# A Joint Denoising Learning Model for Weight Update Space-Time Diversity Method +
## 5 Evaluation and Result Analysis
### Simulation Results
\[\max_{m-1,\cdots,M}|\kappa(\mathbf{u}_{nt},\mathbf{u}_{\omega_{m}})|\leq\mu_{0} \tag{29}\]  
The CNN-based noise-reduction method refers to the structure in the literature [x]. In this case, the network is divided into three parts: the first part is Conv+ReLU (1 layer); the second part is Conv+BN+ReLU (3 layers); the third part is Conv (1 layer). The learning objective is the residuals between signals, and the loss function uses the mean-squared error (MSE) criterion. The input of the CNN noise-reduction method and the proposed method are the same data, and the difference is that the CNN method does not have the same pre-processing process as the proposed method. We compared the recognition rate and root-mean-squared error (RMSE) and the proposed algorithm for the received signals. The above algorithm comparisons were made in the case of \(\theta 1=30^{\circ}\), and the compared methods include Wiener filtering, the KBM-ANC, the CNN, and the proposed method, where \"Ours1\" denotes the noise-reduction processing model of the first stage in the proposed method. The above experiments were repeated 200 times, and the SNR varied from \(-20\) to \(10\) dB. The statistical signal recognition rate is the probability that the noise-reduced signal \(\hat{\mathbf{y}}(t)\) can be judged as the transmit signal \(\mathbf{s}(t)\). The signal recognition rate reflects the noise-reduction effect of each algorithm, and the RMSE reflects the stability of each of the above algorithms. Figure 18a shows the signal recognition rate comparison of each method. Figure 18b shows the RMSE comparison of each method. As can be seen in Figure 18a, the proposed algorithm shows a more excellent signal recognition rate when dealing with noise-reduction processing, which indicates that the proposed algorithm has the best noise-reduction effect. It is rather obvious that the other three methods have extremely poor noise-reduction at lower SNRs because none of the above three can handle complex-type data. However, it is worth noting that the CNN method significantly improves noise-reduction compared to KBM-ANC. The Wiener algorithm has the worst noise-reduction effect, and this is because the simulation environment we designed is a nonlinear system, which causes it to be not applicable. Figure 18b shows that the proposed algorithm also maintains the same stability advantage in the RMSE. Figure 18: Comparison of signal recognition rate and RMSE of each algorithm: (**a**) the signal recognition rate comparison of each method; (**b**) the RMSE comparison of each method. Theoretically, after the noise-reduction in the first stage, the BER of STD diversity processing in the second stage will decrease. Because the STD's beamforming performance will be improved when the effect of noise is reduced, the system's estimation of the main path angle will also be more accurate, resulting in a lower BER of the communication. The ability to cope with the effect of MAI is also reflected in the performance of the BER. The lower the BER, the better the system suppresses MAI. To verify the suppression effect of each type of method on MAI, in Figure 19a, we compare the RMSR of the above noise-reduction methods jointly processed by STD and the RMSE of the above noise-reduction methods jointly processed by STD and weight-based update. In Figure 19b, we also performed the same BER comparison, which is used to illustrate the effect on the communication quality improvement. \"Wiener+STD\" means that the Wiener method is used for noise-reduction in the first stage, and the conventional STD method is used for diversity combining in the second stage. Joint methods such as \"KBM-ANC+STD\", \"CNN+STD\", and \"Ours1+STD\" also exist. \"Ours1+STD\" indicates that the proposed noise-reduction learning model is used in the first stage, and the traditional STD method is used in the second stage. Similarly, these noise-reduction methods can be jointly processed with the proposed weight-based update STD.