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Channels with a sparse impulse response arise in a variety of wireless communication applications, such as high definition television (HDTV) terrestrial transmission and underwater acoustic communications. By exploiting the sparsity of the channel, this paper proposes a fast algorithm for sparse channel estimation based on a greedy algorithm called orthogonal matching pursuit (OMP). The proposed fast OMP-based channel estimation algorithm has a low computational complexity of O (K N log N) with K and N the channel sparsity level and signal length, respectively. The fast OMP is competitive to the ℓ1-minimization based methods in terms of estimation accuracy. In addition, the fast OMP is faster and easier to implement. Therefore it is an attractive alternative to the ℓ1-minimization approaches. Simulation results are provided to demonstrate the performance of the fast OMP algorithm.