A method for compensating for frequency and phase offsets in a multiple antenna system, MAS, with multi-user, MU, transmissions, MU-MAS, comprising: transmitting by a base station a first training signal from each antenna (202, 305, 405, 605, 705, 802, 902, 1002) of said base station (200, 300, 400, 500, 600, 700, 800, 900, 1001) to one or a plurality of wireless client devices (204-207, 306-308, 406-408, 506-508, 606-608, 706-708, 804-808, 904-908, 1004); analyzing by said one or plurality of wireless client devices each first training signal to generate frequency offset compensation data, and transmitting by said one or plurality of wireless client devices the frequency offset compensation data to the base station; computing by said base station a plurality of MU-MAS precoder weights based on the frequency offset compensation data to pre-cancel the frequency offset at the transmitter; precoding by said base station a second training signal using the MU-MAS precoder weights to generate precoded training signals for each antenna of said base station; transmitting by said base station the precoded second training signals from each antenna of said base station to one or a plurality of wireless client devices; analyzing by said one or plurality of wireless client devices each precoded second training signal to generate channel characterization data, and obtaining the channel characterization data at the base station; computing by said base station a plurality of MU-MAS precoder weights based on the channel characterization data, the MU-MAS precoder weights calculated to pre-cancel frequency and phase offset and inter-user interference; precoding by said base station a plurality of data signals using the MU-MAS precoder weights to generate precoded data signals for each antenna of the base station; and transmitting by said base station the precoded data signals through each antenna of said base station to each respective wireless client device. transmitting by a base station a first training signal from each antenna (202, 305, 405, 605, 705, 802, 902, 1002) of said base station (200, 300, 400, 500, 600, 700, 800, 900, 1001) to one or a plurality of wireless client devices (204-207, 306-308, 406-408, 506-508, 606-608, 706-708, 804-808, 904-908, 1004); analyzing by said one or plurality of wireless client devices each first training signal to generate frequency offset compensation data, and transmitting by said one or plurality of wireless client devices the frequency offset compensation data to the base station; computing by said base station a plurality of MU-MAS precoder weights based on the frequency offset compensation data to pre-cancel the frequency offset at the transmitter; precoding by said base station a second training signal using the MU-MAS precoder weights to generate precoded training signals for each antenna of said base station; transmitting by said base station the precoded second training signals from each antenna of said base station to one or a plurality of wireless client devices; analyzing by said one or plurality of wireless client devices each precoded second training signal to generate channel characterization data, and obtaining the channel characterization data at the base station; computing by said base station a plurality of MU-MAS precoder weights based on the channel characterization data, the MU-MAS precoder weights calculated to pre-cancel frequency and phase offset and inter-user interference; precoding by said base station a plurality of data signals using the MU-MAS precoder weights to generate precoded data signals for each antenna of the base station; and transmitting by said base station the precoded data signals through each antenna of said base station to each respective wireless client device.