We consider MIMO single-carrier block transmission over time-varying multipath channels, under the assumption that the channel parameters are not exactly known but are estimated via the least-squares training technique. While the channel temporal variation is known to negate the tone-by-tone frequency-domain equalization facility, it is otherwise shown that in the time domain the signal signatures can be arranged into groups of orthogonal components, leading to a very natural yet efficient group-by-group symbol recovery scheme. To realize this figure of merit we propose a constrained-optimization based receiver which also takes into account the mitigation of channel mismatch effects caused by time variation and imperfect estimation. The optimization problem is formulated in an equivalent unconstrained generalized-sidelobe-canceller setup. This enables us to directly model the channel mismatch effect into the system equations through the perturbation technique and, in turn, to further exploit the statistical assumptions on channel temporal variation and estimation errors for deriving a closed-form solution. Within the considered framework the proposed robust equalizer can be further combined with the successive interference cancellation mechanism for further performance enhancement.