end{table}
Table 4: Preliminary analysis on the impact of various hardware features upon the capacity to distinguish between transmitters, based on Section 7: 0 = no impact, + = positive impact (i.e., can increase the RFF accuracy).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Classifier Type**} & \multicolumn{6}{c}{**Feature Extraction Transform**} \\ \cline{2-6}  & **EVM** & **Kurtosis** & **TKEO** & **Spectrogram** & **CWT** & **DWT** \\ \hline
**Classification via kNN** & + & + & + & + & + & + \\ \hline
**Classification via SVM** & + & ++ & + & +++ & + & ++ \\ \hline
**Classification via CNN** & + & + & + & +++ & + & + \\ \hline
**Classification via Thresholding** & + & +++ & + & + & + & + \\ \hline \hline \end{tabular}
\end{table}
Table 3: Preliminary analysis on the suitability of various feature-extraction transforms for various classification methods (+ = low, ++ = medium, +++ = high) in the context of pre-correlation GNSS data.