# Pilot-Assisted OFDM for Underwater Acoustic Communication
## 5 Simulation Results  
In this section, we present the simulation results for both the pilot-based channel estimation and the linear equalization. To evaluate the performance of the proposed system, a CP-OFDM transceiver communicating over a UWA channel was assumed. The parameters used for the OFDM transceiver are shown in Table 1. In our simulations, we used 10,000 iteration runs for each Eb/N0 point. Every iteration had one OFDM symbol with N subcarriers. Figure 3: Channel impulse response for a shallow underwater acoustic channel. Figure 4 is a BER plot for BPSK CP-OFDM as a function of the number of pilots used when the number of subcarriers were 64, 128, 256, and 512. The transmitter-receiver distance was kept at 50 m. As shown in Figure 4a, 16 pilots offered the best BER performance for 64 subcarriers; using 4 or 8 pilots gave an unacceptably poor performance. This was because 4 or 8 pilots were insufficient to capture the channel behavior. It was also noted that increasing the number of pilots from 16 to 32 marginally deteriorated the BER. For 128 subcarriers, 16 pilots also gave the best BER, as evident from Figure 4b. The case of 256 subcarriers is shown in Figure 4c. It was noted that the best BER was given by 32 and 64 pilots as it was hard to distinguish between the two cases. Figure 4d shows the BER performance when the number of subcarriers was 512. In this case, the best BER was observed when the number of pilots was either 32 or 64. By comparing the four figures, it can be seen that for 64 subcarriers, the optimum number of pilots was one-fourth the number of subcarriers; for 128, it was one-eighth the number of subcarriers; for 256, it was also one-eighth; and, finally, for 512 subcarriers, it was one-sixteenth the number of subcarriers. The BER performance of the proposed system as a function of the pilot energies is shown in Figure 5. In this figure, the number of pilots was 16, the number of subcarriers was 64, and the transmitter-receiver distance was 50 m. It was noted that as we increased the energy of the pilots, the BER degraded. The reason for this behavior was that as the overall energy of the symbol was kept constant, increasing the pilot energy decreased the energy of the data symbols, which resulted in BER degradation. Figure 6 shows the BER performance of QPSK CP-OFDM as a function of the equalizers used. In this plot, the number of subcarriers was 128, the number of pilots was 32, and the transmitter-receiver distance was 800 m. As expected, the performance was poor when no equalizer was used. It was also observed that the BER given by both the LS and ZF equalizers was almost the same for a low SNR. At a high SNR, the ZF outperformed the LS equalizer. Figure 7 shows the BER plots when using the LS and ZF equalizers with multiple transmitter-receiver separations that ranged from 50 to 1250 m. The number of subcarriers was 64 with 16 pilots and BPSK was used in the mapper. As expected, increasing the transmitter-receiver distance deteriorated the BER performance. However, even at 1250 m, the performance was acceptable and a good error correcting code would bring down the BER curve even further. \begin{table}
\begin{tabular}{c l l} \hline \hline
**Type** & **Parameters** & **Values** \\ \hline \multirow{4}{*}{Transceiver} & Number of Subcarriers & 64, 128, 256, 512 \\  & Number of Pilots & 8 to 128 (typically one-fourth of the number of subcarriers) \\  & Modulation Scheme &
\begin{tabular}{l} BPSK, QPSK \\ One-fourth of the number of subcarriers \\ 8 kbps for BPSK and 16 kbps for QPSK \\ 10 kHz \\ 30 kHz \\ 3 \\ 3 \\ 3 \\ 4 \\ 50 to 1250 m \\ 6 \\ 7 \\ \end{tabular} \\ \multirow{4}{*}{Channel} & Transmitter Depth & 20 m \\  & Receiver Depth & 20 m \\  & Doppler Frequency & 10 Hz \\  & Path Gains & \((0;-8.3;-4.4;-6.2)\) \\  & Delay & \((0;1.5\times 10^{-3};4\times 10^{-3};7\times 10^{-3})\) s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters.