{"title":"天空中的互联网:3D无线网络的容量","authors":"P. Gupta, P. Kumar","doi":"10.1109/CDC.2000.914139","DOIUrl":null,"url":null,"abstract":"Consider n nodes located in a sphere of volume V m/sup 3/, each capable of transmitting at a data rate of W bits/sec. Under a protocol based model for successful receptions, the entire network can carry only /spl Theta/(WV1/3n2/3) bit-meters/sec, where 1 bit carried a distance of 1 meter is counted as 1 bit-meter. This is the best possible performance even assuming the node locations, traffic patterns, and the range/power/timing of each transmission, are all optimally chosen. If the node locations and their destinations are randomly chosen, and all transmissions employ the same power/range, then each node only obtains a throughput of /spl Theta/(w/(nlog/sup 2/n)1/3) bits/sec, if the network is optimally operated. Similar results hold under an alternate physical model where a minimum signal-to-interference ratio is specified for successful receptions. The proofs of these results require determination of the VC-dimensions of certain geometric sets, which may be of independent interest.","PeriodicalId":217237,"journal":{"name":"Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)","volume":"32 6","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2000-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"69","resultStr":"{\"title\":\"Internets in the sky: capacity of 3D wireless networks\",\"authors\":\"P. Gupta, P. Kumar\",\"doi\":\"10.1109/CDC.2000.914139\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consider n nodes located in a sphere of volume V m/sup 3/, each capable of transmitting at a data rate of W bits/sec. Under a protocol based model for successful receptions, the entire network can carry only /spl Theta/(WV1/3n2/3) bit-meters/sec, where 1 bit carried a distance of 1 meter is counted as 1 bit-meter. This is the best possible performance even assuming the node locations, traffic patterns, and the range/power/timing of each transmission, are all optimally chosen. If the node locations and their destinations are randomly chosen, and all transmissions employ the same power/range, then each node only obtains a throughput of /spl Theta/(w/(nlog/sup 2/n)1/3) bits/sec, if the network is optimally operated. Similar results hold under an alternate physical model where a minimum signal-to-interference ratio is specified for successful receptions. The proofs of these results require determination of the VC-dimensions of certain geometric sets, which may be of independent interest.\",\"PeriodicalId\":217237,\"journal\":{\"name\":\"Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)\",\"volume\":\"32 6\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2000-12-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"69\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.2000.914139\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2000.914139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Internets in the sky: capacity of 3D wireless networks
Consider n nodes located in a sphere of volume V m/sup 3/, each capable of transmitting at a data rate of W bits/sec. Under a protocol based model for successful receptions, the entire network can carry only /spl Theta/(WV1/3n2/3) bit-meters/sec, where 1 bit carried a distance of 1 meter is counted as 1 bit-meter. This is the best possible performance even assuming the node locations, traffic patterns, and the range/power/timing of each transmission, are all optimally chosen. If the node locations and their destinations are randomly chosen, and all transmissions employ the same power/range, then each node only obtains a throughput of /spl Theta/(w/(nlog/sup 2/n)1/3) bits/sec, if the network is optimally operated. Similar results hold under an alternate physical model where a minimum signal-to-interference ratio is specified for successful receptions. The proofs of these results require determination of the VC-dimensions of certain geometric sets, which may be of independent interest.
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