# Radio Frequency Fingerprinting for Frequency Hopping Emitter Identification
## 3 Proposed RF Fingerprinting-Based Emitter Identification Method
### Attacker Emitter Detection  
The last step of the RFEI method is an outlier detection step implemented to detect the imitated FH signal. An outlier is a sample included in specific emitter IDs that is not considered during training. In this study, the imitated FH signal was the outlier. This step is aimed at detecting the differences in the classifier output characteristics between the outputs of the classifier when the trained and outlier samples are input. This objective can be achieved by comparing the classifier outputs [29; 30; 31], exposing the outliers during the training step to magnify the differences between the trained and outlier samples [32; 33], and analyzing the likelihood of the inputs from a generative adversarial network [34; 35]. The proposed outlier detection scheme is presented in Figure 8. We considered the outlier detection framework proposed in [30]. Temperature scaling [36] and the opposite application of an adversarial attack [37] have been reported to be effective in detecting outlier samples. After preprocessing the input sample, outliers can be detected when the maximum probability of the output vector is lower than the threshold. The key idea of this approach is that the output vector of the outlier represents a much smaller value than the output vector of the trained sample. Figure 7: Stacking ensemble approach for the multimodal SF signals. Utilizing this approach, we constructed the outlier detector to alert the signal input when the imitated FH signal was input by performing two steps: (1) calibration of the output vector of the classifier by a temporal scaling factor, \(T_{s}\), and (2) comparison of the maximum probability of the output vector to the outlier detection threshold, \(\lambda\). In this study, opposite application of the adversarial attack was not performed because a small perturbation of the input sample may affect the SFs, defined as subtle differences in the FH signal. Mathematically, the temporal scaling process was applied to Equation (17) such that  
\[ \begin{array}{rl}p(c_{l};\mathbf{s}_{\text{SF}},T_{s})&=\text{softmax}( \mathbf{y}/T_{s})\\ &=\frac{\exp(\mathbf{y}[c_{l}]/T_{s})}{\sum_{l=1}^{\zeta}\exp(\mathbf{y}[c_{l }]/T_{s}))}\end{array}  \tag{21}\]  
In the case of the ensemble approach, the probability in Equation (19) was modified as the temporal scaled version as follows  
\[ \begin{array}{rl}p(c_{l};\mathbf{s},T_{s})&=\prod\limits_{\mathbf{S}\in \{\text{RT},\text{SS},\text{FT}\}}p(c_{l};\mathbf{s}_{\text{SF}},T_{s})\\ &=\prod\limits_{\mathbf{S}\in\{\text{RT},\text{SS},\text{FT}\}}\text{softmax}( \mathbf{y}_{\text{SF}}/T_{s})_{c_{l}}\end{array}  \tag{22}\]  
Based on the scaled output probability, the detection rule for the outlier sample can be defined as follows  
\[ \begin{array}{rl}p(c_{out};\mathbf{s},T_{s},\lambda):=\begin{cases}1&if\text {max}_{c_{l}}p(c_{l};\mathbf{s},T_{s})\leq\lambda\\ 0&if\text{max}_{c_{l}}p(c_{l};\mathbf{s},T_{s})>\lambda\end{cases}\end{array}  \tag{23}\]  
where \(p(c_{out};\mathbf{s},T_{s},\lambda)\) is the probability that the current input sample is an outlier. This detection rule is a binary classifier with trained class \(c_{train}\) and outlier class \(c_{out}\). Thus, parameters \(T_{s}\) and \(\lambda\) were optimized experimentally based on the minimum false positive rate (i.e., the part of the actual outliers that were misdetected as trained samples, FPR) when the true positive rate (i.e., the part of the actual trained samples that were detected as trained samples, TPR) was higher than 95%. The final version of the algorithm used for our proposed RFEI process is presented in Algorithm 2. Figure 8: Attacker detection scheme based on stacking ensemble approach. ```
Input: The target baseband hop signal \(s_{h}^{\text{k}}(t)\) Initialize:\(i=1\), \(T^{\text{RT}}=T^{\text{FT}}=\{\}\) for time periods, \(W_{E}\) and bandwidth of interest (BOI) \(BW_{\text{BOI}}\). Step 1: (Extract the target SF) whiledo: Detect the transient signal with Equation (10). Extract the target SF \(\mathbf{s}_{\text{SF}}\) with Equation (11).