The recognizing performance of CNN-ST for randomly overlapping dual-component radar signals under different SNR is evaluated. To demonstrate better classification performance over others, CNN-DQLN and CNN-Softmax in [47] are also utilized for conducting comparative analyses.

## 5.1. Datasets and Training Parameters

The typical eight types of signals that including 2FSK, BPSK, 4FSK, FRANK, NS, EQFM, LFM, and SFM are adopted in this paper. Table 2 lists the detailed radar signal parameters. Noting that the training, validation, and testing datasets contain randomly overlapping dual-component radar signals under different SNR, which are preprocessed by using SPWVD transformation. The SNR ranges from − 14 dB to 10 dB, and every 2 dB is selected. The number of each class dual-component radar signals under different SNR is set as 300, and a total of 1,419,600 samples are obtained in the training dataset. For the validation dataset, the number of each class dual-component radar signals under different SNR is set as 100, and a total of 473,200 samples is obtained. For the testing dataset, the number of each class dual-component radar signals under different SNR is set as 30, and a total of 5,160 samples is obtained.

**Table 2. **Parameters of various radar signals

The synchronous training on a computer as well as the deep learning framework Pytorch is conducted. The training parameters are as follows: batch size is 128; epoch is 100; epsilon is 0.001; momentum is 0.01; initial learning rate is set as 0.01; learning decay rate is 0.1 every 10 epochs; dropout is 0.8; weight decay is set as 1e-5; batch normalization with average decay is set as 0.999.

## 5.2. Results and Analysis

To explicitly explore the recognition accuracy of CNN-ST and conduct the comparative analyses, Fig. 5 illustrates the overall recognition accuracies of CNN-ST, CNN-DQLN, and CNN-Softmax as a function of SNR. Therein, the testing dataset used in this subsection represents the dual-component radar signals under the same SNR.

Figure 5 demonstrates that an increase of SNR leads to first increasing overall recognition accuracies of CNN-ST, CNN-DQLN, and CNN-Softmax, and then leveling off. Therein, the increasing trend for CNN-ST at the lower SNR is faster than CNN-DQLN and CNN-Softmax, which achieves better recognition performance over others. The recognition performance of CNN-ST, CNN-DQLN, and CNN-Softmax are 50.88%, 37.37%, and 26.49% at -10 dB, respectively. The recognition performance of CNN-ST is 13.51% higher than that of CNN-DQLN, and 24.39% higher than that of CNN-Softmax. The recognition accuracy of CNN-ST is 82.58% at -8 dB, while 74.74% and 57.02% for CNN-DQLN and CNN-Softmax, respectively. Moreover, the recognition accuracies can be reached to 100%, 98.77%, and 95.44% for CNN-ST, CNN-DQLN, and CNN-Softmax at 4 dB, respectively. Therefore, CNN-ST achieves superior recognition accuracy than CNN-DQLN and CNN-Softmax. The reason is that the adopted swin transformer in the CNN-ST can extract the more detailed features of the radar signals.

For clearly expressing the recognition performance of each type of radar signal, Fig. 6 illustrates the variation of the recognition accuracy of eight types of signals with SNR.

Figure 6 demonstrates that the recognition accuracies of eight types of signals increase as increasing SNR. While, increasing trend levels off at the higher SNR. It means that the lower SNR exerts an important effect on recognition accuracy. Moreover, 2FSK and LFM demonstrate superior recognition performance over others. That is because the clear TFIs for 2FSK and LFM are, the easier the detailed features are extracted, and the better recognition performance can be obtained. The recognition accuracies of 2FSK, EQFM, 4FSK, BPSK, LFM, SFM, NS, and FRANK are 90.83%, 82.14%, 77.98%, 67.62%, 80.71%, 75.95%, 73.45%, and 71.91% at SNR of -10 dB, respectively. Moreover, the recognition accuracies of all types of radar signals are basically up to 1 at larger than 0 dB. Therefore, the designed CNN-ST model demonstrates better recognition performance at the same SNR.

To investigate the influence of different SNR on the recognition accuracy of dual-component signals, Fig. 7 demonstrates the recognition accuracy as a function of different SNR. Therein, SNR is -12 dB to 4 dB; dual-component radar signals include: overlapping 2FSK and 4FSK (2FSK-4FSK), overlapping 2FSK and BPSK (2FSK-BPSK), overlapping 2FSK and EQFM (2FSK-EQFM), overlapping 2FSK and FRANK (2FSK-FRANK), overlapping 2FSK and LFM (2FSK-LFM), overlapping 2FSK and NS (2FSK-NS), overlapping 2FSK and SFM (2FSK-SFM), overlapping LFM and 4FSK (LFM-4FSK), overlapping LFM and BPSK (LFM-BPSK), overlapping LFM and EQFM (LFM-EQFM), overlapping LFM and FRANK (LFM-FRANK), and overlapping LFM and SFM (LFM-SFM).

Figure 7 shows that the recognition accuracies of six types of randomly overlapping dual-component radar signals increase as increasing different SNR. When the different SNR of dual-component radar signal is higher than − 2 dB, the increasing trend gradually levels off, and the recognition accuracies are up to 1. It means that the different SNR of dual-component radar signal exerts less effect on the recognition accuracy, especially at the higher SNR. That is because the higher the different SNR is, the lesser the noise interferes with the TFIs is, and the easier the effective features of the TFIs can be extracted. The recognition accuracies of 2FSK-4FSK, 2FSK-BPSK, 2FSK-EQFM, 2FSK-FRANK, 2FSK-LFM, 2FSK-NS, 2FSK-SFM, LFM-4FSK, LFM-BPSK, LFM-EQFM, LFM-FRANK, and LFM-SFM are up to 76.25%, 63.75%, 82.625%, 75.625%, 70.625%, 72%, 67.5%, 71.5%, 60.625%, 78.25%, 73.75%, and 70.625% at different SNR of -12 dB, respectively. When SNR of 2FSK is -12 dB and 4FSK is 4 dB, the recognition accuracy of 2FSK-4FSK is up to 88.56%. For 2FSK at 4 dB and 4FSK at -6 dB, the recognition accuracy of 2FSK-4FSK is 1. When SNR of 2FSK is -4 dB and 4FSK is -2 dB, the recognition accuracy of 2FSK-4FSK is up to 1. For 2FSK at -6 dB and 4FSK at -8 dB, the recognition accuracy of 2FSK-4FSK is 93.125%. When SNR of 2FSK is -12 dB and BPSK is 4 dB, the recognition accuracy of 2FSK-BPSK is up to 81.875%. For 2FSK at 4 dB and BPSK at -6 dB, the recognition accuracy of 2FSK-BPSK is 98.75%. When SNR of 2FSK is -4 dB and BPSK is -2 dB, the recognition accuracy of 2FSK-BPSK is up to 96.125%. For 2FSK at -6 dB and BPSK at -8 dB, the recognition accuracy of 2FSK-BPSK is 85.25%. When SNR of 2FSK is -12 dB and EQFM is 4 dB, the recognition accuracy of 2FSK-EQFM is up to 92.625%. For 2FSK at 4 dB and EQFM at -6 dB, the recognition accuracy of 2FSK-EQFM is 1. When SNR of 2FSK is -4 dB and EQFM is -2 dB, the recognition accuracy of 2FSK-EQFM is up to 1. For 2FSK at -6 dB and EQFM at -8 dB, the recognition accuracy of 2FSK-EQFM is 96.5%. Noting that the recognition accuracies of randomly overlapping dual-component signals are all more than 90% at -2 dB, which demonstrates better recognition performance. The reason is the powerful feature extraction and classification ability. Therefore, this work offers important experimental guidance in further enhancing recognition performance under different SNR and promoting the actual applications.

The floating point of operations (FLOPs), parameters, and time are adopted to investigate computational complexity. Table 3 lists the computational complexity of CNN-ST, CNN-DQLN, and residual neural network (ResNet) [48].

Table 3

Computational complexity of three methods

Parameter | CNN-ST | CNN-DQLN | ResNet |

FLOPs (G) | 3.7 | 5.2 | 3.9 |

Parameters (M) | 20.6 | 34.9 | 21.7 |

Time (ms) | 33 | 59 | 34 |

As can be known from Table 3 that FLOPs, parameters, and time of CNN-ST are all lower than CNN-DQLN and ResNet. Therefore, the proposed CNN-ST demonstrates higher computational accuracy and lower computational complexity over others, and possesses enough computational novelty.