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This paper defines a new metric: a relay gain that measures the performance gain of users using relaying channels at distance s from a base station. The paper derives the closed form of the relay gain for urban macro-cells and rural areas, and shows that the closed form provides much information about how to maximize the performance gain of relay systems. Further, this paper investigates the fairness improvement of relay systems based on the relay gain, and confirms the superiority of relay systems over systems without relaying. Simulation results confirm that the relay gain metric predicts the performance of real relay systems accurately.
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