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

arXiv: https://arxiv.org/abs/2404.05536 · HTML: https://mlsanity.com/paper/2404.05536/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2024.

## Built on by (most cited first, 4 of 4)

- [Linear and Nonlinear MMSE Estimation in One-Bit Quantized Systems under a Gaussian Mixture Prior](https://mlsanity.com/paper/2407.01305/) (2024)
- [Model-Based Learning for DOA Estimation with One-Bit Single-Snapshot Sparse Arrays](https://mlsanity.com/paper/2502.17473/) (2025)
- [Energy-Efficient State Estimation with 1-Bit Sensing: A Bussgang-Kalman Framework for Internet of Things](https://mlsanity.com/paper/2507.17284/) (2025)
- [Weighted Bayesian Cramacuteer-Rao Bound for Mixed-Resolution Parameter Estimation](https://mlsanity.com/paper/2508.20761/) (2025)

## Abstract (arXiv)

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 channel estimator has not been fully investigated in this context due to its general non-linearity and computational complexity. Instead, the typically suboptimal Bussgang linear MMSE (BLMMSE) estimator has been widely adopted. In this work, we develop a new framework to compute the MMSE channel estimator that hinges on computation of the orthant probability of the multivariate normal distribution. Based on this framework, we determine a necessary and sufficient condition for the BLMMSE channel estimator to be optimal and 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 channel estimator that are particularly convenient for computation when certain system dimensions become large, thereby enabling a comparison between the BLMMSE and MMSE channel estimators in these cases.