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 an attempt to maintain physical constraints, while, simultaneously, to attain substantial performance gain, 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, where the number of measurements defines the matrix dimensions and thus, may not be 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. We discuss two common special cases of the LGO model: 1) scalar parameter estimation, and 2) channel estimation in multiple-input multiple-output (MIMO) communication systems with mixed analog-to-digital converters (ADCs). We then solve the resource allocation optimization problem under the LGO model, with the proposed tractable MSE as an objective function and under a power constraint by using a one-dimensional search. Further, we present the concept of dithering for mixed-resolution models and optimize the dithering noise as part of the resource allocation optimization problem. Simulations show that the proposed resource allocation and dithering policies provide significant performance improvement.

中文翻译：

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使用混合分辨率数据的贝叶斯参数估计的资源分配和抖动

信号量化是现代信号处理应用（例如传感、通信和推理）的一个组成部分。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，同时获得显着的性能增益，我们考虑具有混合分辨率、1 位量化和连续值数据的系统。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) 估计量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了矩阵维度，因此可能不是优化和系统设计的易处理工具。所以，我们提出了线性高斯正交 (LGO) 测量模型，并推导出该模型下 LMMSE 估计量的 MSE 的封闭形式解析表达式。我们讨论 LGO 模型的两种常见特殊情况：1) 标量参数估计，以及 2) 具有混合模数转换器 (ADC) 的多输入多输出 (MIMO) 通信系统中的信道估计。然后，我们在 LGO 模型下解决资源分配优化问题，以提出的易处理 MSE 作为目标函数，并在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，并将抖动噪声优化为资源分配优化问题的一部分。