Channel state information in a closed-loop, multiple-input, multiple-output wireless networks is fed back from each mobile station to a base station by first determining a transmit covariance matrix R, and applying a singular value decomposition (SVD) R=UΣVH, where U, V are left and right singular vector matrices, Σ is a diagonal matrix with singular values. The matrix V includes column vectors V. A beamforming vector vmax=[1 exp(jΦ)exp(j2Φ) . . . exp(jΦ)]/√{square root over (N)}] is approximated by the column vector V having a maximum magnitude, where Φ is a real number. Then, only the angle Φ is fed back using a phase modulation mapping of the components exp(jΦ) onto the associated subcarrier.