Partially Linear Bayesian Estimation Using Mixed-Resolution Data

In this letter, we consider Bayesian parameterestimation using mixed-resolution data consisting of both analog and 1-bit quantized measurements. We investigate the use of the partially linear minimum mean-squared-error (PL-MMSE) estimator for this mixed-resolution scheme. The use of the PL-MMSE estimator, proposed for general models with “straightforward” and “complicated” parts, has not been demonstrated for quantized data. We derive closed-form analytic expressions for the linear minimum mean-squared-error (LMMSE) and for the PL-MMSE estimator for the mixed-resolution scheme with linear Gaussian orthonormal measurements. We discuss the properties of the proposed PL-MMSE estimator and show that in this case, the PL-MMSE is the sum of a linear function of the quantized measurements and a general Borel measurable function of the analog measurements. In the simulations, we show that the PL-MMSE estimator outperforms the LMMSE estimator for the problem of channel estimation in multiple-input-multiple-output (MIMO) communication systems with mixed analog-to-digital converters (ADCs).