For eigenmode transmission with minimum mean square error (MMSE) receiver spatial processing, a transmitter performs spatial processing on N.sub.S data symbol streams with steering vectors to transmit the streams on N.sub.S spatial channels of a MIMO channel. The steering vectors are estimates of transmitter steering vectors required to orthogonalize the spatial channels. A receiver derives a spatial filter based on an MMSE criterion and with an estimate of the MIMO channel response and the steering vectors. The receiver (1) obtains N.sub.R received symbol streams from N.sub.R receive antennas, (2) performs spatial processing on the received symbol streams with the spatial filter to obtain N.sub.S filtered symbol streams, (3) performs signal scaling on the filtered symbol streams with a scaling matrix to obtain N.sub.S recovered symbol streams, and (4) processes the N.sub.S recovered symbol streams to obtain N.sub.S decoded data streams for the N.sub.S data streams sent by the transmitter.