# A Joint Denoising Learning Model for Weight Update Space-Time Diversity Method +
## 5 Evaluation and Result Analysis  
Numerical simulations and a lake trial were conducted to evaluate the performance of the proposed algorithms. The transmit signal is designed for data framing according to the structure shown in Figure 14. Under a low SNR, the time-bandwidth product of the linear frequency modulation (LFM) signal should be large enough for frame synchronization detection. Thus, the detection probability of the received signal is improved by obtaining a more significant gain of the correlation operation. The first LFM signal is used in the correlation operation of the received signal to detect the implementation of frame synchronization and the time delay estimation of the multipath. The latter LFM signal is used to perform a coarse estimate of the Doppler frequency offset. In addition to the transmitted information bits, the modulated signal in the data frame carries a training sequence used to train the channel estimator to guarantee the convergence of its tap coefficients. The parameter settings of DS-CDMA in the simulations and lake trial are shown in Table 1. In the simulation system, the specifications of our computer were as follows: Intel(R) Core(TM) i5-6400 CPU 2.7 GHz (4 cores), 16 GB RAM, 1 TB memory with Windows and MATLAB installed. We simulated the noise with the amplitude \(A\) of the linear part of the spectrum in VURN as a normalized value, \(A=0.3\); the number of propeller blades is \(n_{b}=3\); the shaft frequency of the propeller is \(f_{p}=100\) Hz; the number of line spectra is \(N=8\); the initial phase is \(\varphi_{i}=45\). In the continuous spectrum, the duration period is \(M=10\); the degree of mixing between consecutive signals is \(\sigma_{i}\), which takes the value of 0.4. To make the simulation effect as close as possible to the lake test, we set the SNR as the broadband SNR, taking the value of \([-20,\,10]\) dB. Figure 15a shows the time-domain visualization results of VURN, and Figure 15b shows the spectral characteristics of VURN, which contains both linear spectra and continuous spectra. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values of the Simulations and Lake Trial** \\ \hline Bandwidth & 5 kHz \\ Carrier frequency & 10 kHz \\ Spread spectrum code & 7-order m-sequence \\ Filter roll-off factor & 0.25 \\ Bit rate & 26.5 bps \\ Frame synchronization signal pulse width & LFM (50 ms) \\ Carrier synchronization & 2-order phase-locked loop \\ Channel coding & 1/2 convolutional codes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameter settings of DS-CDMA in the simulations and lake trial. Figure 14: Design of transmitting signal structure. Figure 15: Visualization results of the time-domain and frequency spectrum of VURN: (**a**) the time-domain visualization results of VURN; (**b**) the spectral characteristics of VURN. In the simulation experiment, the input data are received signal \(\mathbf{y}(t)\) and reference noise \(\tilde{\mathbf{n}}(t)\). After pre-processing, 4000 frames \(\left(\mathbf{TR}_{y},\mathbf{TI}_{y}\right)\) and 4000 frames \(\left(\mathbf{TR}_{\tilde{n}},\mathbf{TI}_{\tilde{n}}\right)\) were obtained. \(\left(\mathbf{TR}_{y},\mathbf{TI}_{y}\right)\) and \(\left(\mathbf{TR}_{\tilde{n}},\mathbf{TI}_{\tilde{n}}\right)\) denote the orthogonal compression features of \(\mathbf{y}(t)\) and \(\tilde{\mathbf{n}}(t)\). The 3000 frames of data are the training dataset, and 1000 frames of data were used for the testing dataset. During the training of the noise-reduction learning model, the learning rate was set to 0.001, the learning step was 2, and the batch size was 16, and the training was complete after 400 epochs of data iterations. In the structure of the complex-CGAN, the input feature size of the GM was \(4\times 32\), which was downsampled into \(4\times 4\) feature data after convolution and pooling layers. Then, processed by depthconcat and the activation function to form data of size \(4\times 32\), the final output upsampling result was \(4\times 128\).