# Compressive Toeplitz Covariance Estimation From Few-Bit Quantized Measurements With Applications to DOA Estimation

arXiv: https://arxiv.org/abs/2512.22527 · HTML: https://mlsanity.com/paper/2512.22527/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 51 references that are in the map.
- First posted on arXiv 27 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization](https://mlsanity.com/paper/2202.13157/) (2022)
- [Quantizing Heavy-tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recovery](https://mlsanity.com/paper/2212.14562/) (2022)
- [Structured Covariance Matrix Estimation with Missing-Data for Radar Applications via Expectation-Maximization](https://mlsanity.com/paper/2105.03738/) (2021)
- [Quantized Low-Rank Multivariate Regression with Random Dithering](https://mlsanity.com/paper/2302.11197/) (2023)
- [Sample Efficient Toeplitz Covariance Estimation](https://mlsanity.com/paper/1905.05643/) (2019)
- [New Methods for MLE of Toeplitz Structured Covariance Matrices with Applications to RADAR Problems](https://mlsanity.com/paper/2307.03923/) (2023)
- [A Parameter-Free Two-Bit Covariance Estimator with Improved Operator Norm Error Rate](https://mlsanity.com/paper/2308.16059/) (2023)
- [Subspace Learning with Partial Information](https://mlsanity.com/paper/1402.4844/) (2014)
- [A Robust and Statistically Efficient Maximum-Likelihood Method for DOA Estimation Using Sparse Linear Arrays](https://mlsanity.com/paper/2203.13433/) (2022)
- [Nonasymptotic performance analysis of ESPRIT and spatial-smoothing ESPRIT](https://mlsanity.com/paper/2201.03457/) (2022)
- [Bit Efficient Toeplitz Covariance Estimation](https://mlsanity.com/paper/2412.12678/) (2024)
- [Model-Based Learning for DOA Estimation with One-Bit Single-Snapshot Sparse Arrays](https://mlsanity.com/paper/2502.17473/) (2025)

## Abstract (arXiv)

This paper addresses the problem of estimating the Hermitian Toeplitz covariance matrix under practical hardware constraints of sparse observations and coarse quantization. Within the triangular-dithered quantization framework, we propose an estimator called Toeplitz-projected sample covariance matrix (Q-TSCM) to compensate for the quantization-induced bias, together with its finite-bit counterpart termed the 2k-bit Toeplitz-projected sample covariance matrix (2k-TSCM), obtained by truncating the pre-quantization observations. Under the complex Gaussian assumption, we derive non-asymptotic error bounds of the estimators that reveal a quadratic dependence on the quantization level and capture the effect of sparse sampling patterns through the so-called coverage coefficient. To further improve performance, we propose the quantized sparse and parametric approach (Q-SPA) based on a covariance-fitting criterion, which enforces additionally positive semidefiniteness at the cost of solving a semidefinite program. Numerical experiments are presented that corroborate our theoretical findings and demonstrate the effectiveness of the proposed estimators in the application to direction-of-arrival estimation.