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The capacity of non-coherent fading relay channels is studied, where the communication between the transmitter and the receiver is supported by a relay, where the links between the terminals are fading channels, and where all terminals are aware of the fading statistics, but not of their realizations. It is shown that if the link between the transmitter and the receiver supports higher communication rates than the link between the relay and the receiver, then at high SNR it is best to turn the relay off.
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