Revealing the evanescent components in Kronecker-product based codebooks: insights and implications

TL;DR

This paper analyzes the high spatial-frequency components in Kronecker-product based codebooks for MIMO systems, revealing their redundancy and proposing their removal to improve system performance based on theoretical and simulation evidence.

Contribution

It provides a theoretical and empirical investigation into the evanescent (high spatial-frequency) components in Kronecker-product codebooks, suggesting their elimination for better MIMO performance.

Findings

High spatial-frequency codewords are redundant in Kronecker-product codebooks.

Removing these codewords can enhance MIMO system performance.

Theoretical analysis and simulations support the proposed removal strategy.

Abstract

The orthogonal bases of discrete Fourier transform (DFT) has been recognized as the standard spatial-domain bases for Type I, Type II and enhanced Type II codewords by the 3rd Generation Partnership Project (3GPP). For uniform planar arrays, these spatial-domain bases are derived as the Kronecker product of one-dimensional DFT bases. Theoretically, each spatial basis corresponds to a beam directed towards a specific angle of departure and the set of bases represent the orthogonal beams that cover the front hemisphere of an array. While the Kronecker-product based precoding scheme facilitates the concise indexing of a codeword in the codebooks through precoding matrix indicators (PMIs) in channel state information feedback, it introduces redundant spatial beams characterized by high spatial-frequency components. This paper investigates the presence of codewords representing high spatial-frequency components within the Kronecker-product based codebooks. Through theoretical analysis and simulations, we confirm the redundancy of these codewords in MIMO communications, advocating for their removal from the codebooks to enhance system performance. Several topics relevant to the high spatial components are also involved in the discussion. Practical suggestions regarding future standard design are provided based on our theoretical analysis and simulation results.