标题： 关于一比特量化系统中的均方误差最优估计器 显示英文标题

标题： On the Mean Square Error Optimal Estimator in One-Bit Quantized Systems

摘要： 本文研究了在联合高斯输入的信道估计背景下，一比特量化系统中的均方误差（MSE）最优条件均值估计器（CME）。我们分析了一般非线性CME与基于Bussgang定理的线性Bussgang估计器之间的关系。我们强调了一个新的观察结果，即Bussgang估计器等于CME在不同特殊情况下，包括单变量高斯输入的情况和在量化前不存在加性噪声的多导频信号的情况。对于一般情况，我们进行了数值模拟以量化Bussgang估计器与CME之间的差距。该差距随着维度的增加和导频序列的变长而增大。我们提出了一种最优导频序列，其灵感来自于CME的见解，并推导出该情况下的新颖闭式表达式。随后，我们在导频数量渐近大的情况下找到了MSE的闭式极限，该极限也适用于Bussgang估计器。最后，我们展示了针对各种系统参数和不同性能指标的数值实验，这些实验揭示了量化范围内最优信道估计器的行为。在此背景下，出现在量化系统中的著名随机共振效应可以被量化。 显示英文摘要

摘要： This paper investigates the mean square error (MSE)-optimal conditional mean estimator (CME) in one-bit quantized systems in the context of channel estimation with jointly Gaussian inputs. We analyze the relationship of the generally nonlinear CME to the linear Bussgang estimator, a well-known method based on Bussgang's theorem. We highlight a novel observation that the Bussgang estimator is equal to the CME for different special cases, including the case of univariate Gaussian inputs and the case of multiple pilot signals in the absence of additive noise prior to the quantization. For the general cases we conduct numerical simulations to quantify the gap between the Bussgang estimator and the CME. This gap increases for higher dimensions and longer pilot sequences. We propose an optimal pilot sequence, motivated by insights from the CME, and derive a novel closed-form expression of the MSE for that case. Afterwards, we find a closed-form limit of the MSE in the asymptotically large number of pilots regime that also holds for the Bussgang estimator. Lastly, we present numerical experiments for various system parameters and for different performance metrics which illuminate the behavior of the optimal channel estimator in the quantized regime. In this context, the well-known stochastic resonance effect that appears in quantized systems can be quantified.