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International Journal of Digital Multimedia Broadcasting
Volume 2009 (2009), Article ID 146578, 9 pages
Research Article

A Geometry-Inclusive Analysis for Single-Relay Systems

1Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA 18015, USA
2Baskin School of Engineering, University of California, Santa Cruz, CA 95064, USA

Received 14 January 2009; Accepted 31 March 2009

Academic Editor: Daniel Iancu

Copyright © 2009 Meng Yu 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.


Successful message relay, or the quality of the interuser channel, is critical to fully realize the cooperative benefits promised by the theory. This in turn points out the importance of the geometry of cooperative system. This paper investigates the impact of the relay's location on the system capacity and outage probability for both amplify-forward (AF) and decode-forward (DF) schemes. Signal attenuation is modeled using power laws, and capacity is evaluated using the max-flow min-cut theory. A capacity contour for DF, the more popular mode of the two, is provided to facilitate the derivation of engineering rules. Finally, a selective single-relay system, which selects the best relay node among a host of candidates according to their locations, is analyzed. The average system capacity and outage, averaged over all possible candidates' locations, are evaluated. The result shows that the availability of a small candidate pool of 3 to 5 nodes suffices to reap most of the cooperative gains promised by a selective single-relay system.