New challenges in covariance estimation: multiple structures and coarse quantization

TL;DR

This paper reviews recent advances in covariance matrix estimation, emphasizing structured models and quantization effects, and introduces new insights on estimation under coarse one-bit quantization.

Contribution

It provides a comprehensive survey of recent theoretical progress and offers unpublished insights on leveraging combined structural constraints and quantization in covariance estimation.

Findings

Covariance estimation is feasible with structured models and quantized data.

New methods enable accurate covariance estimation under one-bit quantization.

Structural constraints improve estimation accuracy in practical scenarios.

Abstract

In this self-contained chapter, we revisit a fundamental problem of multivariate statistics: estimating covariance matrices from finitely many independent samples. Based on massive Multiple-Input Multiple-Output (MIMO) systems we illustrate the necessity of leveraging structure and considering quantization of samples when estimating covariance matrices in practice. We then provide a selective survey of theoretical advances of the last decade focusing on the estimation of structured covariance matrices. This review is spiced up by some yet unpublished insights on how to benefit from combined structural constraints. Finally, we summarize the findings of our recently published preprint "Covariance estimation under one-bit quantization" to show how guaranteed covariance estimation is possible even under coarse quantization of the samples.