Robust blind methods using $\ell_p$ quasi norms

TL;DR

This paper investigates the robustness of blind subspace methods using _1 and _p quasi-norms, providing theoretical conditions for channel identifiability and analyzing factors affecting robustness.

Contribution

It offers the first theoretical analysis of _1 and _p quasi-norms in blind subspace methods, including necessary and sufficient conditions for channel identifiability.

Findings

Derived necessary and sufficient conditions for channel identifiability with _1 norm

Analyzed the frequency of channel parameter occurrences affecting robustness

Assessed the impact of channel parameters on method robustness

Abstract

It was shown in a previous work that some blind methods can be made robust to channel order overmodeling by using the $\ell_1$ or $\ell_p$ quasi-norms. However, no theoretical argument has been provided to support this statement. In this work, we study the robustness of subspace blind based methods using $\ell_1$ or $\ell_p$ quasi-norms. For the $\ell_1$ norm, we provide the sufficient and necessary condition that the channel should satisfy in order to ensure its identifiability in the noise-less case. We then study its frequency of occurrence, and deduce the effect of channel parameters on the robustness of blind subspace methods using $\ell_1$ norms.