## 3 Signal Demodulation
### PLS-Based Detection Method
#### 3.2.2 Demodulation with PLS Regression
): \(\mathcal{T}_{PLS}=n\times T\times f_{s}\). Similarly, the time complexity of the matched filter is \(\mathcal{T}_{MF}=n\times T^{2}\times f_{s}^{2}\). As for the forward propagation of a BP network, when the size of a hidden layer is \(n-1\), its time complexity is \(\mathcal{T}_{BP}=(n-1)\times T\times f_{s}+n^{2}\). With the experiment protocol of this paper, PLS model clearly has the lowest time complexity, whereas matched filter the highest. Table 3 lists the implementations of the proposed and the two reference algorithms. They are implemented by using the multi-core CPU platform presented in Section 4. The indices \"_ori\" and \"_opt\" refer to the original and optimized implementations, respectively. The detection step of the matched filter (see Equation (2)) and the message generation steps of all the three algorithms are parallelized. The running speed measurements cover all the accelerated steps, including detection and decision. The CPU used is Intel(R) Corel(TM) i7-6700 CPU 3.4 GHz. The ratio of the running time, known as acceleration ratio, is used as the efficiency evaluation criterion, and the running time of _ntf_ori_ with \(T=0.3\) s (72.8 ms per symbol) is set as the measuring basis. Figure 12 displays the acceleration ratios of all the implementations. Firstly, we can see that the implementations based on machine learning methods are much more efficient than the matched filters. Their running speed gaps are hundreds of times. With matched filters, the received symbol is correlated with the replicas of the original symbols point by point along the time axis, which is quite time-costly. By contrast, the PLS model and the forward propagation process of BP networks are essentially matrix/vector multiplication operations with low computation intensity. So, even if the running speed has been multiplied through multi-thread optimization, their temporal efficiency performance are still not on the same order of magnitude. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Names** & **Algorithms** & **Optimzations** \\ \hline _mf\_ori_ & Matched filter & None \\ _mf\_opt_ & & Multi-thread parallelization \\ \hline _bp\_ori_ & BP network & None \\ _bp\_opt_ & & Multi-thread parallelization \\ \hline _pls\_ori_ & PLS regression & None \\ _pls\_opt_ & & Multi-thread parallelization \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Description of multi-core CPU implementations. Figure 12: Running speed comparison results: \(f_{s}=4000\) Hz. Secondly, comparing with the original implementations, the optimized implementations are accelerated by around three times. In this experiment, a four-core CPU is used, so the speed-up should have been four times higher than measured values (in theory). This is caused by the following two reasons:

1. the implementations are partly optimized instead of completely parallelized. The multi-thread optimizations of _pls_cpu_ and _bp_cpu_ cover only the message generations without detection steps;
2. the shared memory architecture is constrained by the von Nuemann bottle neck, the memory access conflicts may be occurred when multiple thread functions are invoked simultaneously. Depending on the efficiency evaluation result, the time costs of all the implementations are lower than \(T\), satisfying the constraints of real-time processing. Therefore, the communication rate \(\mathcal{R}\) is only constrained by \(T\). Given that a symbol represents a bit stream of 8-bits with ASCII code, \(\mathcal{R}\) can be estimated as \((8\times m)/(m\times T+d/c_{s})\) in theory, where \(m\) is the received symbol number or the size of the transmitted message, \(d\) is the distance between the sender and receiver and \(c_{s}\) is the underwater sound speed. ## 6 Conclusions

This paper presents a novel machine learning available demodulation scheme for underwater communication applications based on the chaos phase modulation spread spectrum techniques. Thanks to the characteristic of a large number of phase-shift keying, it is more appropriate for confidential communication applications.