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Block transmission has recently been considered as an alternative to the conventional continuous transmission technique. In particular, block transmission techniques with zero padding (ZP) and cyclic prefix (CP) are becoming attractive procedures for their ability to eliminate both intersymbol interference (ISI) and interblock interference (IBI). In this paper, we present a unified approach to blind-channel estimation and interference suppression for block transmission using ZP or CP in both single-carrier (SC) and multicarrier (MC) systems. Our approach uses a generalized multichannel minimum variance principle to design an equalizing filterbank. The channel estimate is then obtained from an asymptotically tight lower bound of the filterbank output power. Through an asymptotic analysis of the subspace of the received signal, we determine an upper bound for the number of interfering tones that can be handled by the proposed schemes. As a performance measure, we derive an unconditional Cramer-Rao bound (CRB) that, similar to the proposed blind channel estimators, does not assume knowledge of the transmitted information symbols. Numerical examples show that the proposed schemes approach the CRB as the signal-to-noise ratio (SNR) increases. Additionally, they exhibit low sensitivity to unknown narrowband interference and favorably compare with subspace blind-channel estimators.