Kerdock Codes for Limited Feedback Precoded MIMO Systems



Takao Inoue and Robert W. Heath Jr.


IEEE Trans. on Signal Processing, Vol. 57, No. 9, pp. 3711 - 3716, Sept, 2009.


Codebook based limited feedback is a practical way to obtain partial channel state information at the transmitter in a precoded multiple-input multiple-output wireless system. In this correspondence, we propose a systematic codebook design. The proposed Kerdock codebook consists of multiple mutually unbiased unitary basis matrices with quaternary alphabet and the identity matrix. We propose to derive the beamforming and precoding codebooks from this base codebook, eliminating the requirement to store multiple codebooks. Furthermore, we show that quaternary alphabet facilitates efficient codebook storage and codeword search. We derive the chordal distance for two and four antenna codebooks, showing that the proposed codebooks compare favorably with prior designs. Monte Carlo simulations compare achievable rates and error rates for different codebooks sizes.

Available on IEEE Xplore

The original preprint is available on arXiv

Available Codes:

The Kerdock codebooks presented in this paper for Nt = 2 and 4 are available below for download in two formats. The codebooks are saved as single wide matrix with variable name same as the file name.

Nt = 2 Kerdock_2Nt.mat
Nt = 4 Kerdock_4Nt.mat

For other related codebook archive maintained by Takao Inoue, visit here.