## Abstract

The rules governing the availability and quality of connections in a wireless network are described by physical models such as the signal-to-interference & noise ratio (SINR) model. For a collection of simultaneously transmitting stations in the plane, it is possible to identify a reception zone for each station, consisting of the points where its transmission is received correctly. The resulting SINR diagram partitions the plane into a reception zone per station and the remaining plane where no station can be heard. SINR diagrams appear to be fundamental to understanding the behavior of wireless networks, and may play a key role in the development of suitable algorithms for such networks, analogous perhaps to the role played by Voronoi diagrams in the study of proximity queries and related issues in computational geometry. So far, however, the properties of SINR diagrams have not been studied systematically, and most algorithmic studies in wireless networking rely on simplified graph-based models such as the unit disk graph (UDG) model, which conveniently abstract away interference-related complications, and make it easier to handle algorithmic issues, but consequently fail to capture accurately some important aspects of wireless networks. The current paper focuses on obtaining some basic understanding of SINR diagrams, their properties and their usability in algorithmic applications. Specifically, based on some algebraic properties of the polynomials defining the reception zones we show that assuming uniform power transmissions, the reception zones are convex and relatively well-rounded. These results are then used to develop an efficient approximation algorithm for a fundamental point location problem in wireless networks.

Original language | English |
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Title of host publication | PODC'09 - Proceedings of the 2009 ACM Symposium on Principles of Distributed Computing |

Pages | 200-209 |

Number of pages | 10 |

DOIs | |

State | Published - 9 Nov 2009 |

Event | 2009 ACM Symposium on Principles of Distributed Computing, PODC'09 - Calgary, AB, Canada Duration: 10 Aug 2009 → 12 Aug 2009 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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### Conference

Conference | 2009 ACM Symposium on Principles of Distributed Computing, PODC'09 |
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Country/Territory | Canada |

City | Calgary, AB |

Period | 10/08/09 → 12/08/09 |

## Keywords

- Reception zone
- SINR
- Wireless networks

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications