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This letter develops a fast Fourier transform (FFT)-based method for estimating the impulse response of FIR single-input multiple-output (SIMO) channels driven by an unknown deterministic signal. The proposed algorithm successfully handles very short data sequences, for which the existing second-order statistics based methods, e.g., the subspace (SS), cross-relation (CR), and shifted correlation (SC) algorithms, are known to suffer performance degradation due to inaccurate statistics. The new method significantly outperforms the SS, CR, and SC methods with short sequences of observation data. This proposed method is computationally efficient for achieving good performance when data sequences are inevitably short, as in certain practical applications.