The teachings herein present a method and apparatus that implement and use a factorized precoder structure that is advantageous in terms of performance and efficiency. In particular, the teachings presented herein disclose an underlying precoder structure that allows for certain codebook reuse across different transmission scenarios, including for transmission from a single Uniform Linear Array (ULA) of transmit antennas and transmission from cross-polarized subgroups of such antennas. According to this structure, an overall precoder is constructed from a conversion precoder and a tuning precoder. The conversion precoder includes antenna-subgroup precoders of size NT/2, where NT represents the number of overall antenna ports considered. Correspondingly, the tuning precoder controls the offset of beam phases between the antenna-subgroup precoders, allowing the conversion precoder to be used with cross-polarized arrays of NT/2 antenna elements and with co-polarized arrays of NT antenna elements.