# Chaos-Based Underwater Communication With Arbitrary Transducers and Bandwidth
## 1 Introduction
However, as a complex communication channel, underwater acoustic communication channel suffers from more serious constraints as compared to air-based wireless communication, such as multipath propagation and time-varying delays, Doppler frequency shift phenomenon, and ambient noise. The underwater acoustic communication channel calls for overall better reliability, not just higher bit transmission rate. The chaotic signal has been proved to be an optimal waveform for communication in the sense that it allows for the use of a very simple matched filter structure in a white noise channel [32; 33; 34]. Encouraged by those works, a DCSK system is proposed based on a first order hybrid chaotic system and the PS-DCSK system. In this method, the chaotic signals are generated by the first order hybrid system rather than the logistic maps used in Reference [30]. There is a basis function for the first order hybrid chaotic system. A coherent operation using the received signal and the time reverse of the basis function maximizes the signal to noise ratio (SNR) at the receiver [32]. Moreover, in the proposed DCSK configuration, multi-points with maximum SNR are used to decode the information, which further improves the performance of the proposed method as compared with the PS-DCSK system. The reference signals and the information bearing signals are modulated separately into a sinusoidal signal and its orthogonal waveforms. From the energy point of view, the energy efficiency of our proposed method is the same as the conventional DCSK. However, it not only doubles the data transmission rate by sending one bit information within one time slot, but also simplifies the structure of the communication system by eliminating the delay and switch components, which are necessary and difficult to implement in the conventional DCSK system [22; 27; 28]. The proposed method does not need chaotic synchronization between the transmitter and the receiver, and does not require channel estimation and complicated equalization algorithm, which are necessary for most conventional underwater acoustic communication methods. The proposed method shows strong robustness against channel distortion and multipath propagation in the underwater acoustic channel. In addition, the first order chaotic hybrid system uses an external clock to regulate the updating of the system switching states, which is isolated from the rest of the chaotic system. It avoids the time jitter or phase noise of the switching state in real electronic oscillator circuit, and provides a more accurate state switching interval as compared to that of autonomous chaotic oscillators used in [33; 34], which helps to generate accurate frame duration and to decode the information using the maximum SNR property of the matched filter, thus improving the BER performance. Therefore, the chaotic signal used is easy to generate and control, with practical benefits for communication applications. In the proposed communication system, the reference chaotic signal and the binary information bearing chaotic signal are used to amplitude modulate the sinusoidal and cosines waveform with the same frequency, respectively, and summed together to produce an encoded signal not only compatible with the available transducer for the communication but also suitable for the bandwidth of interest. This paper is organized as follows: The proposed DCSK system is introduced in Section 2. In Section 3, simulation results of the proposed method are given and compared with the conventional DCSK [21], NR-DCSK [23], RM-DCSK [27], HE-DCSK [28], Phase-Separate DCSK [30] (PS-DCSK) and correlation delay shift keying [31] (CDSK). Conclusions are given in Section 4.