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Channel estimation and equalization for single-input multiple-output (SIMO) orthogonal frequency-division multiplexing (OFDM) systems without cyclic prefix (CP) is studied in a finite sample scenario. The OFDM system without CP provides high spectral efficiency at the cost of sacrificing simple one-tap equalization. Without ignoring intersymbol interferences (ISI), the subspace channel estimation is first presented. Due to the block Toeplitz structure of channel matrix, the subspace channel estimation with block matrix is developed. Suppressing the ISI and intercarrier interference (ICI) completely, the ISI/ICI-free equalizers are then designed. Compared with existing methods, the proposed channel estimation and equalization yield good performances in the finite sample scenario.