## 1 Introduction
The matched filters obviously do not have the ability to suppress the non-Gaussian-distributing noise and channel multi-path effects. In underwater communications, it is, therefore, usually combined with the equalization techniques or passive-phase conjugation method to mitigate the distortions form the channels of this type [7; 28; 29; 30]. [PERSON] et al. successfully realized the deep-water 204-km 660-bps, shallow-water  
Figure 1: Period estimations of m- and chaos sequence spread spectrum signals with power spectrum density (PSD) reprocessing [15]. (**a**) m-sequence; (**b**) Chaos sequence. 89-km 1000-bps, and shallow-water 3.7-km 10-kbps underwater communications with equalization optimizations, respectively [28]. It is claimed that a passive-phase conjugation-based communication method achieved an average bit error ratio (BER) of \(10^{-6}\) at \(SNR=-5\) dB with simulations [7], and a successful communication with the distance of 900 km in a deep-water experiment [31]. Yet, unlike common acoustic signal detections which distinguish the interested signal from the ambient noise, chaos spread spectrum signal demodulation is a recognition task that is much more complicated. It has to find out the right class of the received symbol from a large candidate set, necessitating the target classification capacity via feature analysis. In our opinions, today's underwater sound communication techniques can be further improved from the following two aspects:  
* High-performance symbol classification method. Though the conventional matched filters are able to enhance the symbol energy over noise by providing a processing gain with maximal SNRs, all of the components of the symbol sequences or vectors are unintentionally considered to contribute equally to the model precision without feature analysis, resulting in values of the key components that are diluted by the others. Hence, there are still some opportunities to further improve the accuracy performance of the demodulators through feature analysis. * Noise analysis. Submarine noise is one of the main interferences with the quality of underwater communication. They come from a variety of sources, such as marine life, sea quakes, rain, artificial constructions, etc. The ambient noise of transducers are highly random, and the analysis of their statistical distribution feature helps potentially to improve the reliability of underwater communication modalities. For the issues mentioned above, we focus our work on the investigation of machine learning-based chaos spread spectrum signal demodulation techniques. It is motivated by the fact that machine learning methods handle the classification problem by making data-driven predictions or decisions through building a statistical model from sample inputs. It provides a nice solution to statistically analyze the data features from the given sample sets. Because this procedure is automatic, it is especially appropriate to establish the physical models which are hard to be described using a precise analytic function. Within underwater communications, the received signals are distorted from the transmitted signals via the underwater sound channels with random noise interferences, so it can be considered that they contain all of the necessary factors of the propagation model. Learning directly from the original data with a proper approach may help to build a precise model to benefit underwater communication techniques from signal and environment feature analysis. This paper is devoted to the underwater acoustic communication scheme. A new proposed chaos phase modulation method for underwater communication [32] is used to modulate the communication symbols. The chaos phase modulation method first arose in the 1990s [33; 34] and was then used in radar systems [35; 36] and high-performance multi-channel secure underwater communications [32].