  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.
