# A Joint Denoising Learning Model for Weight Update Space-Time Diversity Method +
## 5 Evaluation and Result Analysis
### Lake Experimental Results  
To further verify the proposed algorithms, a real lake experiment was performed at Huating Lake, Anhui Province, China, in July 2021. The transmit signal was consistent with the simulation test. The receiving array was 5 m away from the tugboat, and the transmit angle was 30 and 60. The receiving array was a four-element ULA with a 2 m array spacing, and the transmitting end was 100 m from the receiving array. Before the on-lake communication test, we performed channel measurements with LFM signals and measured the on-lake SNR to about 5 dB. In the experiment on the lake, the tugboat was at  
Figure 19: Comparison of RMSE and BER performance between various joint algorithms: (**a**) the RMSE performance comparison between various joint algorithms; (**b**) the BER performance comparison between various joint algorithms. a standstill, but the engine was always in working condition; the effect of noise was always present. The received signal, as shown in Figure 20, was obtained from four array elements. To verify the noise-reduction capability of the proposed method for the experimental data on the lake, we performed a time-frequency-based visualization comparison of the noise-reduction results. The UWA signal has both the characteristics of an acoustic signal and the two-dimensional properties that can be represented as an image. A two-dimensional visual comparison of the noise-reduction signal can reflect the effect of noise-reduction. Figure 21 shows the two-dimensional visualization comparison of the four noise-reduction methods after processing. The better the noise-reduction, the clearer the two-dimensional visualization. The visualization results in Figure 21 show that the proposed noise-reduction learning model maintains the same advantage in the on-lake experiments. Noise-reduction of the received signal will give a more accurate angle of beamforming estimation in the STD. To verify the improvement of STD performance by noise-reduction methods, we compared the statistics of STD-estimated angles after processing by various noise-reduction methods. We performed 100 operations under each angle for the statistics. Figure 22 shows the statistics of angle estimation. The results show that Wiener filtering and the KBM-ANC can hardly improve the accuracy of angle estimation; although the convergence of the angle estimates of the CNN method is better, the accuracy is still low; the proposed method has the best convergence for angle estimation and has a more significant accuracy of angle estimation. The above comparison results show that the noise-reduction process has performance improvement for STD, which is reflected in the accurate estimation of the main diameter angle. Figure 21: The two-dimensional visualization comparison of the four noise-reduction methods after processing. Figure 20: Time-domain visualization of the received signal in the on-lake experiment. Both the noise-reduction effect and the performance improvement of noise-reduction on STD showed the effectiveness of the proposed method. To further verify the inhibitory ability of the proposed method on MAI, a two-stage comparison of the joint method was carried out in the on-lake experiment. The statistical results are shown in Table 3 and include the RMSE and BER for the two emission angles \(\theta 1=30^{\circ}\) and \(\theta 2=60^{\circ}\). The proposed method maintains a better suppression of MAI from the statistical results in both perspectives. In the on-lake experiments, the proposed method effectively resists MAI due to the adoption of CDMA signals and improves the communication quality. To more intuitively reflect the suppression effect of the proposed method on MAI, we also compared the constellation plots. A constellation plot is a visualization used to describe improvements to communication quality. The more convergent the constellation plot is, the better the communication is indicated in this paper, i.e., the better the suppression of MAI.