In this paper, we design a segment training based individual channel estimation scheme in the classical three-node amplify-and-forward one-way relay network (OWRN). We investigate the underlying power allocation at the relay to minimize the mean-square-error (MSE) of the individual channel estimation and to maximize the average effective signal-to-noise ratio (AESNR) of the data detection. The optimal/sub-optimal power allocation schemes are also derived for the two objectives. Extensive numerical results are provided to corroborate the proposed studies.