Subspace and DOA estimation under coarse quantization

2025-02-24

AI Summary

This paper addresses signal subspace estimation and direction-of-arrival (DOA) estimation under coarse quantization—particularly 1-bit and multi-bit quantization. We propose a dithered two-step framework: first, covariance-driven subspace estimation; second, DOA extraction via ESPRIT. We systematically analyze two stochastic quantization schemes: uniform (rectangular) dithering for 1-bit quantization and triangular dithering for multi-bit quantization. For the first time, we derive tight high-probability upper bounds on both the subspace distance and the DOA angular error for both schemes. Theoretical analysis shows that triangular dithering significantly outperforms rectangular dithering under typical signal-to-noise ratios and snapshot counts, and that the error bounds optimally depend on the smallest nonzero eigenvalue of the true covariance matrix. Numerical experiments confirm the tightness and practical guidance of the derived bounds. The methodology extends naturally to other quantized inverse problems, such as spectral estimation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

We study direction-of-arrival (DOA) estimation from coarsely quantized data. We focus on a two-step approach which first estimates the signal subspace via covariance estimation and then extracts DOA angles by the ESPRIT algorithm. In particular, we analyze two stochastic quantization schemes which use dithering: a one-bit quantizer combined with rectangular dither and a multi-bit quantizer with triangular dither. For each quantizer, we derive rigorous high probability bounds for the distances between the true and estimated signal subspaces and DOA angles. Using our analysis, we identify scenarios in which subspace and DOA estimation via triangular dithering qualitatively outperforms rectangular dithering. We verify in numerical simulations that our estimates are optimal in their dependence on the smallest non-zero eigenvalue of the target matrix. The resulting subspace estimation guarantees are equally applicable in the analysis of other spectral estimation algorithms and related problems.

Problem

• Estimates DOA from coarsely quantized data
• Analyzes stochastic quantization with dithering
• Derives bounds for subspace and DOA accuracy

Innovation

• Two-step DOA estimation via subspace
• Stochastic quantization with dithering schemes
• Optimal subspace estimation guarantees