We present a novel turbo equalization scheme for block fading MIMO channels, where diversity is achieved using random signal mapping. We show that the computational complexity of the proposed scheme is not a function of the number of transmit antennas, and compares favorably to the complexity of similar systems based on space–time trellis codes and space–time block codes. Finally, we provide simulation results showing that the proposed scheme achieves full diversity, and investigate its performance in terms of the number of transmit antennas, ISI length and imperfect channel knowledge. Ó 2006 Elsevier Ltd. All rights reserved.