We present a reduced-complexity soft detection (RCSD) scheme geared to multiple-input multiple-output (MIMO) systems with spatial domain multiplexing leading to layered space-time or space-frequency architecture. The proposed algorithm relies on a trellis representation of the MIMO signals and a subsequent formulation of constrained-depth maximum a posterior (MAP) detection in conjunction with soft decision feedback (SDF). Decision feedback is broken into causal and noncausal parts in an effort to maximize the observation window while maintaining a reasonable computational load. Two variations of RCSD are proposed to utilize the noncausal information in different ways. Analysis based on mean squared error (MSE) and log-likelihood ratio (LLR) associated with symbols in different stages of the trellis is done to develop insight into error propagation in the RCSD algorithm, as well as to compare the quality of the soft information obtained by the two RCSD variants. Error-rate simulations ...