Spatial Continuum Model: Toward the Fundamental Limits of Dense Wireless Networks

Jean-Marie Gorce 1 H. Vincent Poor 2 Jean-Marc Kelif 3
1 SOCRATE - Software and Cognitive radio for telecommunications
Inria Grenoble - Rhône-Alpes, UCBL - Université Claude Bernard Lyon 1, CITI - CITI Centre of Innovation in Telecommunications and Integration of services
Abstract : This paper proposes a new model called spatial continuum asymmetric channels to study the channel capacity region of asymmetric scenarios in which either one source transmits to a spatial density of receivers or a density of transmitters transmit to a unique receiver. This approach is built upon the classical broadcast channel (BC) and multiple access channel (MAC). For the sake of consistency, the study is limited to Gaussian channels with power constraints and is restricted to the asymptotic regime (zero-error capacity). The reference scenario comprises one base station in Tx or Rx mode, a spatial random distribution of nodes (resp. in Rx or Tx mode) characterized by a probability spatial density of users u(x) where each of them requests a quantity of information with no delay constraint, thus leading to a requested rate spatial density ρ(x). This system is modeled as an ∞−user asymmetric channel (BC or MAC). To derive the fundamental limits of this model, a spatial discretization is first proposed to obtain an equivalent BC or MAC. Then, a specific sequence of discretized spaces is defined to refine infinitely the approximation. Achievability and capacity results are obtained in the limit of this sequence while the access capacity region DΩ(Pm) is defined as the set of requested rates spatial densities ρ(x) that are achievable with a transmission power Pm. The uniform capacity defined as the maximal symmetric achievable rate is also computed.
Type de document :
Communication dans un congrès
IEEE Globecom, Dec 2016, Washington, United States. IEEE, pp.6, 2016
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Contributeur : Jean-Marie Gorce <>
Soumis le : vendredi 11 novembre 2016 - 10:09:13
Dernière modification le : mardi 16 janvier 2018 - 15:48:40
Document(s) archivé(s) le : jeudi 16 mars 2017 - 11:26:03


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  • HAL Id : hal-01395609, version 1



Jean-Marie Gorce, H. Vincent Poor, Jean-Marc Kelif. Spatial Continuum Model: Toward the Fundamental Limits of Dense Wireless Networks. IEEE Globecom, Dec 2016, Washington, United States. IEEE, pp.6, 2016. 〈hal-01395609〉



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