A system and method for wireless communications with codebook quantization are provided. A method for communications device operations includes estimating a channel between a controller and a mobile device, generating channel state information from the channel estimate, quantizing the channel state information by selecting a codeword from a rank n codebook based on a codeword selection mechanism, where n is a non-negative integer value, transmitting an index corresponding to the selected codeword and receiving a transmission from the controller. The transmission is precoded based on the index. The rank n codebook includes 2K codewords with each codeword comprising n columns of a transformed base matrix of dimension Nt×Nt, where K is a positive integer number representing a number of bits in the rank n codebook, and Nt is a number of transmit antennas at the controller.