Partially adaptive filtering using randomized projections

TL;DR

This paper proposes a partially adaptive filtering method that uses randomized projections to efficiently approximate the main subspace, enabling effective interference suppression without eigenvalue decomposition.

Contribution

It introduces a novel filtering approach combining randomized matrix approximations with adaptive filtering, reducing computational complexity while maintaining performance.

Findings

Performance comparable to principal component filters

No eigenvalue decomposition required

Effective interference suppression in low-rank noise environments

Abstract

This short note addresses the design of a partially adaptive filter to retrieve a signal of interest in the presence of strong low-rank interference and thermal noise. We consider a generalized sidelobe canceler implementation where the dimension-reducing transformation is build resorting to ideas borrowed from randomized matrix approximations. More precisely, the main subspace of the auxiliary data $Z$ is approximated by $Z\Omega$ where $\Omega$ is a random matrix or a matrix that picks at random columns of $Z$. These transformations do not require eigenvalue decomposition, yet they provide performance similar to those of a principal component filter.