# Performance Analysis of a WPCN-Based Underwater Acoustic Communication System
## 4 Numerical Results and Discussion  
In this section, we present the numerical results for the WPCN-based UWAC systems. The derived expressions of average BER and outage probability given in Equations (24) and (31) are used to investigate the system performance under different parameters. Monte-Carlo simulations are provided to verify the analytical results for Equations (24) and (31) as well. Unless otherwise specified, the parameters set in our simulations are shown in Table 2. Note that, for simplicity, the energy harvesting efficiency \(\eta\) is set as a constant in our work. In Figure 4, the average BER and the outage probability of the WPCN-based UWAC systems under various transmit powers are plotted against the transmission distance. It is shown that the analytical results match very well with the Monte-Carlo simulations. Not surprisingly, it can be observed that the average BER and outage probability increase as the distance increases, since the longer the transmission distance is, the more severe the path loss will be. It can also be observed that as the transmission distance increases, the benefits coming from the increase in the transmit power of H-AP decrease rapidly. Specifically, when the transmit power increases from 150 dB re \(\upmu\)Pa to 180 dB re \(\upmu\)Pa, an average BER performance improvement of 94.65% is achieved for the system with a transmission distance of 20 m, while the average BER performance improvement is only 12.81% when the transmission distance is 200 m.  
To examine the impact of the time allocation factor \(\tau_{0}\) on the performance of the WPCN-based UWAC systems, we plot the achievable rate against the time allocation factor for the systems with various H-AP transmit powers and various transmission distances in Figure 5a,b, respectively. It is shown that despite the variation in H-AP transmit power and transmission distance, there exists an optimal time allocation factor \(\tau_{0}^{*}\) (which is marked with a bold circle) for the systems to achieve the maximum information rate. Specifically, for the transmit power of 150 dB re \(\upmu\)Pa and 180 dB re \(\upmu\)Pa, a maximum information rate of 0.1574 bps/Hz and 2.5333 bps/Hz can be achieved at a transmission distance of 80 m, respectively. Moreover, it can also be observed that the optimal time allocation factor becomes more and more large when the H-AP transmit power decreases or the transmission distance increases. This can be explained as follows. For a smaller H-AP to transmit power, the terminal node needs more time to harvest enough energy for information transmission. While for a larger transmission distance, the downlink energy transmission of the H-AP subjects to a severe path loss, which significantly decreases the power harvested by the terminal node, thus more time is needed for the terminal node to harvest enough energy for information transmission. Therefore, both the smaller H-AP transmit power and the larger transmission distance increase the time required for energy harvesting at the terminal. \begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{1}{c}{**Parameters**} & **Symbol** & **Value** \\ \hline Spreading factor & \(m\) & 1.5 \\ Shipping activity factor & \(s\) & 0.5 \\ Wind speed & \(w\) & 3 m/s \\ Downlink OFDM subcarrier number & \(K\) & 32 \\ Uplink OFDM subcarrier number & \(I\) & 32 \\ Number of multipaths & \(L_{p}\) & 5 \\ Multipath delay & \(\tau\) & 0, 0.3, 0.5, 0.6, 0.8 ms \\ Outage rate threshold & \(R_{th}\) & \(10^{-3}\) bps/Hz \\ Energy conversion efficiency & \(\eta\) & 0.8 \\ Signal center frequency & \(f\) & 10 kHz \\ Signal bandwidth & \(B_{w}\) & 10 kHz \\ Time allocation factor & \(\tau_{0}\) & 0.8 \\ Speed of sound in the water & \(c_{0}\) & 1500 m/s \\ Doppler shift & \(f_{d}\) & 0 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters setup in the simulations.