Iterative detection for a MIMO (multiple-input, multiple-output) wireless communications system uses multiple stages for interference cancellation refinements. Detection is determined by maximizing signal to noise plus interference ratios. Equalization matrix updating uses a matrix-inversion-free recursion. For P transmitter antennas and Q receiver antennas, the soft symbol vector estimates are z=Fr-Gs.sup.hard with F a P.times.Q IMMSE detector, r the received Q vector, and G a P.times.P interference canceller with s.sup.hard hard decisions of prior symbols and iterations.