## 5 Simulation and Analysis  
In this section, the performance of the proposed method is evaluated. In a simulation, Matlab was utilized to verify the performance of the proposed frequency domain equalization algorithm, and compare it with the existing algorithm. The CP-OFDM system model has been considered, and the parameters are set as follows:  
Sampling frequency \(f_{sam}\) = 100 kHz, IFFT points \(V\) = 512, symbol period \(T_{m}\) = 5.12 ms, and number of subcarriers \(N\) = 48 [26, 27]. The training sequence is 128 symbols. Each subcarrier was modulated by binary phase-shift keying. The occupied bandwidth ranged from 10.156 kHz to 19.336 kHz. The underwater channel simulation environment parameters are shown in Table 1[12]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Surface height (depth) (h0) [m] & 100 \\ Transmitter depth [m] & 58 \\ Receiver depth [m] & 50 \\ Bandwidth [kHz] & 9.18 \\ Minimum frequency [kHz] & 10.156 \\ Distance between Tx and Rx [km] & 1 \\ Time resolution [ms] & 50 \\ Frequency resolution [Hz] & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Underwater acoustic environment parameters. According to the classical underwater acoustic channel model, the parameters for the acoustic rays of two channels are given in Table 2, including direct path, surface reflection path, and seabed reflection path [12]. As revealed in Table 2, the maximum multipath time delay of Channel 1 is 4.26 ms, and the frequency selective fluctuation is 22.883 dB. Hence, the length \(\Delta\) of the cyclic prefix under OFDM is set to 5.12 ms. In other words, the length of the symbol period at this time is \(T^{\prime}=T+\Delta=10.24\) ms. The information transmission rate is 4687.5 bps [34]. Figure 3 presents the compensation for the frequency selective fading of the underwater acoustic channel, which is treated by the existing OFDM-based frequency domain equalization algorithm, at the signal-noise ratio \(SNR=20\) dB. It is evident that the frequency selective fading caused by multipath effect results in the dramatic fluctuation within the OFDM effective communication frequency bands. However, the multipath component does not exceed the length of the cyclic prefix in this case, so that the existing frequency domain adaptive equalization algorithm makes satisfying compensation for the frequency selective fading. As revealed by the simulation results, the symbol error ratio is lower (in \(10^{-4}\)) when the signal-noise ratio is higher (>15 dB), which guarantees the reliability of the entire communication system. Under the same background, the compensation for Channel 2 with the existing frequency domain equalization algorithm was simulated. The frequency selective fluctuation of Channel 2 is 22.296 dB (equivalent to that of Channel 1). The maximum multipath time delay is 17.95 ms, greater that the length of the cyclic prefix for the OFDM communication signals. The compensation for the frequency selective fading after treating with the exist \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Parameter** & **AC 1** & **AC 2** & **AC 3** & **Fluctuation** \\ \hline \multirow{3}{*}{Channel 1} & Relative time delay (s) & 0 & 0.00123 & 0.00426 & \multirow{3}{*}{22.883 dB} \\ \cline{2-5}  & Normalization degree & 1 & 0.65 & \(-\)0.55 & \\ \hline \multirow{3}{*}{Channel 2} & Relative time delay (s) & 0 & 0.00967 & 0.01795 & \multirow{3}{*}{22.296 dB} \\ \cline{2-5}  & Normalization degree & 1 & 0.7 & \(-\)0.52 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Acoustic parameters of the channel. Figure 3: Compensation for Channel 1 with the existing frequency domain equalization algorithm. ing OFDM-based frequency domain equalization algorithm is presented in Figure 4. As illustrated in the figure, the time delay exceeds the multipath component of the length of the cyclic prefix.