A wireless access point (AP) includes multiple transmit antennas and circuitry. The circuitry is configured to transmit multiple sounding frames to a receiver that includes one or more receive antennas, the sounding frames are transmitted via respective different partial subgroups of the transmit antennas, to receive from the receiver feedback information that specifies for each of the sounding frames a respective channel between the transmit antennas in the respective partial subgroup and the receive antennas, and, to determine a steering matrix based on the feedback information, and transmit to at least the receiver via at least some of the transmit antennas using the steering matrix.