Hermite Expansion Model and LMMSE Analysis for Low-Resolution Quantized MIMO Detection

TL;DR

This paper introduces a novel Hermite polynomial-based linear approximation model for low-resolution MIMO detection, improving the analysis and performance of LMMSE equalizers in quantized systems.

Contribution

It proposes the second-order Hermite expansion (SOHE) model for low-resolution MIMO, providing a more accurate characterization of quantization effects without common simplifying assumptions.

Findings

SOHE model explains observed phenomena in low-resolution MIMO reception.

Enhanced LMMSE algorithm with symbol-level normalization improves detection performance.

Simulation results demonstrate the effectiveness of the proposed approach in Rayleigh fading channels.

Abstract

In this paper, the Hermite polynomials are employed to study linear approximation models of narrowband multiantenna signal reception (i.e., MIMO) with low-resolution quantizations. This study results in a novel linear approximation using the second-order Hermite expansion (SOHE). The SOHE model is not based on those assumptions often used in existing linear approximations. Instead, the quantization distortion is characterized by the second-order Hermite kernel, and the signal term is characterized by the first-order Hermite kernel. It is shown that the SOHE model can explain almost all phenomena and characteristics observed so far in the low-resolution MIMO signal reception. When the SOHE model is employed to analyze the linear minimum-mean-square-error (LMMSE) channel equalizer, it is revealed that the current LMMSE algorithm can be enhanced by incorporating a symbol-level normalization mechanism. The performance of the enhanced LMMSE algorithm is demonstrated through computer simulations for narrowband MIMO systems in Rayleigh fading channels.