A base station used in a wireless communications system with multiple transmission ranks is disclosed. The base station comprises a memory to store a codebook for a transmission rank, a beamforming controller to precode data with a precoding matrix selected from the codebook, and a transmitter to transmit 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.