A method and system is disclosed for precoding in a two transmit antenna MIMO system, for example, a wireless backhaul network. The method only uses the first column of the 2×2 precoder as the feedback information. When the feedback information is available to the transmitter, the transmitter performs an interpolation and reconstruction procedure to obtain the precoder matrix for each subcarrier. The method offers no significant loss in performance, with reduced computational complexity and feedback overhead compared to conventional known matrix representation methods.