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Mathematical Problems in Engineering
Volume 2015, Article ID 185262, 11 pages
http://dx.doi.org/10.1155/2015/185262
Research Article

On Modeling and Analysis of MIMO Wireless Mesh Networks with Triangular Overlay Topology

1Department of Computer Science, South China Normal University, Guangzhou, Guangdong 510631, China
2Department of Computer Science, University of Memphis, Memphis, TN 38152, USA
3School of Computer Science & Education Software, Guangzhou University, Guangzhou, Guangdong 510006, China
4Department of Computer Science, Middle Tennessee State University, Murfreesboro, TN 37132, USA

Received 27 September 2014; Revised 17 January 2015; Accepted 27 January 2015

Academic Editor: Hsuan-Ling Kao

Copyright © 2015 Zhanmao Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Multiple input multiple output (MIMO) wireless mesh networks (WMNs) aim to provide the last-mile broadband wireless access to the Internet. Along with the algorithmic development for WMNs, some fundamental mathematical problems also emerge in various aspects such as routing, scheduling, and channel assignment, all of which require an effective mathematical model and rigorous analysis of network properties. In this paper, we propose to employ Cartesian product of graphs (CPG) as a multichannel modeling approach and explore a set of unique properties of triangular WMNs. In each layer of CPG with a single channel, we design a node coordinate scheme that retains the symmetric property of triangular meshes and develop a function for the assignment of node identity numbers based on their coordinates. We also derive a necessary-sufficient condition for interference-free links and combinatorial formulas to determine the number of the shortest paths for channel realization in triangular WMNs.