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Two models for AF relaying, namely, fixed gain and fixed power relaying, have been extensively studied in the literature given their ability to harness spatial diversity. In fixed gain relaying, the relay gain is fixed but it's transmit power varies as a function of the source-relay channel gain. In fixed power relaying, the relay transmit power is fixed, but its gain varies. The authors revisit and generalize the fundamental two-hop AF relaying model. They present an optimal scheme in which an average power constrained AF relay adapts its gain and transmit power to minimize the Symbol Error Probability (SEP) at the destination. Also derived are insightful and practically amenable closed-form bounds for the optimal relay gain.
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