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.

中文翻译：

---

用于低分辨率量化 MIMO 检测的 Hermite 扩展模型和 LMMSE 分析

在本文中，Hermite 多项式用于研究具有低分辨率量化的窄带多天线信号接收（即，MIMO）的线性逼近模型。该研究使用二阶 Hermite 展开 (SOHE) 产生了一种新颖的线性近似。SOHE 模型并非基于现有线性近似中常用的那些假设。相反，量化失真由二阶 Hermite 核表征，信号项由一阶 Hermite 核表征。结果表明，SOHE 模型几乎可以解释目前在低分辨率 MIMO 信号接收中观察到的所有现象和特征。当采用 SOHE 模型分析线性最小均方误差 (LMMSE) 信道均衡器时，结果表明，可以通过结合符号级归一化机制来增强当前的 LMMSE 算法。增强型 LMMSE 算法的性能通过瑞利衰落信道中窄带 MIMO 系统的计算机模拟得到证明。