## 3 Signal Demodulation
### PLS-Based Detection Method
#### 3.2.2 Demodulation with PLS Regression
Compared to the reference algorithms, experiments demonstrate that the proposed approach possesses higher accuracy performance with low SNR and high communication rate. The main originalities and contributions of this paper include:

1. The proposed demodulation scheme handles the signal demodulation as a target recognition problem, allowing us to incorporate advanced classification methods into it, benefiting from the recent progresses of pattern recognition techniques. Because machine learning methods are able to statistically analyze the symbol features and noise characters, it can provide better demodulation accuracy performance than matched filters with shorter symbol sequences. That is, if the same accuracy performance is desired, the conventional matched filters need long symbol sequences in order to get enough time gains, so adopting machine learning methods, especially PLS regression, can considerably improve the underwater communication applications in terms of communication rates;
2. It is found that the chaos-spreading spectrum signals have the characteristic of multicollinearity which may potentially impact the performance of certain classifiers negatively. Fortunately, the algorithm family of PLS can somehow overcome this disadvantage by modeling the relationships between the predictor and response variables, even with a sparse training dataset;
3. The running cost of the proposed approach is very low. The detection steps of the proposed scheme costs only several milliseconds with the experiment protocol of this paper, which even can be ignored during the overall demodulation procedure, so it possesses high temporal efficiency performance;
4. The proposed demodulation algorithm can be easily transplanted to other hardware platforms for different purposes. The detection process of the proposed algorithm is actually an operation of matrix production, which can be easily implemented and optimized by using any currently available computing platforms. Meanwhile, some issues exist still. Firstly, the spatial variations and frequency-shift characteristic of underwater sound propagations are not considered in the simulation; some more evaluations with real-life experiment data are strongly required in future studies. Secondly, the experiment of this paper demonstrates that PLS regression has better accuracy performance than BP networks. However, it cannot be concluded that PLS regression is always the best classifier for all the three mentionedmethods, because the training set of this paper is sparse, far away from the requirement of deep learning. In the future work, we aim to attempt to further improve the evaluation experiment with the standard of deep learning. Thirdly, the PLS-based demodulator is able to resist some variation of communication channel, but it should be noted that the underwater sound channels sometimes rapidly vary in real-life applications. The training frequency of the PLS model will, therefore, be studied and a solution with real-time learning will be investigated. Finally, the parallel implementation of the training process of the proposed algorithm is not discussed in this paper. Some optimization properties within the instruction and data levels with other refined development tools, i.e., MPI for multi-core CPUs or CUDA for GPUs, still exist and are worth being investigated further. [PERSON] and [PERSON] conceived the paper and analyzed the paper. [PERSON] and [PERSON] conceived the paper. * _[PERSON] et al. (2009)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] A Spectral Method for Period Detection of PN Sequence for Weak DS-SS Signals in Dynamic Environments. In Proceedings of the 2009 International Conference on Networks Security, Wireless Communications and Trusted Computing, Wuhan, China, 25-26 April 2009; pp. 266-269. * [PERSON] and [PERSON] (2002) [PERSON]; [PERSON] Chaos communications-principles, schemes, and system analysis. _Proc. IEEE_**2002**, _90_, 691-710. [CrossRef]
* [PERSON] (2004) [PERSON] A Survey of Chaotic Secure Communication Systems. _Int. J. Comput.