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Estimation of time-varying relay channels together with optimal energy allocation is considered. In the proposed frame structure, a priori known pilot symbols multiplexed with the data symbols are employed together with the decisions on the data symbols in an iterative fashion. This scheme is shown to a achieve bit error rate (BER) off the known channel bound by 1.5 dB in signal-to-noise ratio (SNR) and the advantage over the conventional pilot only case can be as large as 3 dB. This attractive performance is shown to be achieved by a single-tap bidirectional least-mean-squares (BiLMS) algorithm at a very low complexity as compared to the minimum mean-square error (MMSE) filter with multiple taps. Under a fixed energy budget, the optimal energy allocation is also shown through an allocation factor for which a closed form expression under a suboptimal operation is computed and evaluated in various realistic scenarios to have a satisfactory performance.