## 4 Simulations and Analysis
### Sea Surface Boundary  
In a real ocean environment, the sea surface boundaries are usually not flat. The last simulation is designed to model UWA channels with different sea surface boundaries and analyse the impact on OFDM channel estimation. In this simulation, the receiving depth is fixed at 10 m and UWA channels are modelled in the sea area of scenario A with flat sea bottom boundary, according to the experience of previous simulations. For the sake of high complexity in stochastic channel simulation, LS algorithm is used to estimate UWA channel in this simulation. First, four UWA channels are modelled with different sea surface boundaries, which are generated by Gauss-Lagrange wave model with measured SWH (1.29 m). Figure 12 shows the eigenrays of different sea surface boundaries. As can be seen from the figures, the stochastic wave boundaries have variable influence on reflection angle, which leads to the number of reflection changes. Furthermore, Figure 13 shows the normalized CIRs of channels with different sea surface boundaries. In this figure, the effect of sea surface appears as the change of time delay and response amplitude. The CIRs of channels with sea surface 2, sea surface 3, and sea surface 4 are more  
Figure 11: **(a)** BER performance of channels in different sea bottom boundaries, estimated by LS and LMMSE algorithms, respectively. **(b)** MSE performance of channels in different sea bottom boundaries, estimated by LS and LMMSE algorithms, respectively. Figure 10: Normalized CIRs of channel with different sea bottom boundaries. Sea bottom boundaries of each figure: **(a)** rising bottom; **(b)** falling bottom; **(c)** protruding bottom; **(d)** sagged bottom. concentrated than that with sea surface 1. Furthermore, the CIR of channel with sea surface 4 has the maximum amplitude (0.9702). Figure 12: Eigenrays of channel with different sea surface boundaries. The color of lines indicates whether eigenrays hit surface boundary or bottom boundary of the sea. Sea surface boundaries of each figure: (**a**) Sea Surface 1; (**b**) Sea Surface 2; (**c**) Sea Surface 3; (**d**) Sea Surface 4. Figure 13: Cont. Figure 14a shows BER performance in different sea surface boundaries. Comparing with the BER performance in UWA channel with flat sea surface boundary channel in Figure 8a, the Gauss-Lagrange waves can improve or deteriorate the BER performance of OFDM channel estimation to some extent. The BER performance of channels with sea surface 1, sea surface 2 and sea surface 3 has a range of deterioration from 1.50 dB to 19.38 dB, while the BER performance of channel with sea surface 4 has an improvement of 10.86 dB.The MSE performance of the four channels has the same value as that in previous simulations, which are illustrated in Figure 14b. From the figures above, the result of different BER value is mainly caused by the stochastic effect of sea surface on the reflection angle of interfering eigenrays. The main energy of CIRs comes from the blue eigenrays (eigenrays hitting bottom only) that are the same in the four channels. Owing to the stochastic effect of sea surface on the reflection angle of interfering eigenrays which are mainly composed of black eigenrays that stand for the eigenrays hitting both boundaries, the amplitudes and delay of interfering eigenrays are different. In the channel with sea surface 1, the interfering eigenrays have more rebounds than that in the channel with sea surface 4. As a result, the interfering eigenrays in the channel with sea surface 1 have shorter time delay and higher amplitudes, which leads to a worse channel estimation performance. The result above reveals the stochastic effect of sea surface and explains the reason for the deviation between modelled channels and real channels in [20]. In order to further investigate the statistical effect on OFDM channel estimation, batch of channels with 0.5 m, 1.29 m, and 2 m SWH are modelled and compared in terms of BER performance. Figure 15a shows the BER curves of channels with different SWH.