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For a three node amplify-and-forward (AF) relay system in which only destination D is equipped with a channel estimator, we derive lower bound on training-based mutual information per transmission block. For a given transmission block length and a fixed total transmit power constraint between source S and relay R, we investigate jointly optimal number of training symbols, optimal power allocation between training and data, and optimal power allotment between S and R, such that the mutual information lower bound is maximized. For the AF relay system without direct link we provide analytical solutions to the joint optimization problem and relate the solutions to the relay location. For the AF relay system with direct link we resort to numerical evaluations to find the optimal solutions.