An apparatus and a method. The apparatus includes a singular value decomposition (SVD) processor configured to receive a channel matrix H and output samples y of an optimal precoding matrix for H; a linear phase estimation (LPE) processor connected to the SVD processor and configured to determine a phase estimate {circumflex over (θ)}l of an angle θl of a horizontal discrete Fourier transform (DFT) index l, where l is an integer; and a decision processor connected to the LPE processor and configured to determine a hard estimate of l.