# Deep-Learning-Based Recovery of Frequency-Hopping Sequences for Anti-Jamming Applications
## 4 Performance Analysis
### Performance of FH Sequence Recovery  
In order to evaluate the performance of the proposed method, the network that only used the convolutional part of the CNN-GRU network in this paper was selected as a comparison, which was recorded as a CNN network. The two networks were trained under the same dataset and hyperparameter settings. The test samples were generated as follows: The signal-to-jamming ratio ranged from \(-18\) dB to \(0\) dB with an interval of 2 dB. In total, 500 time-frequency diagrams under single jamming and mixed jamming were generated, respectively. In each case, a total of 30,000 frequency bins had to be classified. The results are shown in Figure 7. It can be seen that the estimation accuracy of the frequency-hopping sequence of the CNN-GRU network was higher than that of the CNN network under single jamming or mixed jamming which did not appear in training. This proves that the CNN-GRU network can correctly learn the features of different jamming signals, and its learning ability is stronger than that of the CNN network. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Jamming signal & five kinds of jamming signals \\ The number of frequencies & 16 \\ The number of hops of each signal & 60 \\ signal-to-jamming ratio & \(-10\) dB to \(10\) dB \\ The frequency-hopping received signals & 2200 \\ The window length of STFT & 1024 \\ The number of time–frequency images & 13,200 \\ The mini-batch size & 60 \\ The initial learning rate & 0.001 \\ convolution kernel size & 77 \\ Stride & 2 \\ The number of convolution kernels & 64 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The physical parameters. To be more specific, as can be seen from Figure 7a, when the signal-to-jamming ratio was greater than \(-6\) dB, the estimation accuracy of the frequency-hopping sequence of the CNN-GRU network under various single jamming scenarios was close to \(100\%\). Compared with other jamming signals, the CNN-GRU network had a lower estimation accuracy of the frequency-hopping sequence under jamming 5 (sweeping collision-blocking jamming). This was due to the case of the same signal-to-jamming ratio, the frequency band of the swept-frequency collision-blocking jamming was narrower than in other jamming scenarios, and the energy was more concentrated. Moreover, the swept-frequency collision-blocking jamming also had the characteristics of frequency hopping, which was closer to the frequency-hopping signal than other jamming scenarios in the time-frequency diagram, which increases the difficulty of the CNN-GRU network to extract the characteristics of the frequency-hopping signals. Similarly, it can be seen from Figure 7b that when the signal-to-jamming ratio was greater than \(-8\) dB, the estimation accuracy of the frequency-hopping sequence of the CNN-GRU network was higher than \(-8\) dB. Figure 7: Frequency-hopping sequence estimation accuracy: (**a**) single jamming; (**b**) mixed jamming. hopping sequence of the CNN-GRU network was close to 100%. The trend observed in the estimation accuracy curve of the frequency-hopping sequence of the CNN-GRU network under mixed jamming was the same as that under single jamming, which indicates that the CNN-GRU network has good generalization ability. We now analyze the robustness of the CNN-GRU network to various frequency-hopping sequence lengths. The CNN-GRU network was tested by using the frequency-hopping received signals with lengths of 30 hops, 60 hops, 90 hops, and 120 hops, respectively. Other parameter settings remained unchanged. The results are shown in Figure 8. It can be seen that the estimation accuracy curves of the CNN-GRU network for the frequency-hopping sequences of different lengths were very close and had good robustness. This is because the network architecture of recurrent connections was adopted in designing the network, which enabled the network to handle sequence inputs of arbitrary length.