## 4 Propagation Model Evaluation
### Evaluation Results  
In this section we are going to evaluate the different propagation models proposed in Section 3, assuming we have a CSMA/CA MAC protocol and the scenario and simulation parameters defined above. The simulation framework is based on OPNET, MATLAB and Bellhop ray tracing tool, and uses information related to underwater scenario characteristics like bathymetry, salinity, and seafloor composition, found at real worldwide locations which it is downloaded from NOAA and GEBCO worldwide ocean databases. This information is combined with the OPNET network scenario module in order to create the corresponding environmental files. With these files OPNET connects to MATLAB through its interface and runs Bellhop obtaining the result files. A fully explanation of the simulator framework can be found in [24]. The performance metrics we will show are:  
Figure 6: Reachability of gateway from Node \(\#1\) (bottom leftmost). 1. **Goodput**, defined as the throughput found at the application layer (note that in top of MAC layer we have no other network layers, only the application), so only data packets that successfully arrive to the gateway node are taken into account. This also means that control packets like RTS, CTS, and ACK are not considered in the computation of goodput. 2. **Average Packet Delay**, defined as the average delay incurred by a packet to reach its destination. This delay is calculated from the time when MAC layer gets the packet at source node to start delivery until the instant when this packet is correctly received at gateway node. In Figure 7, we can see the average goodput from 10 random scenarios (as defined in previous subsection) is shown. As it can be observed, the results appear to follow the same pattern with clearly different goodput values depending on the propagation model used. The Thorp propagation model gets the best performance, MMPE is estimable worse and finally Bellhop is the one with the worst behavior. This behavior agrees with the prediction stated before as the connection links between the nodes that are farther from gateway suffer the consequences of using more accurate propagation models like MMPE and Bellhop. In other words, Thorp model always prov  
Figure 8: Valencia’s (scenario location) annual average sound speed as a function of node depth. Figure 7: Average Goodput with different acoustic propagation models. network nodes during the simulation; however MMPE loses communication due to the wave effect and this leads to reduced goodput performance. This behavior is even more pronounced with Bellhop model where signal attenuation is calculated in a more accurate way, resulting in a higher number of dropped packets during the n-way handshaking process of CSMA/CA protocol. On the other hand we measure the average packet delay which will strongly depend on the channel propagation delay. So, the propagation delay (\(T_{prop}\)) depends on the distance (\(d\)) between sensor and gateway nodes, the specified inter frame delay (_SIF_), and the sound speed propagation (\(T_{sp}\)) that may change with node depth and water temperature, as shown in Figure 8 obtained through databases [22,23]. In expression (10) we define the delay experienced by a packet delivery in one-hop transmission without network contention/interference, taking into account the CSMA/CA protocol handshake and the distance and sound speed parameters. \[ \begin{split} T_{prop}=d/T_{spy},\ T_{pkt}=packet\_size/data\_rate,\ SIF=Inter\_Frame\_Delay\\ Delay=T_{prop}\ (RTS)+T_{pkt}\ (RTS)+SIF+T_{prop}\ (CTS)+T_{pkt}\ (CTS)+SIF+T_{prop}\ (DATA)+T_{pkt}\ (DATA)\end{split}  \tag{10}\]  
So the experienced delay of packet sent by a sensor located 1,500 m away from gateway node and with 10 m depth would be:  
\[ \begin{split} T_{prop}\ (RTS)=\ T_{prop}\ (CTS)=T_{prop}\ (DATA)=1,500/1,520=0.986 8\,s\\ T_{pkt}\ (RTS)=T_{pkt}\ (CTS)=24/5,000=0.0048\,s\\ T_{pkt}\ (DATA)=1,024/5,000=0.2048\,s\\ SIF=0.02048\,s\\ Delay=3*0.9868+2*0.0048+0.2048+2*0.02048=3.21576\,s\\ \end{split}