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