Comparison of codebooks for beamforming in limited feedback MIMO systems

The quantization codebook design is an essential part of the limited feedback scheme in multiple-input multiple-output (MIMO) systems. In this paper, we provide a review of four different types of codebooks, namely, Grassmannian codebook, random vector quantization (RVQ) codebook, discrete Fourier transform (DFT) codebook and Lloyd codebook for beamforming in limited feedback MIMO systems. The design ideas of the four codebooks are discussed respectively. The codebook qualities are measured by the minimum and root-mean-square (rms) codeword distances. Performance comparison in terms of the capacity of the quantized beamforming MIMO systems based on the four different codebooks are given by simulation results.