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This paper provides three channel estimations including LS (least square) estimation, LMMSE (linear minimum mean square error) estimation and Lr-MMSE (low rank minimum mean square error) estimation utilized to the relay channel to approximate the optimal solution in OFDM system. The simulation results show that LMMSE estimation outperforms the other two estimations, but it is too complicated. The performance of LrMMSE estimation approaches that of the LMMSE estimation, but LrMMSE lessens the number of the multiplications. We also present the approximate average symbol error (ASER) of variable gain relay for the 16QAM modulation and give the tight bounds and the simpler form without integral expression is proposed to simplify the bound expression.