# Design of an Underwater Acoustic Waveform and Integrated System for Communication and Detection
## 4 Simulations
### Simulations on Ambiguity Function and BER of CPM-LFM Signals in AWGN Channels
However, an increase in \(M\) increases the number of CPM phases, leading to a greater demodulation complexity. Thus, there is a tradeoff between communication performance and system complexity. An increase in the correlation length \(L\) results in an improvement in the BER if \(h\) is also increased. This is because increasing \(h\) will increase \({d_{B}}^{2}\). Otherwise, if \(h\) is small, the BER may increase with an increase in \(L\). The above results indicate that, in a practical system design, the parameters should be chosen to achieve a balance between BER and complexity. Figure 16: BER with different modulation indices \(h\). Figure 17: BER with different modulation orders \(M\). Figure 18: BER with different correlation lengths \(L\). Simulations on the Ambiguity Function and BER of CPM-LFM Signals in BELLHOP Underwater Acoustic Channels  
Underwater acoustic channels are more complex than terrestrial wireless channels, with characteristics such as large delays and significant Doppler and time variations. The speed of sound varies at different depths, and multipaths occur for sound waves underwater, due to factors such as reflection, refraction, and scattering. The underwater acoustic channel is modeled to evaluate the communication performance of the proposed system. This research utilizes the BELLHOP ray model. The specific simulation parameters are presented in Table 2.  
Next, simulations on the ambiguity function and BER of the proposed shared waveform and the hydroacoustic integrated system under the BELLHOP underwater acoustic channel are conducted. The parameters of the designed waveform and integrated system are given in Table 3.  
Figure 19 presents the ambiguity with the proposed SS-CPM-LFM. This shows that the signal ambiguity has a very pronounced peak, indicating good velocity and range resolution. Figure 20 shows that signals with and without SS have the same speed ambiguity, as it is inherited from the good speed resolution of LFM signals. However, Figure 21 indicates that the distance ambiguity with SS has significantly lower side lobes. This reduces the sensitivity to the data and improves ranging performance. To further evaluate the ranging performance, Hamming window compression was applied to the proposed signal with zero Doppler frequency. The results in Figure 22 show that the SS-CPM-LFM with windowing has a single peak with a main lobe to side lobe ratio of 17.72 dB. This is sufficient for effective ranging. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Sea water depth & 200 m \\ Longitudinal wave velocity & 1500 m/s \\ Interpolation method & C-type linear \\ Sound source depth & 10 m \\ Receiver depth & 10 m 50 m 100 m 150 m \\ Distance between sound source and receiver & 1000 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters of BELLHOP. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Signal bandwidth \(B\) & 1000 Hz \\ pulse width \(T_{p}\) & 0.5 s \\ Modulation index \(h\) & 0.5 \\ Correlation length \(L\) & 2 \\ Symbol pulse function \(g(t)\) & \(g(t)=\left\{\begin{matrix}\frac{1}{2T}&(0\leq t\leq LT)\\ 0&\text{else}\\ \end{matrix}\right.\) \\ Modulation order \(M\) & 2 \\ carrier frequency \(f_{c}\) & 1500 Hz \\ Total number of symbols in a frame & 598 \\ Data1 & 35 \\ Data2 & 400 \\ Preamble & 128 \\ Doppler deviation of frequency \(f_{d}\) & 0.2 \\ Phase deviation \(\varphi_{d}\) & 0.1\(\pi\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters of the designed waveform and integrated system. Figure 19: Ambiguity function for the SS-CPM-LFM signal. Figure 20: Velocity ambiguity comparison. Next, the BER of three signals, CPM, CPM-LFM, and SS-CPM-LFM, under underwater acoustic channels are simulated. The SS frame structure allows the receiver to employ a two-step frequency and phase estimation and compensation method.