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In this paper, we develop receiver concepts for transmission with space-time block codes (STBC) over frequency-selective fading channels. The focus lies on Alamouti's STBC, but the results may be generalized to related STBC. We show that a straightforward combination of conventional equalizers and a space-time block decoder is only possible if at least as many receive antennas as transmit antennas are employed, but not for the practically interesting case of pure transmit diversity. This restriction is circumvented by our approach. Equalizers with widely linear (WL) processing are designed, utilizing the structural properties of the transmit signal of space-time block coding, which is shown to be improper (rotationally variant). These schemes are especially suited for equalization of high-level modulated signals, which are used in third-generation time-division multiple access mobile communications standards such as EDGE (Enhanced Data Rates for GSM Evolution).