A method of precoding implemented in a base station used in a wireless communications system with multiple transmission ranks is disclosed. The method includes having a codebook for a transmission rank, precoding data in one or more layers with a precoding matrix selected from the codebook, and transmitting the precoded data to a user equipment, wherein the precoding matrix is selected according to a first description and a second description, which are unique to the precoding matrix, and wherein the second description provides a finer description of the codebook than the first description. Other methods, systems, and apparatuses also are disclosed.