## 2 MCSK Communication Technique  
### Principle of MCSK  
The MCSK communication method combines M-ary modulation with CSK modulation. In the M-ary spread spectrum, the transmitter generates several spread spectrum sequences of the same length. The binary data are grouped first, and the amount of information in each group is \(\log_{2}M\) bits, where \(M\) is the number of sequences. Different spread spectrum sequences modulate different groups of information. Therefore, the amount of information carried by one sequence increases from 1 bit to \(\log_{2}M\) bits. In the CSK method, the transmitter generates only one spread spectrum sequence. CSK can modulate multiple bits of information when the generated spread spectrum sequence is cyclically shifted. It uses the cyclic shift of the spread spectrum sequence to map the information [18]. Namely, it uses the phases of spread spectrum sequences to carry information. Therefore, the length of the spread spectrum sequence affects the amount of information contained in each sequence. Pseudo-random sequences have good correlation characteristics, so they are often used as spread spectrum sequences to carry information. There is a series of spread spectrum sequences of the same length as required at both the transmitter and the receiver in the MCSK system. Assuming that M-ary modulation carries \(k_{0}\) bits of information, CSK modulation carries \(k_{1}\) bits of information. The spread spectrum sequence generator is implemented by linear shift registers, and it generates multiple spread spectrum sequences \(c_{i}(t)\), \(1\leq i\leq M\), where \(M\) is the number of spread spectrum sequences. Then, the spread spectrum sequence selector cyclically shifts \(c_{i}(t)\) to obtain \(c_{i,j}(t)\), \(1\leq j\leq N\), where \(N\) is the length of the sequence. Figure 1 shows the MCSK communication scheme. Firstly, the binary data stream is converted from serial to parallel, that is, each \((k_{0}+k_{1})\) bits of information is divided into a group. M-ary modulation of the first \(k_{0}\) bits of information is used to decide which \(c_{i}(t)\) to choose, and CSK modulation of the last \(k_{1}\) bits of information is used to determine the number of cyclic shifts of \(c_{i}(t)\). Therefore, one cyclic shift sequence \(c_{i,j}(t)\) can carry \((k_{0}+k_{1})\) bits of information in MCSK modulation. Compared with DSSS modulation, the amount of information carried by one sequence has been greatly increased, and the signal modulated by the carrier is  
\[s(t)=Ac_{i,j}(t)\cos(2\pi f_{c}t+\varphi_{0}) \tag{1}\]  
where \(A\) is the amplitude of the transmitted signal, \(f_{c}\) is the frequency of the carrier and \(\varphi_{0}\) is the phase of the carrier. After passing through UWA channels, \(s(t)\) is affected by multipath fading and additive noise \(n(t)\). If the propagation delay of the multipath signal is \(\tau_{l}\), \(1\leq l\leq L\), where \(L\) is the number of multipath and the amplitude of the multipath signal at the receiver is \(A_{l}\). The received signal is then expressed as  
\[s_{r}(t)=\sum\limits_{l=1}^{L}A_{l}c_{i,j}(t+\tau_{l})cos(2\pi f_{c}t+\varphi_ {l})+n(t) \tag{2}\]  
At the receiver, spread spectrum sequences are also obtained by the sequence selector and cyclic shift, then the received signal is despread by these spread spectrum sequences and demodulated by the local carrier. Therefore, we can get a matrix \(V_{k,m}(t)\), which is the MCSK integral judgments within the duration of one spread spectrum sequence.