In connection with transmitted space-time, trellis encoded, signals that pass through a transmission channel that is characterized by memory, improved performance is realized with a receiver that combines a decoder with an equalizer that selects the trellis transition, s, that minimizes the metric.xi..function..function..times..function..times..function..time- s..function..times..function. ##EQU00001## where {tilde over (h)}.sub.j(l) is related to both the transmission channel and to the encoding structure in the transmitter, {tilde over (s)}(k) are the (trial) symbols according to a certain transition and s(k) are the symbols that were previously decided.