## 4 Simulations and Analysis
### Sea Bottom Boundary  
Seabed terrain has some structures that result from common physical phenomena. In the shallow sea, the depth of seabed usually changes slowly and the sea bottom boundary can be considered as flat in short distances, which is modelled in previous simulation. Furthermore, the seabed may rise or fall rapidly in the littoral area and have protruding or sagged structures under specific conditions. The four special types of seabed above will be modelled in this simulation to analyse the influence of sea bottom boundary on channel estimation. The rising and falling sea boundaries are sampled from scenario B with opposite transmitting and receiving positions. The protruding and sagged sea boundaries are rare to find in real bathymetry data. Therefore, the sea bottom boundary of scenario A is adjusted to produce the boundaries artificially. In this simulation, the receiving depth is fixed at 10 m, which has been confirmed to yield the best channel estimation performance among other depths in previous simulation. The sea surface boundary is set as flat to control the stochastic effect.  
Figure 9 shows the eigenrays of channels with different sea bottom boundaries. The channel with rising bottom has more eigenrays than others because rising bottom increases the length of eigenrays transmission path and disperses the eigenrays gradually in the process of transmission. The falling bottom can also disperse the eigenrays. Since falling bottom decreases the length of eigenrays transmission path, the number of eigenrays in channel with falling bottom reduces a lot. The channel with protruding bottom has shorter length of eigenray transmission path than the channel with sagged bottom as the impact of seabed terrain.  
Figure 10 illustrates the normalized CIRs of channels above. Overall, the length of normalized CIRs of channels with rising and sagged bottom are larger than that of channels with falling and protruding bottom. It is obvious that the CIR of channel with rising bottom has more multipaths than that with falling bottom. Owing to the seabed terrain, the relative time delay of path with maximum amplitude in protruding channel bottom is less than that in sagged channel.  
Figure 11 is plotted to compare the BER and MSE performance between the four channels. The BER performance of different channels in LS algorithm is all around 0.0075 when SNR is 30 dB. The value is similar to the worse BER value in Figure 8a, implicating that there may exist a worst-case performance bound of UWA channel estimation through LS algorithm. In addition, the BER performance of different channels in LMMSE algorithm has a few differences. The channel with falling bottom is estimated in the best BER performance while the channel with sagged bottom is estimated in the worst BER performance. The performance of MSE also has similar characteristics to that of BER in LMMSE algorithm, shown in Figure 11b.  
Figure 8: (**a**) bit error rate (BER) performance of channels in different receiving depth, estimated by LS and LMMSE algorithms, respectively. (**b**) MSE performance of channels in different receiving depth, estimated by LS and LMMSE algorithms, respectively.  
Figure 10: _Cont._  
Figure 9: Eigenrays of channel with different sea bottom boundaries. The color of lines indicates whether eigenrays hit surface boundary or bottom boundary of the sea. Sea bottom boundaries of each figure: (**a**) rising bottom; (**b**) falling bottom; (**c**) protruding bottom; (**d**) sagged bottom.