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A tap-selective maximum likelihood (TS-ML) channel estimation algorithm is proposed for long-range broadband block transmission system over sparse multipath channels. Based on a combined detection-estimation problem formulation, the TS-ML estimator for sparse channels is first derived by estimating a reduced set of significant channel taps. A low-complexity TS-ML algorithm based on fast Fourier transform (FFT) and recursive minimum description length (MDL) criteria is then presented, which not only considerably outperforms the conventional non- sparse ML method, but also has minimum preamble overhead. Simulation results show that the proposed TS-ML algorithm with MDL criterion can achieve the optimal performance bound, and adapt itself to make full use of channel sparsity.