For data transmission with spatial spreading, a transmitting entity (1) encodes and modulates each data packet to obtain a corresponding data symbol block, (2) multiplexes data symbol blocks onto N.sub.S data symbol streams for transmission on N.sub.S transmission channels of a MIMO channel, (3) spatially spreads the N.sub.S data symbol streams with steering matrices, and (4) spatially processes N.sub.S spread symbol streams for full-CSI transmission on N.sub.S eigenmodes or partial-CSI transmission on N.sub.S spatial channels of the MIMO channel. A receiving entity (1) obtains N.sub.R received symbol streams via N.sub.R receive antennas, (2) performs receiver spatial processing for full-CSI or partial-CSI transmission to obtain N.sub.S detected symbol streams, (3) spatially despreads the N.sub.S detected symbol streams with the same steering matrices used by the transmitting entity to obtain N.sub.S recovered symbol streams, and (4) demodulates and decodes each recovered symbol block to obtain a corresponding decoded data packet.