New challenges in covariance estimation: multiple structures and coarse quantization

arXiv (Cornell University)

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 This review is spiced up by some yet unpublished insights on how to benefit from combined structural constraints.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.

Authors 5

1. Johannes Maly

   Catholic University of Eichstätt-Ingolstadt

   Affiliation as printed

   Catholic University of Eichstaett-Ingolstadt , Ostenstraße 26-28 , 85072 Eichstätt , Germany

2. Tianyu Yang

   Technische Universität Berlin

   Affiliation as printed

   Technical University of Berlin , Einsteinufer 25 , 10587 Berlin , Germany

3. Sjoerd Dirksen

   Utrecht University

   Affiliation as printed

   Utrecht University , Budapestlaan 6 , 3584 CD Utrecht , Netherlands

4. Holger Rauhut Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , Pontdriesch 10 , 52062 Aachen , Germany

5. Giuseppe Caire

   Technische Universität Berlin

   Affiliation as printed

   Technical University of Berlin , Einsteinufer 25 , 10587 Berlin , Germany