# MCRB for Parameter Estimation from One-Bit Quantized and Oversampled Measurements

arXiv: https://arxiv.org/abs/2503.22860 · HTML: https://mlsanity.com/paper/2503.22860/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 61 references that are in the map.
- First posted on arXiv 28 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [High Dimensional Channel Estimation Using Deep Generative Networks](https://mlsanity.com/paper/2006.13494/) (2020)
- [UNO: Unlimited Sampling Meets One-Bit Quantization](https://mlsanity.com/paper/2301.10155/) (2022)
- [Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications](https://mlsanity.com/paper/1709.08210/) (2017)
- [Deep Learning based Channel Estimation for Massive MIMO with Mixed-Resolution ADCs](https://mlsanity.com/paper/1908.06245/) (2019)
- [Neural Network-Optimized Channel Estimator and Training Signal Design for MIMO Systems with Few-Bit ADCs](https://mlsanity.com/paper/2003.09007/) (2020)
- [Multiuser-MIMO Systems Using Comparator Network-Aided Receivers With 1-Bit Quantization](https://mlsanity.com/paper/2211.10025/) (2022)
- [One-bit mmWave MIMO Channel Estimation using Deep Generative Networks](https://mlsanity.com/paper/2211.08635/) (2022)

## Abstract (arXiv)

One-bit quantization has garnered significant attention in recent years for various signal processing and communication applications. Estimating model parameters from one bit quantized data can be challenging, particularly when the quantization process is explicitly accounted for in the estimator. In many cases, the estimator disregards quantization effects, leading to model misspecification. Consequently, estimation errors arise from both quantization and misspecification. Traditional performance bounds, such as the Cramer-Rao bound (CRB), fail to capture the impact of misspecification on estimation performance. To address this limitation, we derive the misspecified CRB (MCRB) for parameter estimation in a quantized data model consisting of a signal component in additive Gaussian noise. We apply this bound to direction-of-arrival estimation using quantized measurements from a sensor array and to frequency estimation with oversampled quantized data. The simulations show that the MCRB is asymptotically achieved by the mean-squared-error of the misspecified maximum-likelihood estimator. Our results demonstrate that, unlike in finely quantized scenarios, oversampling can significantly enhance the estimation performance in the presence of misspecified one-bit quantized measurements.