One or more non-transitory computer-readable media having instructions that, when executed by one or more processors of a base station , cause the base station to: process a feedback transmission from a mobile station to determine first, second and third codebook indices; determine a first beamforming matrix component based on the first codebook index; determine a second beamforming matrix component based on the second codebook index; determine a third beamforming matrix component based on the third codebook index; and determine a beamforming matrix based on the first, second and third beamforming matrix components; and form a beam, based on the beamforming matrix, to transmit data to the mobile station in one or more streams; wherein the first codebook index is associated with a quantized beamforming matrix having a quantization error and the second codebook index is to be used to reduce the quantization error and the third codebook index is to be used to further reduce the quantization error, and wherein the second codebook index is associated with a quantized difference matrix determined at the mobile station as representative of a difference between a beamforming matrix determined at the mobile station and the quantized beamforming matrix determined at the mobile station, and wherein the third codebook index is associated with a second quantized difference matrix determined at the mobile station as representative of a difference between the quantized difference matrix and a difference matrix determined at the mobile station, the difference matrix representative of the difference between the beamforming matrix determined at the mobile station and the quantized beamforming matrix determined at the mobile station. process a feedback transmission from a mobile station to determine first, second and third codebook indices; determine a first beamforming matrix component based on the first codebook index; determine a second beamforming matrix component based on the second codebook index; determine a third beamforming matrix component based on the third codebook index; and determine a beamforming matrix based on the first, second and third beamforming matrix components; and form a beam, based on the beamforming matrix, to transmit data to the mobile station in one or more streams; wherein the first codebook index is associated with a quantized beamforming matrix having a quantization error and the second codebook index is to be used to reduce the quantization error and the third codebook index is to be used to further reduce the quantization error, and wherein the second codebook index is associated with a quantized difference matrix determined at the mobile station as representative of a difference between a beamforming matrix determined at the mobile station and the quantized beamforming matrix determined at the mobile station, and wherein the third codebook index is associated with a second quantized difference matrix determined at the mobile station as representative of a difference between the quantized difference matrix and a difference matrix determined at the mobile station, the difference matrix representative of the difference between the beamforming matrix determined at the mobile station and the quantized beamforming matrix determined at the mobile station. <EOS>