## 4 Results and Discussions  
PEADO-OFDM and ADO-OFDM are simulated and compared in the proposed full-duplex UOWC system with parameters listed in Table 3. In the simulation, a random binary sequence (RBS) is firstly generated and mapped into 4-QAM symbols. Then, the new proposed PEADO-OFDM transmitter structure is applied to generate the PEADO-OFDM signals. The signal powers of both PEADO-OFDM and ADO-OFDM schemes are normalized to unity. An additive white Gaussian noise model is utilized in the simulation to simulate different Eb/N0 between signal and noise. At the receiver, the output binary data  
Figure 3: A new PEADO-OFDM transmitter with a dual-branch structure. from the demodulation process will be compared with the transmitted binary sequence to evaluate the system BER. We denote the number of subcarriers assigned to the ACO-OFDM branch as \(N_{ACO}\). Here, \(N\) is the number of total subcarriers, which is divided into odd subcarriers and even subcarriers for ACO-OFDM and DCO-OFDM, respectively, and the number of subcarriers assigned to the ACO-OFDM branch is fixed to \(N/2\) in traditional ADO-OFDM. In PEADO-OFDM, the ACO-OFDM branch only occupies a portion of odd subcarriers so that \(N_{ACO}\) can be flexibly adjusted to different sizes, i.e., \(N/2\), \(N/4\) and \(N/8\). Figure 4 shows the BER comparison of PEADO-OFDM and ADO-OFDM with the proposed scheme in three types of water, where \(N_{ACO}\) is set to 1024, which means that all the odd subcarriers are assigned to the ACO-OFDM branch. Figure 4a,b show that the BER performances in the clear and coastal waters are almost identical. However, in the harbor water, as shown in Figure 4c, the BER performances of both PEADO-OFDM and ADO-OFDM become worse. This result corresponds to the time delay spread shown by the impulse response in Figure 1. Compared with traditional ADO-OFDM in various UOCMs as exhibited in Figure 4, the BER performance of the ACO-OFDM branch in PEADO-OFDM is not changed obviously, while the DCO-OFDM branch in PEADO-OFDM is improved significantly. The PE operation will not affect the demodulation of the ACO-OFDM branch and the DCO-OFDM branch can be demodulated independently without depending on the demodulation of the ACO-OFDM branch. Therefore, the overall BER performance of PEADO-OFDM is optimized. In addition, the BER performances of the DCO-OFDM branch and ACO-OFDM branch with different \(N_{ACO}\) are simulated in the clear water, and the simulation results are given in Figure 5a,b, in which \(N_{ACO}\) is set to 1024, 512 and 256. It can be seen from the Figure 5a that with the increase in \(N_{ACO}\), the BER performance of the DCO-OFDM branch in PEADO-OFDM will be improved and the required Eb/N0 for a BER of \(10^{-3}\) is about 14.80 dB, 15.95 dB and 16.37 dB, achieving about 2.62 dB, 1.29 dB and 0.78 dB gains compared with that in ADO-OFDM when \(N_{ACO}=1024\), 512 and 256, correspondingly. The BER performance of the DCO-OFDM branch depends on the channel state and noise when the bias index \(\beta\) is large enough. The larger the \(N_{ACO}\) is, the more negative ACO-OFDM signals will be clipped, resulting in lower power of the transmitted signals. Therefore, the noise will lower with the same signal-to-noise ratio, leading to a lower BER. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Simulation Parameters** & **Symbol** & **Value** \\ \hline The number of total subcarriers & N & 2048 \\ The constellation order & M & 4 \\ The bias index of the real branch & \(\beta_{Re}\) & 10 dB \\ The bias index of the imaginary branch & \(\beta_{Im}\) & 10 dB \\ Link communication distance & L & 10 m \\ The duration of channel impulse response & \(\Delta T\) & 5 ns \\ Bit rate & bps & \(1\times 10^{9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters for dual-branch full-duplex UOWC system. Figure 4: BER performance comparisons of dual-branch ADO-OFDM and PEADO-OFDM in (**a**) clear, (**b**) coastal and harbor water channels. (**c**) the BER performances of both PEADO-OFDM and ADO-OFDM become worse.