## 3 Results and Discussion  
With random selection, the database is split into three sections: training, validation, and test, with a ratio of 6:2:2 for each class. The loss function is categorical cross-entropy, and Adam is the optimizer. The training procedure ends, and the training model is saved with the lowest validation loss when the validation loss does not drop after five epochs of multiplication by a coefficient of 0.5. The GeForce GTX1050 GPU and the experiments are implemented using Keras as the front end and Tensorflow as the back end. Further tests were carried out that produced definitive findings, even if it was a typical series of experiments to identify beneficial architectures and hyperparameter settings. We performed a contrast experiment to confirm the efficacy of phase and frequency correction in order to compare the efficiency of the suggested strategy. Four sets of comparison experiments were conducted, which were no correction, single frequency correction, single phase correction, and proposed frequency and phase correction method. The effect of \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Standard deviation is offset by sampling rate. & 0.01 Hz \\ Maximum offset for sampling rate & 50 Hz \\ Maximum offset for carrier frequency & 500 Hz \\ Standard deviation of carrier frequency offset & 0.01 Hz \\ Sample length & 128 \\ SNR range & \(-\)20 dB-18 dB \\ Sampling rate & 200 kHz \\ Number of samples & 1,200,000 \\ Modulation modes & 10 \\ \hline \end{tabular}
\end{table} 
Table 1: Main parameter of RadioML2016.10b dataset. Figure 3: Comparison of constellation between the corrected signal and the original signal. frequency offset included the effect of phase offset. Figure 4 shows that the proposed method has better performance in recognition accuracy than the other three comparative experimental methods. Figure 5 shows the confusion graph of ten modulation signals in 10 dB SNR with different correction methods. The performance of the correction module is better than that without it. However, these three correction methods only have slight differences because they only represent the predicted classification results and cannot directly reflect the specific recognition accuracy details. In the part before, an effective structure based on a two-layer GRU network was suggested; an experiment was then carried out to confirm it. First, set up a comparison experiment with different numbers of GRU layers: 1 layer, 2 layers, 3 layers, and 4 layers. Figure 6 indicates the performance of 2-layer GRU is better than the others. There is a little difference between the 3-layer GRU and 1-layer GRU in recognition accuracy, and 4-layer GRU is not as good as the other three groups due to overfitting. Figure 4: Comparison of ablation experiments with different methods. Figure 5: Confusion graph of ten modulation signals in 10 dB SNR with different correction methods. (**a**) No correction module; (**b**) Frequency correction module; (**c**) Phase correction module; (**d**) Frequency and phase correction module. Also, using the suggested two-layer GRU model, we confirmed the impact of the quantity of units in each layer and set up five groups of comparative experiments with 20, 30, 40, 50, and 60 different units, respectively. In this way, the most appropriate number of units to fit the neural network is determined. Figure 7 shows that the number of GRU units are 30 and 40 for the best performance, and the recognition accuracy is slightly better when the number of units is 40. The performance of other groups is poor due to insufficient training or too many learning features. In a similar vein, the batch size has an impact on recognition accuracy. It shows how many samples were chosen for a training set. As a result, we conducted comparative studies to ascertain the neural network's ideal batch size. Parallelizing stochastic gradient descent is challenging since it is continuous and employs small batches.