The Minimum Principle of SINR: A Useful Discretization Tool for Wireless Communication

Erez Kantor, Zvi Lotker, Merav Parter, David Peleg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations

Abstract

Theoretical study of optimization problems in wireless communication often deals with zero-dimensional tasks. For example, the power control problem requires computing a power assignment guaranteeing that each transmitting station is successfully received at a single receiver point. This paper aims at addressing communication applications that require handling 2-dimensional tasks (e.g., Guaranteeing successful transmission in entire regions rather than in specific points). A natural approach to such tasks is to discretize the 2-dimensional optimization domain, e.g., By sampling points within the domain. This approach, however, might incur high time and memory requirements, and moreover, it cannot guarantee exact solutions. Towards this goal, we establish the minimum principle for the SINR function with free-space path loss (i.e., When the signal decays in proportion to the square of the distance between the transmitter and receiver). We then utilize it as a discretization technique for solving two-dimensional problems in the SINR model. This approach is shown to be useful for handling optimization problems over two dimensions (e.g., Power control, energy minimization), in providing tight bounds on the number of null-cells in the reception map, and in approximating geometrical and topological properties of the wireless reception map (e.g., Maximum inscribed sphere). Essentially, the minimum principle allows us to reduce the dimension of the optimization domain without losing anything in the accuracy or quality of the solution. More specifically, when the two dimensional optimization domain is bounded and free from any interfering station, the minimum principle implies that it is sufficient to optimize over the boundary of the domain, as the 'hardest' points to be satisfied reside on boundary and not in the interior. We believe that the minimum principle, as well as the interplay between continuous and discrete analysis presented in this paper, may pave the way to future study of algorithmic SINR in higher dimensions.

Original languageEnglish
Title of host publicationProceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015
PublisherIEEE Computer Society
Pages330-349
Number of pages20
ISBN (Electronic)9781467381918
DOIs
StatePublished - 11 Dec 2015
Event56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015 - Berkeley, United States
Duration: 17 Oct 201520 Oct 2015

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2015-December
ISSN (Print)0272-5428

Conference

Conference56th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2015
Country/TerritoryUnited States
CityBerkeley
Period17/10/1520/10/15

Keywords

  • SINR
  • minimum principle
  • power control
  • rational polynomials

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