## 5 Simulation Results  
### Simulation Analysis of Fractal Features  
Multiple Amplitude Shift Keying (MASK, \(M=2\), 4), Multiple Frequency Shift Keying (MFSK, \(M=2\), 4, 8), Multiple Phase Shift Keying (BPSK), 16 QAM (Quadrature Amplitude Modulation), and 32 QAM were used to conduct the simulation. Signal correlation parameters were carrier frequency \(f_{c}=\)4 MHz \(f_{c}=\) 4 MHz, sampling frequency \(f_{s}=4\times f_{c}\), the initial frequency of MFSK, \(f_{1}=\)4 MHz, and frequency deviation \(\Delta f=\) 1 MHz. Signal length \(N_{s}=\) 2048, digital signal symbol rate \(R_{s}=\)1000 Sps. Random codes forming a baseband signal were used. The SNR range was \(-5\) to 10 dB. The simulation results of the calculated signals are shown in Figure 3.  
Through Figure 3, we can directly see that even for eight digitally modulated signals, the difference in features between the signals were more obvious. Meanwhile, in the whole SNR range, the feature distribution was slightly fluctuating. That is, the fractal feature was not sensitive to the noise environment. Under each fractal feature, the data distribution interval was quite different, and the number of signal features of the Katz dimension jumped the most among the eight signal features. The box dimension distinguished the eight signals better, and the Katz dimension and Sevcik dimension distinguished 4 ASK, 16 QAM, and 32 QAM better. The Petrosian dimension distinguished the 2 PSK and 16 QAM signals better. The Higuchi fractal dimension characteristic signal was the worst. The aliasing between signals was serious. One of the main difficulties in automatic modulation pattern recognition is the problem of most recognition methods having poor recognition in a large dynamic SNR environment. In practical applications, the SNR changes rapidly during the working process and it is difficult to maintain stability. Therefore, high requirements are placed on the adaptability of large dynamic SNR (i.e., noise robustness). For the characteristics of the automatic recognition algorithm based on feature extraction and machine learning, the noise robustness of the recognizer is mainly reflected in the selection of  
Figure 2: Random forest structure. features. From Figure 3 we can see that for various modulated signals, each fractal feature under different SNR showed low noise sensitivity. When evaluating the noise robustness of each feature, an algorithm to analyze the overall anti-noise performance was used as follows. According to Figure 3, the differences among the eight different signals were obvious. Meanwhile, in the whole SNR range, the feature distribution was slightly fluctuating, which means that the fractal feature was not sensitive to the noise environment. Comparing the five different fractal features, the data distribution was also quite different. The Katz dimension differed the most among the five different features. The box dimension could distinguish the eight signals effectively. Katz and Sevcik dimensions could better distinguish 4 ASK, 16 QAM, and 32 QAM. Petrosian dimension could better distinguish the 2 FSK and 16 QAM signals. The Higuchi fractal dimension was the worst. The aliasing among signals was serious. Figure 3: Fractal dimension of different communication modulation signals. One of the main difficulties in automatic modulation recognition is the problem of poor recognition rate in a large dynamic SNR environment. In practical applications, the SNR changes rapidly with the environment and it is difficult to maintain stability. Therefore, high requirements are placed on the adaptability of large dynamic SNR. For automatic modulation recognition based on feature extraction and machine learning, the noise robustness of the classifier mainly depends on the selection of features. From Figure 3, we can see that the fractal feature under different SNRs showed low noise sensitivity. Therefore, an algorithm for analyzing the overall anti-noise performance is provided as follows.