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Relaying can improve performance of a wireless network, es- pecially when dierent transmission modes with distance/cost tradeos are available. Examples of such modes include data rates or transmission power. This paper geometrically analyzes the probability that a high-cost direct transmission can be replaced by a combination of low-cost relay transmissions. The main result of the analysis is a technology-agnostic characterization of a communication system's amenability to relaying strategies and some recommendations for how to structure such systems.

A Geometric Derivation of the Probability of Finding a Relay in Multi-rate Networks