# The Cramer-Rao Bound for Signal Parameter Estimation from Quantized Data

arXiv: https://arxiv.org/abs/2209.13182 · HTML: https://mlsanity.com/paper/2209.13182/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2022.

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

- [Generalized Linear Models with 1-Bit Measurements: Asymptotics of the Maximum Likelihood Estimator](https://mlsanity.com/paper/2501.04937/) (2025)
- [Learned Bayesian Cram'er-Rao Bound for Unknown Measurement Models Using Score Neural Networks](https://mlsanity.com/paper/2502.00724/) (2025)
- [Quantized Signal Recovery with Interference via Parametrized Look-Up Tables](https://mlsanity.com/paper/2507.18370/) (2025)
- [Weighted Bayesian Cramacuteer-Rao Bound for Mixed-Resolution Parameter Estimation](https://mlsanity.com/paper/2508.20761/) (2025)

## Abstract (arXiv)

Several current ultra-wide band applications, such as millimeter wave radar and communication systems, require high sampling rates and therefore expensive and energy-hungry analogto-digital converters (ADCs). In applications where cost and power constraints exist, the use of high-precision ADCs is not feasible and the designer must resort to ADCs with coarse quantization. Consequently the interest in the topic of signal parameter estimation from quantized data has increased significantly in recent years. The Cramer-Rao bound (CRB) is an important yardstick in any parameter estimation problem. Indeed it lower bounds the variance of any unbiased parameter estimator. Moreover, the CRB is an achievable limit, for instance it is asymptotically attained by the maximum likelihood estimator (under regularity conditions), and thus it is a useful benchmark to which the accuracy of any parameter estimator can and should be compared. A formula for the CRB for signal parameter estimation from real-valued quantized data has been presented in but its derivation was somewhat sketchy. The said CRB formula has been extended for instance in to complex-valued quantized data, but again its derivation was rather sketchy. The special case of binary (1-bit) ADCs and a signal consisting of one sinusoid has been thoroughly analyzed in . The CRB formula for a binary ADC and a general real-valued signal has been derived.