[论文解读] Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data

Itai E. Berman, Tirza Routtenberg|arXiv (Cornell University)|Sep 17, 2020

Distributed Sensor Networks and Detection Algorithms参考文献 52被引用 7

一句话总结

该论文提出了一种基于混合分辨率数据（结合1比特量化与连续值测量）的贝叶斯参数估计的可计算框架，通过引入线性高斯正交（LGO）模型，推导出LMMSE估计器的闭式均方误差（MSE）表达式，从而在功率约束下实现高效的资源分配与抖动优化。仿真结果表明，该方法在性能上优于纯量化或纯模拟系统。

ABSTRACT

Quantization of signals is an integral part of modern signal processing applications, such as sensing, communication, and inference. While signal quantization provides many physical advantages, it usually degrades the subsequent estimation performance that is based on quantized data. In order to maintain physical constraints and simultaneously bring substantial performance gain, in this work we consider systems with mixed-resolution, 1-bit quantized and continuous-valued, data. First, we describe the linear minimum mean-squared error (LMMSE) estimator and its associated mean-squared error (MSE) for the general mixed-resolution model. However, the MSE of the LMMSE requires matrix inversion in which the number of measurements defines the matrix dimensions and thus, is not a tractable tool for optimization and system design. Therefore, we present the linear Gaussian orthonormal (LGO) measurement model and derive a closed-form analytic expression for the MSE of the LMMSE estimator under this model. In addition, we present two common special cases of the LGO model: 1) scalar parameter estimation and 2) channel estimation in mixed-ADC multiple-input multiple-output (MIMO) communication systems. We then solve the resource allocation optimization problem of the LGO model with the proposed tractable form of the MSE as an objective function and under a power constraint using a one-dimensional search. Moreover, we present the concept of dithering for mixed-resolution models and optimize the dithering noise as part of the resource allocation optimization problem for two dithering schemes: 1) adding noise only to the quantized measurements and 2) adding noise to both measurement types. Finally, we present simulations that demonstrate the advantages of using mixed-resolution measurements and the possible improvement introduced with dithering and resource allocation.

研究动机与目标

• 解决现代系统中因信号量化导致的参数估计性能下降问题。
• 开发一种可计算的分析框架，用于利用混合分辨率（1比特与连续）数据进行参数估计。
• 在功率约束下，优化模拟与1比特测量之间的资源分配。
• 将抖动整合到估计框架中，以提升性能。
• 通过仿真展示混合分辨率系统的优越性。

提出的方法

• 引入线性高斯正交（LGO）测量模型，以推广常见的估计场景。
• 在LGO模型下，推导出LMMSE估计器均方误差（MSE）的闭式解析表达式。
• 将LGO模型应用于两个关键场景：标量参数估计与混合ADC大规模MIMO信道估计。
• 利用Woodbury矩阵恒等式，以闭式表达计算自相关矩阵的逆矩阵。
• 在给定最优量化测量数的前提下，通过关于模拟测量数的一维搜索求解资源分配问题。
• 针对两种方案优化抖动噪声：仅对量化测量进行抖动，以及对两种测量类型均进行抖动。

实验结果

研究问题

• RQ1 能否在混合分辨率数据下，为LMMSE估计推导出闭式MSE表达式？
• RQ2 混合分辨率系统的性能与纯模拟或纯1比特系统相比如何？
• RQ3 在功率约束下，模拟与1比特测量之间的最优资源分配是什么？
• RQ4 抖动如何提升混合分辨率系统中的估计性能？
• RQ5 所提出的框架能否推广至大规模MIMO等实际系统？

主要发现

• LGO模型使得LMMSE估计的MSE可实现闭式表达，避免了计算代价高昂的矩阵求逆。
• 在模拟测量数固定的情况下，为最小化MSE，在功率约束下应最大化1比特测量数。
• 最优资源分配通过关于模拟测量数的一维搜索获得。
• 抖动可提升估计性能，尤其在对两种测量类型均应用抖动时效果更显著。
• 仿真结果证实，经优化分配与抖动的混合分辨率系统，性能优于纯1比特或纯模拟系统。
• 该框架适用于实际系统，如采用混合ADC架构的大规模MIMO系统。