混合分辨率数据下贝叶斯参数估计的资源分配与抖动
Resource Allocation and Dithering of Bayesian Parameter Estimation Using Mixed-Resolution Data
摘要：
信号的量化是现代信号处理应用（例如传感、通信和推理）的组成部分。虽然信号量化提供了许多物理优势，但它通常会降低基于量化数据的后续估计性能。为了保持物理约束，同时带来大量的性能增益，在这项工作中，我们考虑系统的混合分辨率，1位量化和连续值，数据。首先，我们描述了一般混合分辨率模型的线性最小均方误差（LMMSE）估计及其相关的均方误差（MSE）。然而，LMMSE的MSE需要矩阵求逆，其中测量的数量定义矩阵维度，因此，不是用于优化和系统设计的易于处理的工具。因此，我们提出了线性高斯正交（LGO）测量模型，并推导出一个封闭形式的解析表达式下的LMMSE估计的MSE。此外，我们提出了LGO模型的两种常见的特殊情况：1）标量参数估计和2）混合ADC多输入多输出（MIMO）通信系统中的信道估计。然后，我们解决了资源分配优化问题的LGO模型与建议的易于处理的形式的MSE作为目标函数和功率约束下使用一维搜索。此外，我们提出了混合分辨率模型的抖动概念，并优化抖动噪声作为两种抖动方案的资源分配优化问题的一部分：1）仅向量化测量添加噪声和2）向两种测量类型添加噪声。最后，我们提出了模拟，证明了使用混合分辨率测量的优点和可能的改进引入抖动和资源分配。
英文摘要：
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.
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