# Single-Channel Blind Source Separation of Spatial Aliasing Signal Based on Stacked-LSTM
## 5 Experiment
### Case Study 2: Effect under Noisy Environment  
Experimental purpose: First, verify the generalization performance and noise robustness of the Stacked-LSTM algorithm under different noise transmission conditions. The signal-to-noise ratio range was set to SNR = 5\(\sim\)20 dB. Secondly, calculate the time for the six algorithms to separate a single signal to comprehensively compare the running time and separation accuracy of the algorithm. Figure 6 is a graph of the waveform results of 10 mixed signals of the Stacked-TCN algorithm under the condition of SNR = 15 dB. It can be seen that most of the separation results were relatively good, which are basically consistent with the source signal, and have a good separation effect. Compared with the 1-D CNN block, the Bi-LSTM block could overcome the limitation of the receiving domain and convert the sequential input into a 3-D tensor, which had a higher separation potential. It was a more adequate way to model the long-term dependence of the source signal. At the same time, the attention mechanism of the SE module was added to the Bi-LSTM block, which could capture global information and obtain the correlation between different channels, thereby suppressing useless channel information, strengthening useful channel information, and dynamically adjusting the network. In addition, the excellent fitting ability of the LSTM deep neural network could better learn the time domain mask of the source signal. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mixture** & \begin{tabular}{c} **Stacked-** \\ **LSTM** \\ \end{tabular} & \
\begin{tabular}{c} **Conv-** \\ **TasNet** \\ \end{tabular} & **TasNet** &
\begin{tabular}{c} **Wave-** \\ **U-Net** \\ \end{tabular} & **ICA** & **NMF** \\ \hline BPSK\_8 PSK & \(-24.61\) & \(-22.51\) & \(-2.94\) & \(-17.22\) & \(5.36\) & \(9.92\) \\ BPSK\_16 QAM & \(-20.35\) & \(-18.71\) & \(-4.06\) & \(-17.02\) & \(1.64\) & \(6.32\) \\ BPSK\_64 QAM & \(-23.20\) & \(-22.83\) & \(-1.44\) & \(-19.08\) & \(6.02\) & \(8.72\) \\ BPSK\_PAM4 & \(-29.98\) & \(-28.44\) & \(-2.35\) & \(-12.09\) & \(5.92\) & \(8.19\) \\
8 PSK\_16 QAM & \(-13.53\) & \(-13.00\) & \(-3.63\) & \(-13.55\) & \(4.87\) & \(9.82\) \\
8 PSK\_64 QAM & \(-10.89\) & \(-5.96\) & \(-1.98\) & \(-11.31\) & \(1.07\) & \(7.67\) \\
8 PSK\_PAM4 & \(-18.74\) & \(-15.64\) & \(-1.95\) & \(-18.67\) & \(2.68\) & \(6.13\) \\
16 QAM\_64 QAM & \(-7.20\) & \(-6.32\) & \(-2.51\) & \(-1.51\) & \(5.48\) & \(8.73\) \\
16 QAM\_PAM4 & \(-22.81\) & \(-21.61\) & \(-2.25\) & \(-17.31\) & \(5.32\) & \(7.79\) \\
64 QAM\_PAM4 & \(-15.34\) & \(-5.53\) & \(-2.36\) & \(-11.92\) & \(2.50\) & \(5.98\) \\ AVG & \(-18.67\) & \(-16.05\) & \(-2.55\) & \(-13.97\) & \(4.09\) & \(7.93\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Loss of different algorithms on 20 dB mixture (dB). the separation of nine kinds of mixed data. In the separation of the remaining one kind of mixed signal 64 QAM-PAM4, Stacked-LSTM was superior. Compared with Stacked-TCN, Stacked-LSTM was more robust to noise interference. Fourth, from the overall 5-20 dB signal-to-noise ratio range, for the five mixed signals of BPSK-8 PSK, BPSK-64 QAM, BPSK-PAM4, 8 PSK-16 QAM, 16 QAM-PAM4, Stacked-LSTM and Stacked-TCN methods were basically the same. In the other five cases, Stacked-LSTM. The method obviously had an advantage in separation accuracy. These results are due to the fact that NMF and ICA were model-driven machine learning methods, which are essentially shallow models, suitable for tasks with small samples and precise models. However, single-channel blind source separation is a difficult problem with very little prior knowledge. The shallow model was not enough to describe its essential characteristics, and it failed to make full use of the deep characteristics and information of the signal. The ability to generalize to big data was weak. Under extreme ill-conditioned single-channel conditions, the separation performance was poor.