{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:36:49Z","timestamp":1760243809320,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,30]],"date-time":"2022-09-30T00:00:00Z","timestamp":1664496000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>This paper studies the minimization of nth (positive integer) order rate matching in high-throughput multi-beam satellite systems, based on one-to-many capacity allocation pairings, for the first time in the literature. The offered and requested capacities of gateways and users\u2019 beams are exploited, respectively. Due to the high complexity of the binary optimization problem, its solution is approached with a two-step heuristic scheme. Firstly, the corresponding continuous, in [0, 1], pairing problem is solved applying the difference of convex optimization theory, and then, a transformation from continuous to binary feasible allocation is provided to extract the pairings among gateways and users\u2019 beams. Comparing with the exponential-time optimal exhaustive mechanism that investigates all possible pairs to extract the best matching for minimizing the rate matching, extended simulations show that the presented approximation for the solution of the non-convex optimization problem has fast convergence and achieves a generally low relative error for lower value of n. Finally, the simulation results show the importance of n in the examined problem. Specifically, pairings originated by the minimization of rate matching with larger n result in more fair rate matching among users\u2019 beams, which is a valuable result for satellite and generally wireless systems operators.<\/jats:p>","DOI":"10.3390\/fi14100286","type":"journal-article","created":{"date-parts":[[2022,10,8]],"date-time":"2022-10-08T04:04:56Z","timestamp":1665201896000},"page":"286","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Minimization of nth Order Rate Matching in Satellite Networks with One to Many Pairings"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9121-5503","authenticated-orcid":false,"given":"Anargyros J.","family":"Roumeliotis","sequence":"first","affiliation":[{"name":"School of Electrical and Computer Engineering, National Technical University of Athens, GR-157 80 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christos N.","family":"Efrem","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, National Technical University of Athens, GR-157 80 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4716-3328","authenticated-orcid":false,"given":"Athanasios D.","family":"Panagopoulos","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, National Technical University of Athens, GR-157 80 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/COMST.2020.3028247","article-title":"Satellite Communications in the New Space Era: A Survey and Future Challenges","volume":"23","author":"Kodheli","year":"2021","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"165178","DOI":"10.1109\/ACCESS.2020.3022981","article-title":"Non-Terrestrial Networks in 5G & Beyond: A Survey","volume":"8","author":"Rinaldi","year":"2020","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"V\u00f6lk, F., Liolis, K., Corici, M., Cahill, J., Schwarz, R.T., Schlichter, T., Troudt, E., and Knopp, A. (2019). Satellite integration into 5G: Accent on first over-the-air tests of an edge node concept with integrated satellite backhaul. Future Internet, 11.","DOI":"10.3390\/fi11090193"},{"key":"ref_4","unstructured":"(2022, September 27). Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update, 2017\u20132022, Available online: http:\/\/media.mediapost.com\/uploads\/CiscoForecast.pdf."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chiti, F., Fantacci, R., and Pierucci, L. (2019). Energy efficient communications for reliable IoT multicast 5G\/satellite services. Future Internet, 11.","DOI":"10.3390\/fi11080164"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5411","DOI":"10.1109\/TWC.2014.2339217","article-title":"On the Gateway Diversity for High Throughput Broadband Satellite Systems","volume":"13","author":"Kyrgiazos","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4668","DOI":"10.1109\/JSYST.2020.3016965","article-title":"An Optimized Simple Strategy for Capacity Allocation in Satellite Systems With Smart Gateway Diversity","volume":"15","author":"Roumeliotis","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/LCOMM.2018.2881716","article-title":"Optimal Capacity Allocation Strategies in Smart Gateway Satellite Systems","volume":"23","author":"Roumeliotis","year":"2019","journal-title":"IEEE Commun. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2455","DOI":"10.1109\/LWC.2021.3103828","article-title":"Minimization of Losses and Rate Matching in Satellite Networks With One to Many Pairings","volume":"10","author":"Roumeliotis","year":"2021","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4005","DOI":"10.1109\/JSYST.2021.3128211","article-title":"Capacity Allocation Mechanisms in High-Throughput Satellite Systems: One-to-Many Pairings","volume":"16","author":"Roumeliotis","year":"2022","journal-title":"IEEE Syst. J."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Karagiannis, G.A., and Panagopoulos, A.D. (2019). Dynamic lognormal shadowing framework for the performance evaluation of next generation cellular systems. Future Internet, 11.","DOI":"10.3390\/fi11050106"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2443","DOI":"10.1109\/LCOMM.2020.3036593","article-title":"System Modeling and Design Aspects of Next Generation High Throughput Satellites","volume":"25","author":"Sharma","year":"2021","journal-title":"IEEE Commun. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2448","DOI":"10.1109\/LCOMM.2020.3033357","article-title":"Radio Resource Management Techniques for Multibeam Satellite Systems","volume":"25","author":"Kisseleff","year":"2021","journal-title":"IEEE Commun. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"7057","DOI":"10.1109\/TWC.2021.3080578","article-title":"Collaborative Multi-Resource Allocation in Terrestrial-Satellite Network Towards 6G","volume":"20","author":"Fu","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"7888","DOI":"10.1109\/TWC.2021.3088609","article-title":"Flexible Resource Optimization for GEO Multibeam Satellite Communication System","volume":"20","author":"Abdu","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"11123","DOI":"10.1109\/JIOT.2021.3051603","article-title":"Supporting IoT With Rate-Splitting Multiple Access in Satellite and Aerial-Integrated Networks","volume":"8","author":"Lin","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1109\/LWC.2020.3026700","article-title":"Secure and Energy Efficient Transmission for RSMA-Based Cognitive Satellite-Terrestrial Networks","volume":"10","author":"Lin","year":"2021","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1109\/TCCN.2020.2981016","article-title":"Two-Layer Game Based Resource Allocation in Cloud Based Integrated Terrestrial-Satellite Networks","volume":"6","author":"Zhu","year":"2020","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4675","DOI":"10.1109\/JSYST.2020.3020038","article-title":"Convolutional Neural Networks for Flexible Payload Management in VHTS Systems","volume":"15","author":"Tarchi","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1109\/LCOMM.2019.2955469","article-title":"A Prediction-Based Resource Matching Scheme for Rentable LEO Satellite Communication Network","volume":"24","author":"Han","year":"2020","journal-title":"IEEE Commun. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1612","DOI":"10.1109\/LCOMM.2018.2844243","article-title":"A Deep Reinforcement Learning-Based Framework for Dynamic Resource Allocation in Multibeam Satellite Systems","volume":"22","author":"Hu","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6606","DOI":"10.1109\/TWC.2021.3075289","article-title":"Machine Learning-Based Resource Allocation in Satellite Networks Supporting Internet of Remote Things","volume":"20","author":"Zhou","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1030","DOI":"10.1109\/JSAC.2018.2832820","article-title":"Multiobjective Reinforcement Learning for Cognitive Satellite Communications Using Deep Neural Network Ensembles","volume":"36","author":"Ferreira","year":"2018","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1109\/JCN.2011.6112304","article-title":"Multibeam satellite frequency\/time duality study and capacity optimization","volume":"13","author":"Lei","year":"2011","journal-title":"J. Commun. Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s11081-015-9294-x","article-title":"Variations and extension of the convex\u2013concave procedure","volume":"17","author":"Lipp","year":"2016","journal-title":"Optim. Eng."},{"key":"ref_26","unstructured":"Grajam, R., Knuth, D.E., and Patashnik, O. (1994). Concrete Mathematics, a Foundation for Computer Science, Addison Wesley. [2nd ed.]."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3427","DOI":"10.1109\/TAP.2020.3044370","article-title":"Assessment of Practical Smart Gateway Diversity Based on Multisite Measurements in Q-\/V-Band","volume":"69","author":"Ventouras","year":"2021","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1002\/sat.1065","article-title":"Smart gateways for terabit\/s satellite","volume":"32","author":"Jeannin","year":"2014","journal-title":"Int. J. Satell. Commun. Netw."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1109\/SURV.2013.050113.00015","article-title":"Fairness in Wireless Networks: Issues, Measures and Challenges","volume":"16","author":"SHI","year":"2014","journal-title":"IEEE Commun. Surv. 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