# A Joint Denoising Learning Model for Weight Update Space-Time Diversity Method +
## 4 A Joint Denoising Learning Model for Weight Update STD Method
### The STD Model Based on Weight Update Strategy
The received signals are combined according to the maximum  
Figure 13: The structural composition of the STD model based on the weight update strategy. SINR. The power of the transmitted signal is denoted as \(D[s(t)]=E_{b}\). The transmitting symbols are independent of each other, then the output power of the transmitting signal in the \(p\)th diversity branch is  
\[N_{p}=D\left[\mathbf{w}_{p}^{\text{H}}\left(\sum_{\tau_{p}}^{L}\delta_{i} \mathbf{A}_{l}\mathbf{s}_{l}\big{(}t-\tau_{p}\big{)}\right)+\mathbf{w}_{p}^{ \text{H}}\left(\sum_{l=1}^{L}\mathbf{A}_{l}\mathbf{s}_{l}\big{(}t-\tau_{p} \big{)}+\mathbf{n}(t)\right)\right], \tag{22}\]  
Then, the SINR of the \(p\)th diversity receive branch is  
\[\text{SINR}_{p}=\frac{\sigma_{p}}{N_{p}}, \tag{23}\]  
The purpose of the STD combining is to maximize the value of \(\text{SINR}_{p}\) taken. The signal received by each diversity branch is multiplied by the gain factor \(\sqrt{N_{n}/N_{p}}\), so that it has the same noise output power \(N_{n}\). \(\sigma_{p}\) is the output power of the \(p\)th path signal, space domain then multiplied by the weighting factor \(\eta_{p}\). \(\eta_{p}\) is the eigenvalue of the weight matrix \(\mathbf{w}_{p}\). The combined signal is denoted as:  
\[\mathbf{y}(k)=\sum_{p=1}^{L}\eta_{p}\sqrt{\frac{N_{n}}{N_{p}}}\mathbf{w}_{p}^{ H}s\big{(}t-\tau_{p}\big{)}, \tag{24}\]  
The power of the useful signal in the STD combining signal is:  
\[E_{c}=\left(\sum_{p=1}^{L}\big{|}\eta_{p}\big{|}\sqrt{\frac{N_{n}}{N_{p}}\cdot \sigma_{p}}\right)^{2} \tag{25}\]  
The power of interference and noise in the STD combining signal is:  
\[N_{C}=\sum_{p=1}^{L}\big{|}\eta_{p}\big{|}^{2}N_{n} \tag{26}\]  
According to Equation (23), the SINR of the combined STD signal is obtained using [PERSON]'s inequality as:  
\[\text{SINR}_{c}=\frac{E_{c}}{N_{c}}=\frac{\left(\sum_{p=1}^{L}\big{|}\eta_{p} \big{|}\sqrt{\frac{\sigma_{p}}{N_{p}}}\right)^{2}}{\sum_{p=1}^{L}\big{|}\eta_ {p}\big{|}^{2}}\leq\frac{\left(\sum_{p=1}^{L}\big{|}\eta_{p}\big{|}^{2} \right)\sum_{p=1}^{L}\left(\frac{\sigma_{p}}{N_{p}}\right)}{\sum_{p=1}^{L} \big{|}\eta_{p}\big{|}^{2}}=\sum_{p=1}^{L}\left(\frac{\sigma_{p}}{N_{p}}\right) \tag{27}\]  
When \(\big{|}\eta_{p}\big{|}=\sqrt{\sigma_{p}/N_{p}}\), the SINR can reach the maximum value \(\sum_{p=1}^{L}\big{(}\sigma_{p}/N_{p}\big{)}\). This results in a combined output with the best communication effect. After a thorough analysis of the underwater environment, this paper argues that the UWA signal can refer to the characteristics of the sound and image when applying the DL model. After that, the proposed noise-reduction learning model is applied to complete the noise-reduction process for the received signal. Then, the optimal combining of the noise-reduced signals is achieved using the proposed STD model based on the weight update strategy. An improved STD model effectively suppresses MAI. The final combined signal with a lower SNR is obtained; theoretically, the received signal has a lower BER. We conducted simulation tests and on-lake tests to verify the effectiveness of the proposed method.