A fast-fading-channel estimation algorithm is proposed in this paper for orthogonal frequency-division multiplexing (OFDM) systems with imperfect carrier synchronization. Specifically, diagonalizing decomposition is proposed for autocorrelation of a compact matrix of generalized channel impulse response (G-CIR). In such decomposition, only the diagonal matrix is random. A compressed expression of the G-CIR matrix and its equivalent channel model are derived. Finally, a least square (LS) estimators is formulated to estimate the compressed channel, from which the CIR matrix is reconstructed. Simulation results demonstrated that the proposed scheme has better estimation accuracy and lower bit error rate (BER) over the existing techniques.