Kerdock codes for limited feedback MIMO systems

A codebook based limited feedback strategy is a practical way to obtain partial channel state information at the transmitter in precoded multiple-input multiple-output (MIMO) wireless systems. Construction of conventional codebooks, such as Grassmannian and Fourier codebooks, relies on nonlinear search and iterative algorithms which often does not exhibit structure to ease storage or online search computation. Furthermore, multiple codebooks are needed to support beamforming and spatial multiplexing. In this paper, we propose a new codebook design based on Kerdock codes and mutually unbiased bases which enjoys performance similar to previously known codebooks. The proposed Kerdock codebook with quaternary alphabet has systematic construction, reduced storage, and reduced online search computation. Special structure in the codebook is used to derive a spatial multiplexing codebook from multiple columns of the beamforming codebook resulting in further storage reduction.