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We consider the detection of multiple cochannel single-carrier spatially multiplexed data streams. To this end, we propose a hybrid time-frequency-domain decision feedback equalizer, which performs parallel detection of the data streams. A practical parameter estimation algorithm for these receivers is developed, which estimates the MIMO channel in parallel as a set of effective channel vectors. To avoid interference cancellation, we develop a two-stage frequency-domain (FD) forward section that implements linear cochannel interference (CCI) suppression in cascade with equalization utilizing estimated channel-state information. The resulting receiver architecture outperforms interference-cancellation-based equalizers in the presence of channel estimation errors. Furthermore, all transmitted data streams achieve equal diversity gains.