On Optimal MMSE Channel Estimation for One-Bit Quantized MIMO Systems

Abstract

This paper focuses on the minimum mean squared error (MMSE) channel estimator for multiple-input multiple-output (MIMO) systems with one-bit quantization at the receiver side. Despite its optimality and significance in estimation theory, the MMSE estimator has not been fully investigated in this context due to its general nonlinearity and computational complexity. Instead, the typically suboptimal Bussgang linear MMSE (BLMMSE) channel estimator has been widely adopted. In this work, we develop a new framework to compute the MMSE channel estimator that hinges on the computation of the orthant probability of a multivariate normal distribution. Based on this framework, we determine a necessary and sufficient condition for the BLMMSE channel estimator to be optimal and thus equivalent to the MMSE estimator. Under the assumption of specific channel correlation or pilot symbols, we further utilize the framework to derive analytical expressions for the MMSE estimator that are particularly convenient for the computation when certain system dimensions become large, thereby enabling a comparison between the BLMMSE and MMSE channel estimators in these cases.