# High-Reliability Underwater Acoustic Communication Using an M-ary Cyclic Spread Spectrum
## 3 Simulation Results
### Performance Comparison  
To demonstrate the performance of the proposed MCSS method, it was compared to the conventional CSK, MSS, and MCSK methods. The parameters of the modulated signals are summarized in Table 1. Table 2 lists the parameters for each signal. For the spreading sequence, the maximum length (ML) sequence was used, and all four signals were intended to have the same bandwidth. The BER curves for each SNR after Doppler compensation and the BER for each SNR of the channel with and without Doppler were calculated. At a frequency range of \(-4\) Hz to 4 Hz, artificial Doppler was applied to the channel, with a different Doppler applied to each symbol. When the same bandwidth is used, MCSK and MCSS can have more bits of information per symbol. As a result, we compared their performance in the same bandwidth, the case where the data rates (pps) are the same, and the case where the symbol rates (sps) are the same. The symbol rate was lowered, and the number of spread sequences was increased to have the same bandwidth to compare the performance by matching the bps equally. Figure 9(a) is the result of BER per channel SNR to which only CIR (Figure 7) is applied, and Figure 9(b) is the result of BER per channel SNR to which only CIR (Figure 7) is applied. Figure 9(b) shows the results of BER per SNR in the channels added to CIR in Figure 7 and Doppler in Figure 8 without correcting for Doppler, and Figure 9(c) shows the results of compensating Doppler for each symbol in the channels added to CIR and Doppler. Figure 11 shows the results of comparing the same bit rates. To make the bit rate the same, the symbol rate of MCSK and our proposed MCSS is halved and the number of sequences is doubled to have the same bandwidth. Only CIR is used in Figures 9(a) and 9(a), and the outcome is a performance comparison for orthogonality of signals. At the same symbol rate, MSS was the best, followed by MCSS, MCSK, and CSK. MCSK performed better than CSK at the same bit rate. The results without Doppler compensation in the channel with CIR and Doppler added are shown in Figures 9(b) and 9(b). MSS has the best performance when the symbol rate is the same, followed by MCSS. By superimposing two separate sequences, our proposed MCSS signal contains more information in a single symbol. At the same symbol rate, the two distinct sequences acted as noise to each other, resulting in somewhat worse performance than MSS. Our proposed MCSS, on the other hand, performed better at the same bit rate. Even when the SNR was 0 dB, the BER of the CSK and MCSK signals was measured to be 0.3 or higher, and the result was very sensitive \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Sampling frequency & 192 kHz \\ Carrier frequency & 12.5 kHz \\ Bandwidth & 2 kHz \\ SNR & \(-\)30\(-\)0 dB \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameter** & **CSK** & **MSS** & **MCSK** & **MCSS** \\ \hline Data rate (bps) & 30 & 30 & 60/30 & 60/30 \\ Symbol rate (sps) & 10 & 10 & 10/5 & 10/5 \\ Number of sequences & 127 & 127 & 127/255 & 127/255 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters based on the modulation scheme. to Doppler. CSK and MCSK demodulate at the baseband, so phase variation is included in the desreading process, resulting in poor BER performance. However, MSS and MCSS show more robust results because Doppler frequency correction in passband is included. The results of Doppler compensation in the channel to which CIR and Doppler are added are shown in Figures 10c and 11c. The MSS and MCSS data exhibit similar tendencies to those without Doppler adjustment; however, they perform much better at lower SNRs. In CSK and MCSK, Doppler is compensated for the first symbol using the preamble, and phase is compensated using the PLL. Figure 12 shows \(f_{d}\) measured using the Doppler bank, and Figure 13 shows the change of one symbol length according to \(f_{d}\).