## 3 Throughput Performance Limits of Multimode Underwater Acoustic Networks
### The Method of Solving the Model
#### 3.2.4 Algorithms for Performance Analysis
## 5 Conclusions

We have conducted simulations to demonstrate that considering the differences in the communication capabilities of different links can lead to more accurate throughput limits for multimode networks. The signal-to-noise ratio of received signals at different nodes can vary due to factors such as the network node sound source level, propagation loss, marine environment, and interference signals. Higher received signal-to-noise ratios in communication systems can support higher transmission rates, while lower ratios support lower rates. By leveraging this understanding, we remodeled the throughput analysis process and found that the upper limit of the throughput performance for multimode networks is greater than that of traditional methods. Additionally, we developed a decoding conflict model that incorporates the propagation characteristics of actual underwater acoustic channels, providing a more precise assessment of underwater acoustic signal conflicts. In summary, our proposed methods offer an accurate evaluation of the throughput performance of multisystem underwater acoustic networks. However, it is worth noting that when the network topology becomes more complex or the number of nodes increases, the scale of the state matrix and action matrix becomes very large, rendering the solution algorithm based on the combination of dynamic programming and greedy algorithms impractical. In light of this, we plan to enhance the solution method and propose a new approach that can address the application needs of any network topology. Additionally, we intend to conduct sea tests to apply and validate the method outlined in this paper, with the aim of further refining and improving its effectiveness. Conceptualization, C.W. ; methodology, C.W. ; software, C.W. ; validation, P.D. ; formal analysis, P.D., Z.W. and D.L. ; investigation, Z.W. and D.L. ; resources, C.W. ; data curation, C.W. ; writing--original draft preparation, C.W. ; writing--review and editing, D.L. ; visualization, Z.W. ; supervision, P.D. and Z.W. ; project administration, P.D. ; funding acquisition, C.W. All authors have read and agreed to the published version of the manuscript. This work was supported in part by the Fund of Science and Technology on Sonar Laboratory under Grant No. 2022-JCJQ-LB-031/04, in part by the National Natural Science Foundation of China under Grant No. 62301513. Please contact the author for data requests. The authors are grateful to the anonymous reviewers and for the research funding support. The authors declare no conflicts of interest. ## References

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