# Intelligent Reception of Frequency Hopping Signals Based on CVDP
## 3 Algorithm Simulation and Performance Analysis
### Estimation Performance of Hopping Frequency
#### 3.2.2 Experiment 2  
Estimation performance of hopping frequency in the one-time slot by CVDP network under the influence of fading channels. The propagation of signals can be influenced by various factors such as terrain and obstacles, which may lead to multipath fading in the  
Figure 4: Accuracy of hopping frequency estimation (**a**) Multi-tone interference, (**b**) Single-band interference, (**c**) Multi-band interference, (**d**) Swept frequency interference, (**e**) Mixed interference, (**f**) CVDP network with Different \(h\).  
Figure 3: The time-frequency spectrograms in 20-time slots under five interfering environments (**a**) Multi-tone interference, (**b**) Single-band interference, (**c**) Multi-band interference, (**d**) Swept frequency interference, (**e**) Mixed interference.  
received signals. Additionally, the relative motion between the transmitter and receiver can cause a Doppler shift, as demonstrated in Equation (13)  
\[\Delta f=\frac{fv\cos\theta}{v_{c}}. \tag{13}\]  
where \(f\) is the frequency of the hopping signals, \(v\) is the relative speed between the transmitter and receiver, \(\theta\) represents the angle between the direction of hopping signals motion and the incident direction, and \(v_{c}\) is the speed of light.  
The network's ability to generalize over both frequency flat and frequency selective Rayleigh fading channels was tested due to the potential for severe signal distortion caused by various factors. The maximum Doppler shift was set to 10 Hz, and for frequency-selective Rayleigh fading, three paths were used with path delays of 0 s, 1.5 us, and 90 us, respectively, and the average path gains were 0 dB, \(-\)3 dB, and \(-\)6 dB. The accuracy of hopping frequency estimation in the one-time slot was measured in Figure 5, and the average running time required for training and testing the six networks was shown in Figures 6 and 7 to comprehensively evaluate the network performance.  
From Figure 5, it can be seen that the CVDP and CNN-VIT1 networks exhibit superior accuracy compared to other networks in frequency-flat Rayleigh fading channels, indicating excellent generalization capabilities. However, the network's performance generally degrades in frequency-selective Rayleigh fading channels due to inter-symbol interference and signal fading. Despite this, the CVDP and CNN-VIT1 networks still exhibit the highest accuracy, and the performance gain is more significant than that observed in flat fading channels. Moreover, the CVDP network maintains a similar level of accuracy as the CNN-VIT1 network but requires less computational amount, leading to the best overall performance under both fading channels.  
Figure 5: Accuracy of hopping frequency estimation (**a**) Frequency-flat Rayleigh fading channel, (**b**) Frequency-selective Rayleigh fading channel.  
Figure 6: Average training time bar graph.  
The running speed of the CVDP network, as shown in Figures 6 and 7, is faster than that of the CNN-VIT1 network which utilizes only a dual multi-head self-attention mechanism. Additionally, the running time of the CVDP network is near to that of the CNN-VIT0 network. These results indicate that the incorporation of _Probsparse_ self-attention reduces computation complexity. CNN networks and CNN-GRU networks have simple structures and consequently exhibit the shortest running times.  
In summary, the CVDP network in this paper has superior estimation accuracy and a shorter running time compared to other comparison networks.