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KERDOCK CODES FOR LIMITED FEEDBACK MIMO SYSTEMS Takao Inoue and Robert W. Heath Jr. The University of Texas at Austin Department of Electrical and Computer Engineering Wireless Networking and Communications Group 1 University Station C0803, Austin, TX 78712-0240 USA Email: { inoue, rheath } @ece.utexas.edu ABSTRACT A codebook based limited feedback strategy is a practical way to ob- tain partial channel state information at the transmitter in a precoded multiple-input multiple-output (MIMO) wireless systems. Construc- tion 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 com- putation. 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 un- biased bases which enjoys performance similar to previously known codebooks. The proposed Kerdock codebook with quaternary alpha- bet has systematic construction, reduced storage, and reduced online search computation. Special structure in the codebook is used to de- rive a spatial multiplexing codebook from multiple columns of the beamforming codebook resulting in further storage reduction. Index Terms Array signal processing, MIMO systems, codes, feedback communication. 1. INTRODUCTION Codebook based limited feedback is a practical method to obtain channel state information (CSI) at the transmitter in a multiple-input multiple-output (MIMO) communication system [1]. Conventional codebook design has focused on the achievable capacity and bit error performance without fully addressing practical considerations such as systematic construction, storage, and search complexity [1–5]. In practical systems such as 3GPP long term evolution (3GPP-LTE), multiple codebooks of different sizes are being considered which further increases the storage requirements [6]. Furthermore, up to 300km/h mobility is being considered in 3GPP-LTE which necessi- tates fast search for the optimum codeword. Thus, there has been increasing interest in developing a codebook with structure to ease the storage and search requirements. The central topic of this paper is to connect Kerdock codes to limited feedback codebook design and address practical considerations. Conventional codebook designs such as Grassmannian [2], equi- angular frames [7], and vector quantization (VQ) based [4] code- books typically require extensive numerical search or iterative al- gorithms to design the codebook. While the asymptotic capacity and bit error performance as a function of codebook size have been shown to be near optimal, the codebook usually does not exhibit any This material is based in part upon work supported by the National Sci- ence Foundation under grant CCF-514194 and CNS-626797.
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This note was uploaded on 08/28/2008 for the course EE 343 taught by Professor Kim during the Spring '08 term at 서강대학교.

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