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A reduced-complexity time-domain equalization scheme for wideband turbo-multiple-input multiple-output (turbo-MIMO) systems is presented. This scheme, called iterative trellis search equalization, is based on a modified version of the M-Bahl-Cocke-Jelinek-Raviv (M-BCJR) algorithm, applied to a suitably chosen trellis representation of the wideband MIMO channel process. Exploiting the properties of quadrature amplitude modulation (QAM) signal constellations with block-partitionable labels, this modified M-BCJR algorithm has complexity per bit that is independent of the constellation size, and polynomial in the number of transmit antennas and channel memory. Results from computer simulations show that the new scheme successfully mitigates intersymbol interference even if only a very small fraction of trellis state transitions is considered. It is also demonstrated that asynchronous transmission of the spatially multiplexed symbol streams can result in considerable performance improvement compared to synchronous MIMO systems.