Decision feedback equalization (DFE) is a well-established intersymbol interference mitigating technique for linear, noise, and dispersive channels. In this thesis, we discuss the finite length decision feedback equalization and present a new solution for the receiver based on the signal-to-interference and noise ratio (SINR) criterion. We also extend the DFE receiver concepts to space-time block-coded transmission over frequency-selective multi-input multi-output (MIMO) channels. The focus lies on Alamouti's space-time block code with two transmit and only one receive antenna. Combined equalization and decoding scheme is presented under the constraint of linear processing complexity (no trellis search) at the receiver. Simulation is made over several channels including typical EDGE channels, and significant gains can be observed compared with a single-input single-output DFE scheme.