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We develop receivers for transmission with space-time block codes (STBCs) over fading intersymbol interference (ISI) channels. The focus lies on Alamouti's STBC, but the results may be generalized to related codes. It turns out 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, exploiting the structure of Alamouti's STBC, which is shown to produce an improper (rotationally variant) transmit signal. The presented receivers are especially well suited for high-level modulated signals, which are used in third-generation time-division multiple access (TDMA) mobile communications standards such as EDGE (enhanced data rates for GSM evolution). In contrast to block-based STBCs which have recently been proposed for ISI channels, our approach of combining a symbol-based STBC and equalization can be easily accommodated to channels with time-variant behaviour inside a transmission burst. Furthermore, for our scheme, the present burst structure of the EDGE system can be retained.