# Radio Frequency Fingerprinting for Frequency Hopping Emitter Identification
## 5 Experimental Results and Discussion
### Emitter Identification Accuracy  
We firstly investigated the emitter identification performance of the proposed RFEI algorithm and the baselines. All algorithms were applied to all SFs, and the mean and standard deviation of the experimental values were investigated. The results are listed in Table 3.  
Table 3 demonstrates the efficiency of the proposed RFEI algorithm showing that the proposed algorithm for identifying the emitter ID based on the SS spectrogram and DIN base classifier performs with an accuracy of 95.3%, which is better than other baseline algorithms. In addition, the ensemble approach of RT, FT, and SS based on the proposed algorithm yielded an accuracy of 97.0%, demonstrating its efficiency with a higher identification accuracy than other baseline algorithms. In terms of the SF efficiency, the results show that the SS signal is the most effective SF, as it is more accurate than the RT and FT signal-based results. In addition, in terms of the efficiencies of the feature extraction and classification approaches, the spectrogram feature is effective for representing the differences in the SF for each emitter. The most effective means of identifying the emitter ID in the FH signals is to ensemble the multimodal SFs, i.e., the RT, FT, and SS, trained by a DIN. The emitter identification performance at SNRs is shown in Figure 10. The AWGN signal \(n(t)\) can be artificially added to the received hop signal \(\mathbf{s}\) as follows  
\[\text{SNR}=10\log_{10}\left(\frac{||\mathbf{s}||_{2}^{2}}{N\sigma_{n}^{2}}\right) \tag{29}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Emitters** & **Emitter Type** & \
\begin{tabular}{c} **Number of** \\ **Acquisitions** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Samples** \\ \end{tabular} \\ \hline \multirow{6}{*}{Training dataset} & Emitter 1 & Model 1 & & 170 \\  & Emitter 2 & Model 1 & & 168 \\  & Emitter 3 & Model 1 & & 170 \\  & Emitter 4 & Model 1 & 5 times & 171 \\  & Emitter 5 & Model 2 & & 160 \\  & Emitter 6 & Model 2 & & 169 \\  & Emitter 7 & Model 2 & & 168 \\  & Emitter 8 & Model 3 & & 308 \\  & Emitter 9 & Model 3 & 10 times & 312 \\ \hline Total emitters & & 9 & Total samples & 1796 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of the FH dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **RT** & **SS** & **FT** \\ \cline{2-4}  & \multicolumn{3}{c}{**Mean Accuracy (\%) \(\pm\) Standard Deviation**} \\ \hline Statistical moments * & 61.8 \(\pm\) 0.0 & 92.6 \(\pm\) 0.0 & 66.4 \(\pm\) 0.0 \\ Raw signal ** & 17.7 \(\pm\) 1.3 & 89.5 \(\pm\) 0.7 & 20.4 \(\pm\) 2.1 \\ Spectrogram—residual *** & 83.7 \(\pm\) 2.1 & 93.7 \(\pm\) 1.2 & 93.9 \(\pm\) 1.2 \\ Spectrogram—DIN \(\dagger\) & 84.6 \(\pm\) 1.5 & 95.3 \(\pm\) 1.2 & 92.8 \(\pm\) 1.1 \\ Ensembles \(\dagger\) & & 97.0 \(\pm\) 0.6 & \\ \hline \hline \end{tabular}  
*: (Baseline 1) statistical moments approach in [4; 5]. **: (Baseline 2) raw signal approach in [7]. ***: (Baseline 3) spectrogram and residual block-based approach in [8]. \(\dagger\): (Proposed) spectrogram, DIN classifier, and ensemble-based approach in the proposed method.  
\end{table} 
Table 3: Emitter identification accuracy. where \(N\) and \(\sigma_{n}^{2}\) are the length and variance of the noise signal \(n(t)\), respectively. We found that the classification accuracy obtained by applying the proposed method to the SS signal was nearly 3% above baselines 1 and 2 and at least 1% above baseline 3 over the entire range of SNRs. In addition, the ensemble approach of the proposed algorithm can improve the accuracy by more than 1% compared to the proposed method. In particular, applying the proposed method to the SS signal at 20 dB SNR, which is the typical operating SNR of the FHSS network [39], yielded an accuracy of more than 95.0%. For the ensemble approach, the identification accuracy was measured to be greater than 96.4%, making it the most effective algorithm. These accuracies are higher than those of baseline 1 (87.5%), baseline 2 (89.8%), and baseline 3 (92.5%).