An apparatus for generating a precoding matrix codebook includes a matrix group generator to generate a first group of unitary matrices based on a vector-based codebook for precoding of a multiple input multiple output (MIMO) communication scheme; a matrix group extender to extend the first group of unitary matrices to generate a second group of unitary matrices; and a matrix group selector to select a group of columns corresponding to a communication rank from each of the unitary matrices that are elements of the second group so that the columns are optimized based on a distance between the columns corresponding to the communication rank.