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This paper proposes a novel turbo equalization scheme based on groupwise soft interference cancelling minimum mean-squared error filtering (SC-MMSE) combined with maximum a posteriori signal detection for multiple access single-carrier block transmission. For an efficient implementation of the equalizer, the linear groupwise SC-MMSE filter is directly derived in the frequency domain by introducing an additional design criterion in the optimization. Special focus is given on different heuristic methods for group selection based on mean-squared error (MSE) and spatial channel correlation criteria. The first method dynamically forms groups incorporating a priori information at each turbo iteration, while the second and third methods provide a static grouping that is valid for all turbo iterations. Results of correlation chart analysis and bit error rate simulations demonstrate that the groupwise turbo frequency domain equalizer (FDE) achieves a large performance gain over the conventional SC-MMSE FDE in intersymbol interference multiple access channels with high spatial correlation among the multiple users' transmitted signals. Moreover, it is shown that the simple static correlation-based grouping scheme when applied to the proposed receiver achieves similar performance than the dynamic MSE-based scheme at a significantly reduced complexity. In addition, to assess the practicality of the novel algorithm in real scenarios, we show numerical results obtained by a series of simulations using channel-sounding field measurement data.