# High-Reliability Underwater Acoustic Communication Using an M-ary Cyclic Spread Spectrum
## 3 Simulation Results  
### Simulation Channel Characteristics  
The transmitted signal packet utilized in the simulation is depicted in Figure 5, and the 512-bit \(PN\) sequence used as the preamble is used to find the payload's synchronization and compensate for the first symbol's Doppler. The range of the Doppler bank was run with a 0.1 step size to find \(f_{d}\), taking into account the submarine's speed and assuming that the maximum Doppler is approximately 21 Hz. The program took approximately 48 s to  
Figure 4: Block diagram of the proposed method.  
search the \(-21\) Hz to \(21\) Hz range and approximately \(11.6\) s to use Equation (16) to find \(\Delta\) and run the Doppler bank within that range [27; 28]. Although using the Doppler bank in the passband has the disadvantage of requiring a considerable amount of computation, Equations (15) and (16) show that this can be reduced significantly.  
Figure 6 depicts the sound speed profile measured during the November 2020 sea trial. The channel impulse response was obtained using this method, which involved running a simulation based on the Bellhop model and then applying the UWA communication signal to it. The transmitter and receiver were separated by \(20\) km. Figure 7 shows the channel impulse response at the receiver positioned at a depth of approximately \(229\) m as a result of channel modeling.  
Figure 5: Packet structure for simulation.  
Figure 6: Sound speed profile.  
Figure 7: Channel impulse response by Bellhop model.  
Simulation was used to compare the BER performance of the existing CSK, MSS MCSK, and our proposed MCSS using a channel with the same transfer characteristics as Figure 6. The signal transmission rate is usually designed for 10 sps, but depending on the simulation case, it may be designed for 5 sps. CSK and MSS had three bits per symbol, whereas MCSK and MCSS had up to six bits per symbol. At 1270 bps, the preamble sends an m-sequence of 511 bits with a length of approximately 0.4 s. The length of the information data in the simulation was 1.5\(\times\)10\({}^{3}\) bits and each bit was spread across 127 chips at 10 sps and 255 chips at 5 sps. The simulation outcomes are depicted in the diagram below.  
In Figure 8, the Doppler effect was created by arbitrarily changing the sampling rate in the time domain, and the rate of change in the form of a sine graph was created to confirm both positive and negative Doppler. The value of \(f_{d}\) varies depending on how much the sampling changes. That is, the Doppler shifts in response to the gradient change. Figure 9 shows the Doppler factor (\(\alpha\)), which can be expressed by the following equation:  
\[\text{Doppler factor }(\alpha)=\frac{f_{d}}{f_{c}}\times\frac{(\text{ Chip}_{\text{ns}}\times L)}{f_{s}} \tag{18}\]  
Figure 8: Change of sampling frequency in time domain.  
Figure 9: Doppler factor per symbol.  
Equation (18) represents the rate of change in symbol length and the measured \(f_{d}\) per symbol should be used to compare performance. The rate of change of sampling per symbol is calculated by measuring the gradient of the change of the sampling frequency in Figure 8. It can be confirmed whether the correct \(f_{d}\) is estimated by comparing the rate of change of sampling per symbol with \(\alpha\).