A multi-user MIMO downlink beamforming system with limited feedback (200) is provided to enable precoding for multi-stream transmission, where a channel codeword (ui) and one or more channel quality indicator values (CQIA, CQIB) are computed at the user equipment (201.i) on the basis of maximizing a predetermined SINR performance metric (ρi) which estimates the receive signal-to-noise-ratio (SINR) at the user equipment (201.i). The computed codeword (ui) and CQI values (or differential values related thereto) are quantized and fed back to help the base station (210) which applies a correction to the appropriate CQI value in the course of designing the transmit beamforming vectors w and determining the appropriate modulation and coding level to be used for downlink data transmission.