# High-Reliability Underwater Acoustic Communication Using an M-ary Cyclic Spread Spectrum
## 2 Proposed Method  
### Principle of MCSS  
Each symbol in the M-ary Spread Spectrum (MSS) group of pseudorandom codes can represent M bits and has a quantity of \(Q\) (\(Q=2^{M}\)). Cyclic Shift Keying (CSK) is a communication method in which the pseudonoise (PN) sequence is cyclic shifted and the shifted information is demodulated through the peak. Depending on the amount of cyclic shift, the bit that can be expressed is defined. For example, a cyclic shift of \(2^{N}\) is required to represent N bits [25]. However, since demodulation is performed through the peak position, it is highly prone to Doppler spread. Both are much more efficient in transmitting data than the conventional direct sequence spread spectrum. Via MSS communication, we can express M bits, N bits with CSK communication, and (M + N) bits in a single symbol. As a result, we transmit MSS with \(Q\)_PN_ sequences and CSK with \(1\)_PN_ sequence, resulting in \(Q\ +1\)_PN_ sequences. We created a very long _PN_ sequence (\(2^{k}-1\), where \(k\) is a very large constant) and then cut it to the appropriate length, then used it to generate the \(Q\ +1\)_PN_ sequence. The very long _PN_ sequence is expressed as:  
\[ \begin{split}&\mathbf{c}_{PN}=\big{[}\mathbf{c}_{1},\mathbf{c}_{2},\ \dots\ \mathbf{c}_{2^{k}-1}\big{]}.\end{split}  \tag{1}\]  
\[ \begin{split}&\mathbf{C}(q,l)=\mathbf{c}_{PN}(l+L\times q)\\ & q\in[0,\ \dots\ Q],\quad l\in[1,\ \dots\ L]\end{split}  \tag{2}\]  
where \(\mathbf{C}\) is the \(q\times L\) matrix and \(L\) is the length of a _PN_ sequence used for one symbol. The first row in the \(\mathbf{C}\) matrix is \([\mathbf{C}(0;1),\dots,\mathbf{C}(0;1)]\) and is expressed as \(\mathbf{C}_{0}\). As a result, the \(\mathbf{C}\) matrix has the form \([\mathbf{C}_{0};\mathbf{C}_{1};\ \dots\ ;\ \mathbf{C}_{Q}]\). One of the most significant advantages of MSS is that these multiple code sequences are suitable for communication with a low probability of intercept (LPI). Below, Figure 1 is a four-by-four matrix. The image in the top left, for example, is autocorrelated with the first _PN_ sequence, and the figure to the right of it is a picture of cross-correlating the first _PN_ sequence with the second _PN_ sequence, and so on. The proposed method represents M data in the MSS method and N data in the CSK method. A decimal representation of several bits that make up a single symbol is N and M. If three consecutive bits are of the form '101', for example, \(n\) is 5. The nonshifted _PN_ sequence and the shifted _PN_ sequence are combined to form one symbol. The proposed method applies a _PN_ sequence cyclic shift method, but unlike the conventional CSK method, the MSS and cyclically shifted _PN_ sequences overlap, as shown in Figure 2. The _PN_ sequence used for CSK is denoted by \(\mathbf{C}_{0}\), and the _PN_ sequence used for MSS is not cyclically shifted. As much as \(n\times m\) of the cyclic shift is performed. Here, \(m\ (m\geq 1)\) represents the minimum distance, and the reason for using the minimum distance is that the cyclic shift of one chip does not have discriminating power in demodulation with the peak-to-peak distance. As a result, multiplying by m generates and transmits an adequate distance. If m is large,  
Figure 1: Autocorrelation and cross-correlation of _PN_ sequences. however, \(n\times m\) becomes very large and the orthogonality may be lost. As a result of comparing BER performance according to \(m\) in simulation, it was confirmed that the best performance was achieved when \(m=3\). The \(PN\) sequences for MSS and CSK are merged to create a single sign. An encoder is used to convert a binary number to a decimal number, and then the cyclically shifted \(PN\) sequence and the noncyclically shifted \(PN\) sequence are combined to create an MCSS signal. The proposed method is unique in that the receiver finds M through a cross-collation of \(PN\) sequences in one symbol and then cross-collations \(C_{0}\) from the symbol to find \(n\) as a result of using MCSS by synthesizing MSS and CSK.