# Long-Range Acoustic Communication Using Differential Chirp Spread Spectrum
## 4 Simulation  
The simulation performed two types of verification: performance according to SNR and performance in Doppler effects. In other words, simulations showed how the time-bandwidth product changes with the DCSS rather than CSS, and the performance of the two methods was also compared in the Doppler shift.  
The parameters used in the simulations are represented in Table 2. Through repeated simulations with these parameters, the simulation was conducted with a total of \(10^{8}\) bits. The results are shown in Figure 4a,b. Figure 4a shows the difference in performance of each method according to the SNR. First, the black square is the conventional CSS method with a transmission rate of 50 bps, and the blue circle is the conventional CSS method with a transmission rate of 100 bps. Assuming that the TBP of 100 bps is 1, the TBP is 2 because the TBP is doubled at 50 bps, where the transmission rate is half. Finally, the red scissors are a DCSS method with a transmission rate of 100 bps, and since the matching filter is formed using two symbols, the TBP becomes 2. Figure 4b shows the error accumulation rate according to the speed. This was used to analyze the performance according to the error accumulation degree in the Doppler environment. The blue dotted line is 0 knots, the red solid line is 2 knots and the black dashed line is 4 knots; the circled line is the conventional method and the proposed method is indicated by the scissors mark. It was confirmed that the performance of the proposed method in the figure is more durable due to Doppler than the conventional method.  
Figure 4a shows the performance of each method according to the SNR for simulations conducted at intervals of 1 dB from an SNR of \(-\)15 dB to 5 dB. The traditional CSS method began to generate errors below \(-\)5 dB, and the proposed method was found to be near \(-\)8 dB. The CSS method proposed had a BER of \(10^{-2}\) near \(-\)10 dB, and the proposed method had a BER of about \(10^{-2}\) near \(-\)13 dB, which improves the SNR by about 3 dB compared to the CSS method.  
Figure 4b shows the analysis of the performance of each approach in the environment with Doppler effects. First, we assumed a situation in which the transceiver was moved away at a speed of 4 knots and in which the SNR is 0 dB. In this situation, the \(x\)-axis is expressed in the order of bits listed in the packet, and the cumulative error by bits is expressed on the \(y\)-axis. This determines the performance by increasing the error rate due to the effects of Doppler as the slope of the graph increased.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Sampling frequency & 192,000 Hz & LFM interval & 1 s \\ Carrier frequency & 16,000 Hz & Guard interval & 1 s \\ Data rate & 100 bps & Number of bits & 500 bits \\ Bandwidth & 2000 Hz & Preamble & 128 bits \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
Figure 3: Block diagram of the differential chirp spread spectrum (DCSS) method.  
The cause of the increase in error rate was confirmed by Doppler. The error was accumulated by the motive and the error bit was increased by the bit stream. The CSS method clearly showed that the errors increased after the 200 th bit stream. Next, the DCSS method was found to have a significantly more stable performance than the CSS method, although some errors were accumulated after the 200 th bit stream. This confirmed that the proposed method with increased time-bandwidth product cost was stronger for noise and Doppler than the conventional method.