## 3 Simulation Results and Analysis
The Monte Carlo simulation considers the transmission of a high number sequence of bits, varying the noise and channel conditions in each sequence, and evaluating the number of corrupted bits. The BER is the quotient between the number of corrupted bits and the number of transmitted bits. The simulation time for this graphic was limited to approximately 6 h. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
\begin{tabular}{c} With channel \\ estimation \\ \end{tabular} & 0.3 & With \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of baselines utilized in simulations. Figure 3: Results for 4 \(\times\) 32 MIMO (with and without impulsive noise), without LDPC codes, with ideal channel estimation and without channel correlation between antennas. Figure 4: Results for \(4\times 32\) MIMO, with and without LDPC codes, with impulsive noise, with ideal channel estimation and without channel correlation between antennas. Figure 5: Results for \(4\times 32\) MIMO, with channel estimation, with impulsive noise, with LDPC codes, and without channel correlation versus with correlation 0.3 between antenna elements. Figure 6: Results for 4 \(\times\) 32 MIMO, with and without LDPC codes, with impulsive noise, with channel estimation, and with channel correlation 0.3 between antenna elements. Figure 7: Results for 4 \(\times\) 32 MIMO, with channel estimation, impulsive noise, LDPC codes, and channel correlation 0.3 versus 0.5 and 0.7 between antenna elements. Figure 8: Results for 4 \(\times\) 32 MIMO, with and without LDPC codes, impulsive noise, channel estimation, and channel correlation 0.5 between antenna elements. Figure 9: Results for 4 \(\times\) 32 MIMO versus 4 \(\times\) 256 MIMO, LDPC codes, impulsive noise, channel estimation, and channel correlation 0.3 between antenna elements. Figure 4 (baseline 2) shows the performance results for UWA communications with and without LDPC codes, with 4 \(\times\) 32 MIMO, with impulsive noise, with ideal channel estimation, and without channel correlation between adjacent antenna elements. As expected, the use of LDPC codes corresponds to a performance improvement for all different receiver types. Furthermore, such performance improvement obtained with the LDPC codes is of the order of 5 dB. From these results, we can conclude that the LDPC codes, adopted for 5G communications, are also well suited for UWA communications. The simulation time using LDPC codes increases drastically, as compared to the uncoded scenario. This results from the fact that the required processing is higher and because the BER is lower. With a lower BER, the number of transmitted bits needs to be higher, such that the obtained BER can be viewed as an average value. The simulation time using LDPC codes was around 36 h.  
Figure 5 (baseline 4) shows the performance results for UWA communications without channel correlation versus correlation 0.3 between adjacent antenna elements, for \(4\times 32\) MIMO, channel estimation, impulsive noise, and LDPC codes. As can be seen, having a channel correlation of 0.3 between antennas leads to a very low performance degradation relating to the configuration without correlation. Although of such low performance degradation, this configuration is more realistic because the UWA communications consider carrier frequencies of the order of 15 kHz, whose wavelength is too high. It is known that a minimum distance of around 3 to 4 wavelengths is required between adjacent antenna elements to assure uncorrelated signals, which is difficult to achieve in such a UWA scenario. As previously described, while the results without LDPC are of the order of 6 h, the simulation time using LDPC codes was around 32 h.  
Figure 6 (baseline 5) shows the performance results for UWA communications with and without LDPC codes, with 4 \(\times\) 32 MIMO, with impulsive noise, with ideal channel estimation, and with channel correlation 0.3 between adjacent antenna elements.