Kerdock Codes for Limited Feedback Precoded MIMO Systems

TL;DR

This paper introduces a systematic Kerdock code-based design for MIMO precoding codebooks that simplifies storage and search, providing competitive performance with traditional methods.

Contribution

It proposes a new systematic codebook construction using Kerdock codes and mutually unbiased bases, improving storage efficiency and search complexity in MIMO systems.

Findings

Codebooks derived from Kerdock codes show favorable chordal distance.

Simulation results demonstrate comparable or improved achievable rates.

The structure reduces memory and simplifies codeword search.

Abstract

A codebook based limited feedback strategy is a practical way to obtain partial channel state information at the transmitter in a precoded multiple-input multiple-output (MIMO) wireless system. Conventional codebook designs use Grassmannian packing, equiangular frames, vector quantization, or Fourier based constructions. While the capacity and error rate performance of conventional codebook constructions have been extensively investigated, constructing these codebooks is notoriously difficult relying on techniques such as nonlinear search or iterative algorithms. Further, the resulting codebooks may not have a systematic structure to facilitate storage of the codebook and low search complexity. In this paper, we propose a new systematic codebook design based on Kerdock codes and mutually unbiased bases. The proposed Kerdock codebook consists of multiple mutually unbiased unitary bases matrices with quaternary entries and the identity matrix. We propose to derive the beamforming and precoding codebooks from this base codebook, eliminating the requirement to store multiple codebooks. The propose structure requires little memory to store and, as we show, the quaternary structure facilitates codeword search. We derive the chordal distance for two antenna and four antenna codebooks, showing that the proposed codebooks compare favorably with prior designs. Monte Carlo simulations are used to compare achievable rates and error rates for different codebooks sizes.