# Chaos-Based Underwater Communication With Arbitrary Transducers and Bandwidth
## 4 Conclusions  
In this paper, a DCSK scheme based on a first order hybrid chaotic system is being proposed for the underwater acoustic channel. Different from the conventional DCSK and its enhanced versions that utilize the orthogonality property of the chaotic signal to recover the bit information from the highly distorted receiving signal, the proposed method uses sinusoidal and its orthogonal waveforms to separate the reference signal and the information bearing signal. It not only yields doubled data  
Figure 7: Performance comparison of conventional DCSK, NR-DCSK, HE-DCSK, RM-DCSK, PS-DCSK, CDSK and the proposed method over the underwater acoustic channel.  
transmission rate as compared to the conventional DCSK with the same spreading gain, but also reduces the complexity of the communication system by removing the delay component that is difficult to implement in CMOS technology. It also moves the chaotic signal spectrum to adapt to the bandwidth of the communication equipment so that the modulated signal can be compatible with the conventional transducer or antenna. Our proposed method is insensitive to channel distortion and does not require chaotic synchronization, channel estimation and complicated equalization algorithm. It achieves better BER performance than the conventional DCSK, CDSK, HE-DCSK, PS-DCSK and RM-DCSK in both the AWGN channel and the underwater acoustic channel. It is credited to the use of the special chaotic waveforms and the corresponding matched filter. The matched filter reduces the effects of noise and multipath propagation. Then, the correlation operation using the points with maximal SNR further improves the BER performance. Hence, the proposed method achieves better communication reliability, especially for the complex underwater acoustic channel. A future work will be to extend the present method to more complicated underwater acoustic channels [8; 9] and to validate experimentally the proposed method in a lake or a sea trial. We also plan to investigate the method to improve the data transmission rate (such as using the Orthogonal Frequency Division Multiplexing technique). Finally, the chaotic oscillator uses an external clock to control the switching states of the system. It avoids the timing jitter or phase noise of the electronic oscillator circuit, which ensures the frequency stability of the chaotic signal and provides the possibility of eliminating sampling errors among the different transmission frames in a complex underwater time-varying acoustic channel. All that has additional practical benefits for communication applications.  
This research is supported in part by National Natural Science Foundation of China (61172070), Innovative Research Team of Shaanxi Province (2013 KCT-04), The Key Basic Research Fund of Shaanxi Province (2016 ZDJC-01), EPSRC (EP/I032606/1), [PERSON] was supported by Excellent Ph.D. research fund (310-252071603) at XAUT.  
[PERSON] did the simulations and wrote the draft paper; [PERSON] designed the project and the simulation framework, analysed the results and wrote the paper; [PERSON] wrote the paper and discussed the problem; [PERSON] analysed the simulation results and contributed to writing the manuscript.  
The authors declare no conflict of interest.