# Intelligent Reception of Frequency Hopping Signals Based on CVDP
## 3 Algorithm Simulation and Performance Analysis
### Estimation Performance of Hopping Frequency
#### 3.2.1 Experiment 1  
Estimation of hopping frequency in the one-time slot by CVDP network under multiple interference environments. To analyze the role of each module, four comparison networks are built based on the network model in this paper (as shown in Figure 2). CNN network only retains the CNN module of CVDP, and the global pooling layer and the fully connected layer are added later. CNN-VIT0 network is that the dual multi-head _Probsparse_ self-attention mechanism of CVDP is replaced by the original self-attention mechanism. CNN-VIT1 network is that the dual multi-head _Probsparse_ self-attention mechanism of CVDP is replaced by the dual multi-head self-attention mechanism. CNN-VIT2 network is that the dual multi-head _Probsparse_ self-attention mechanism of CVDP is replaced by the single multi-head _Probsparse_ self-attention mechanism. The above four networks, the CNN-GRU network [25], and the CVDP network of this paper were trained under the same training set with the same hyperparameter settings. Under five interference environments including multi-tone interference, single-band interference, multi-band interference, swept frequency interference, and mixed interference, the generalization ability of the six networks for hopping frequency estimation in the one-time slot is tested respectively. To further investigate the optimal setting for parameter \(h\), the performance of CVDP networks with different values of \(h\) was tested under mixed interference environments. To more audiovisual demonstrate the difference between the interfering signals and the frequency hopping signals, Figure 3 shows the time-frequency spectrograms in 20-time slots under five interfering environments. The accuracy of hopping frequency estimation is shown in Figure 4 when time-frequency spectrograms in the one-time slot are input to the network.  
As seen in Figure 4, the four improved VIT networks (CNN-VIT0, CNN-VIT1, CNN-VIT2, and CVDP) have better network performance than CNN networks and CNN-GRU networks, this is because after combining the inductive bias characteristics of CNN networks and the global inductive modeling capability of VIT networks, the VIT networks demonstrate approximately 15 to 20% improvement in convergence, stability, and robustness on small datasets. Moreover, the self-attention mechanism of the VIT network makes the network focus on the frequency hopping signals region and minimizes the influence of interfering signals. The CNN network and CNN-GRU network cause serious performance degradation because they do not accurately extract the differences between frequency hopping signals and interfering signals in terms of time-frequency characteristics. Among the four improved VIT networks, the CNN-VIT1 network and the CVDP network have better performance, this is because the CNN-VIT1 and CVDP, through a dual multi-head self-attention mechanism, can better extract the positional features of frequency hopping signals in the entire spectrum, capturing global dependencies. The CNN-GRU network is suitable for extracting joint features of multiple time slots, but they are not included in the one-time slot. So its performance deteriorates due to the inability to extract joint features. Therefore, CNN-VIT1 and CVDP networks are more suitable for solving the task of a one-time slot frequency hopping frequency estimation. In addition, the accuracy of the hopping frequency estimation of the CVDP network is only slightly lower than that of the CNN-VIT1 network, indicating that the _Probsparse_ self-attention mechanism can achieve the purpose of reducing the computation while not affecting the network performance. Furthermore, it was found that the \(h\) should not be too large or too small. Therefore, in the case of a total dimension of 256, the \(h\) of one multi-head self-attention layer is set to 8 heads, while the \(h\) of the other multi-head self-attention layer is set to 16 heads, as this combination achieves the best performance.