## 3 Throughput Performance Limits of Multimode Underwater Acoustic Networks
### The Method of Solving the Model
#### 3.2.4 Algorithms for Performance Analysis
When the sound source level is low, only the PRSS mode with the slowest speed can be selected for transmission. However, once the sound source level exceeds 188 dB, all links transition to using the PSK mode with the highest transmission speed. At this threshold, the upper limit of network throughput aligns

Figure 4: The optimal scheduling result under the network topology in Figure 3 (SL = 186 dB). Figure 3: A triangular topology that randomly generates node positions. ### Network Throughput under Different Hydrological Environments

Different hydrological conditions in the marine environment correspond to different propagation losses. The network throughput under three typical hydrological conditions is analyzed. The sound velocity profiles of these three conditions are depicted in Figure 6a, and the corresponding transmission losses at different distances are obtained using the Bell-hop model, as shown in Figure 6. The different hydrological conditions are associated with different transmission losses, with hydrologic condition 1 having the smallest transmission loss and hydrologic condition 3 having the largest transmission loss. The propagation loss under hydrologic condition 1 is 0.48 dB and 1.31 dB smaller than that under hydrologic conditions 2 and 3, respectively. The decodable SNR thresholds were analyzed for different systems and transmission distances using Monte Carlo simulation, yielding the specific results illustrated in Figure 7. In the figure, link 3 represents the transmission link between node 1 and node 2, link 2 represents the transmission link between node 1 and node 3, and link 1 represents the transmission link between node 2 and node 3. The figure reveals the following findings:

(1) Among different communication systems, the PRSS mode requires the smallest decoded SNR threshold, while the PSK mode demands the most. (2) The largest threshold signal-to-noise ratio corresponds to hydrological condition 1, while hydrologic conditions 2 and 3 have smaller threshold signal-to-noise ratios. This difference is due to the complex channel multipath structure under hydrological condition 1, which increases the decoding threshold. On the other hand, hydrologic conditions 2 and 3 have simpler channel structures, resulting in smaller decoding thresholds. (3) In the PRSS mode, decodable signal-to-noise ratio thresholds show minimal variation across different distances and hydrological conditions. However, significant differences exist within the PSK mode when considering various distances and hydrological conditions. This difference can be attributed to the increased sensitivity of the PSK mode to channel multipath structures compared to that of the PRSS mode. The analysis of network throughput under different hydrological conditions is presented in Figure 8. It is evident that the throughput performance limits of each sound source level vary under different hydrological conditions, providing results that are more consistent with real-world situations. Similar to Figure 5, the throughput results under different hydrological conditions are consistent for smaller and larger sound source levels. This is because when the sound source level is large enough, all links support multimode communication, whereas when the sound source level is small, no communication is possible. The maximum difference between the throughput upper limits of the three hydrologic

Figure 6: Simulation of hydrological conditions: (**a**) sound velocity profiles corresponding to three hydrological conditions; (**b**) TL corresponding to three hydrological conditions. conditions is 0.5 kbits/slot. Compared to the traditional method, the average throughput performance is improved by 67.5%, 78.3%, and 67.5%, respectively, under the three hydrological conditions. Figure 8: Network throughput under different hydrological conditions. Figure 7: Comparison of the decodable thresholds of different hydrology systems and links under different communication systems: (**a**) PRSS mode; (**b**) MFSK mode; and (**c**) PSK mode.