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A low-complexity space-time turbo equalization algorithm, the soft-output M-algorithm (SOMA), is proposed for frequency-selective time-varying MIMO channels. The SOMA is a soft-output version of the M-algorithm known in sequential decoding. It reduces the complexity of trellis-decoding by retaining only M states per trellis depth. For the log-likelihood ratio computation, the algorithm includes not only survivor paths that reach the end of the trellis but paths that are traversed and discarded. The complexity of the SOMA is independent of the trellis size and increases linearly with M. The algorithm is evaluated in a convolutional-coded system that employs transmit-diversity. Simulation results show a reduction from 4096 states to 96 states with negligible performance loss is possible using the SOMA-equalizer for a 4-tap, equal-power, Rayleigh channel. For a version of a 4-tap, EDGE-like channel, 64 states are sufficient.