Subspace and DOA estimation under coarse quantization

TL;DR

This paper analyzes the problem of estimating directions of arrival from coarsely quantized data using a two-step approach involving covariance estimation and ESPRIT, providing rigorous bounds and insights into dithering schemes.

Contribution

It introduces a rigorous analysis of subspace and DOA estimation under coarse quantization with dithering, including bounds and performance comparisons of dithering schemes.

Findings

Triangular dithering outperforms rectangular dithering in certain scenarios.

Estimates are optimal with respect to the smallest non-zero eigenvalue.

The analysis applies broadly to spectral estimation algorithms.

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.