# Deep Learning-Based Cyclic Shift Keying Spread Spectrum Underwater Acoustic Communication
## 2 System Structure  
### Conventional CSK-SS UWA Communication System Structure  
The CSK-SS UWA communication system uses the cyclic shift characteristic of pseudo-random sequence to encode and map the information bits. The spreading sequence with \(i\)-th order, code length of \(N\) can be cyclic shifted \(2^{i}\) times. In addition, each spreading sequence can carry up to \(i-1\) bits of information after cyclic shift coding mapping. Compared with the conventional DSSS system, each spreading sequence carries 1 bit information, the communication rate of CSK-SS system is \(\lfloor\log_{2}(N)\rfloor\) times higher than that of DSSS system with the same code length under the same conditions. The structure of a conventional CSK-SS UWA communication system is shown in Figure 1. First, a cyclic shift matrix can be defined as  
\[H=\left[ \begin{array}{cc}0_{1\times(N-1)}&1\\ 1&0_{(N-1)\times 1}\end{array} \right], \tag{1}\]  
Each cyclic shift of the spreading sequence can be obtained by multiplying the matrix \(H\) by the spreading sequence once. At the transmitter of the system, the spreading sequence is generated by the code sequence generator. Carry out the serial-parallel conversion on the transmission sequence \(x(n)\), convert the binary bitstream information into a decimal data stream with \(m\) bits, and shift the symbols of the spreading sequence by using the decimal data stream information. \[c_{j} =\mathrm{H}^{j}c, \tag{2}\]  
where \(c\) represents the vector form of the spreading sequence, \(c_{j}\) represents the spreading sequence obtained after \(j\) cyclic shifts of the spreading sequence \(c\), \(1\leq j\leq N\). After carrier modulation, the transmitted signal can be expressed as  
\[s(t)=Ac_{j}(t)\cos(2\pi f_{c}t+\varphi_{0}), \tag{3}\]  
where \(A\) is the amplitude of the transmitted signal and \(c_{j}(t)\) is the spreading code with a code length of \(N\) and chip duration of \(T_{c}\). Assuming that the duration of each symbol is \(T_{s}\), \(T_{s}=NT_{c}\), \(f_{c}\) and \(\varphi_{0}\) are the carrier frequency and initial phase, respectively. The transmitted signal reaches the receiving end of the system after passing through the underwater acoustic channel. In the propagation process, this paper focuses on the impact of multipath fading and noise on the received signal. The received signal can be represented as  
\[ \begin{array}{rcl}r(t)&=\sum\limits_{l=0}^{L}A_{l}c_{j}(t-\tau_{l})\cos(2 \pi f_{c}t+\varphi_{l})+n(t),\\ &=&A_{0}c_{j}(t-\tau_{0})\cos(2\pi f_{c}t+\varphi_{0})+\sum\limits_{l=1}^{L-1} A_{l}c_{j}(t-\tau_{l})\cos(2\pi f_{c}t+\varphi_{l})+n(t),\end{array}  \tag{4}\]  
where \(\tau_{0}\) is the propagation delay of the main path signal and \(A_{0}\) is the amplitude after attenuation. \(\tau_{l}\) is the propagation delay of multipath signal, \(1\leq l\leq L\), \(L\) is the number of multipath signals, \(A_{l}\) is the amplitude of multipath signal reaching the receiving end, \(\varphi_{l}\) is the phase of the multipath signal, \(\varphi_{l}=2\pi f_{c}\tau_{l}+\varphi_{0}\), \(c_{j}(t-\tau_{l})\) is the shift spreading sequence generating delay, and the local carrier is \(\cos(2\pi f_{c}^{\prime}t+\varphi^{\prime})\). When the system carrier is synchronized, \(f_{c}^{\prime}=f_{c}\), \(\varphi^{\prime}=\varphi_{0}\), and \(n(t)\) are additive Gaussian white noise. \(c_{k}(t)\) can be obtained from the locally generated spreading sequence through the sequence selector and cyclic shifter. \(k\) is the symbol shift information, \(1\leq k\leq N\). After the system completes symbol synchronization, \(c_{k}(t-\tau_{0})\) can be obtained. Figure 1: Conventional CSK-SS UWA communication system structure. After passing through the low-pass filter, only the integral output within the duration of one symbol is considered. Within the duration \(\tau_{0}\leq t\leq T_{s}+\tau_{0}\), the output of the integrator can be expressed as  
\[