## 3 Signal Demodulation
### PLS-Based Detection Method
#### 3.2.2 Demodulation with PLS Regression
Equation (21) allows to simulate time variation, multi-path effect, propagation loss and random noise occurred during the underwater acoustic propagations by specifying the channel response \(\mathbf{h}\) and ambient noise \(\mathbf{s}_{n}\). The real-life underwater noise is used as the ambient noise in this work. The sound channel response is estimated from a set of experimental data recorded by the Institute of Acoustics of Chinese Academy of Sciences in the South China Sea. Figure 6 plots the smoothed sound velocity profiles at the sending and receiving sites. The acoustic signal was transmitted from a fixed source to a fixed receiver array. Table 1 displays the parameters of the experimental environment and channel estimation. The time coherence of the experimental environment is evaluated by measuring the normalized correlation of two 10-s chaotic signals with a time interval of 5 min. The result value of 0.82 demonstrates that the underwater sound channels are highly correlated during the measurement time. Figure 6: Smoothed sound velocity profiles at the sender (**left**) and receiver (**right**). In order to obtain an accurate ocean channel, three frequently used channel estimation methods are evaluated for selection, including least mean square (LMS) [53], recursive least squares (RLS) [54] and least squares matching pursuit (LSMP) [55] algorithms. Figure 7 plots the mean square error (MSE) between the original channel response and the ones measured with the three methods over the signal-to-noise ratio. It is obtained with the simulated sparse channel response and spreading frequency signal. Finally, we selected LSMP for its high reliability and accuracy. Figure 8 plots a channel response measured using the LSMP algorithm. It can be seen that the histogram possesses multiple peak points, representing the different multi-path arrivals [55]. We do not normalize it in order to keep the attenuation information. The normalized correlation coefficient between the original probe signal and the signals simulated with Equation (21) is 0.79. \begin{table}
\begin{tabular}{l c l} \hline \hline
**Parameters** & **Values** & **Descriptions** \\ \hline Sea depth & 90–100 m & Minimum and maximum sea depths during the propagation. \\ Distance & 16.5 km & Both of the sender and receiver are stationary during the transmission. \\ Source level & 200 dB & - \\ \hline Impulse period & 2 s & - \\ Impulse form & Chaotic & - \\ Sampling rate \(f_{s}\) & 4000 Hz & - \\ Channel tap number \(W_{h}\) & 400 & \(W_{h}=f_{s}\times 0.1\) s. \\ Channel estimation interval & 10 ms & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental parameters of underwater sound channel estimation. Figure 8: An example of channel response measured using LSMP algorithm. Figure 7: Accuracy comparison of channel estimation methods. Now, we can start to generate the desired dataset with Equation (21). Given an 8-bit ASCII code, there are 256 symbol candidates \(u\); for each one, we generate six sessions of simulated signals \(u^{\prime}\). The dataset, therefore, contains 256 candidates \(\times 6\) sessions \(=1536\) simulated symbols. ### Parameter Configuration

The subject of this experiment is to determine the following two parameters of the proposed algorithm: the time length of the symbol \(T\) and the projection direction number of PLS regression \(k\). To do this, three versions of datasets are generated with different symbol time length: \(T=0.3\), 0.6 and 1 s. Next, the proposed method is evaluated with different projection direction numbers. 3 randomly-selected sessions are used for training and the rests for test. The final experiment results are computed by averaging the results of three independent executions. We seek the optimal value of \(k\) by maximizing the recognition rate of the systems experimentally. The recognition rate is defined as the ratio of the correct classification counts and the number of input test symbols.