of a discrete codebook restricting elements of codebook entries to be within a predetermined finite set of complex numbers and a constant amplitude codebook including each entry in its codebook having equal column norm and equal row norm in a preferred embodiment the digital codebook further includes restricting elements of a finite set in the discrete codebook to be in the form of k a jk b for a base k computer and the constant amplitude codebook further includes being obtained through a series of successive householder transformations in a preferred embodiment the codebook is configured as one of a constrained codebook in which the codebook is configured for multiple scenarios and a discrete codebook application_number US 201213547422 A description multi rank beamforming mrbf is an attractive low complexity precoding scheme which adapts the transmission rank on a fast basis i e once per coherent feedback and employs a precoding codebook having a nested structure the nested structure allows efficient svd based selection to pick the best precoder codeword from the codebook for the given channel state it also allows a low complexity channel quality information cqi metric based precoder selection moreover the nested codebook structure itself imposes no performance penalty when compared to the optimal unstructured codebook.