# Wideband Subspace Estimation Through Projection Matrix Approximation

## TL;DR

This paper introduces a polynomial approximation approach for wideband subspace estimation, reducing parameters and improving DOA estimation accuracy by modeling the signal subspace's projection matrix across frequencies.

## Contribution

It proposes a novel polynomial fitting method for the projection matrix to enhance wideband subspace estimation and DOA accuracy, with theoretical bounds and numerical validation.

## Key findings

- Reduces the number of parameters needed for wideband subspace representation.
- Improves the accuracy of wideband DOA estimators like IC-MUSIC and MTOPS.
- Provides asymptotic bounds for estimation bias and RMS error.

## Abstract

In this paper, we present a wideband subspace estimation method that characterizes the signal subspace through its orthogonal projection matrix at each frequency. Fundamentally, the method models this projection matrix as a function of frequency that can be approximated by a polynomial. It provides two improvements: a reduction in the number of parameters required to represent the signal subspace along a given frequency band and a quality improvement in wideband direction-of-arrival (DOA) estimators such as Incoherent Multiple Signal Classification (IC-MUSIC) and Modified Test of Orthogonality of Projected Subspaces (MTOPS). In rough terms, the method fits a polynomial to a set of projection matrix estimates, obtained at a set of frequencies, and then uses the polynomial as a representation of the signal subspace. The paper includes the derivation of asymptotic bounds for the bias and root-mean-square (RMS) error of the projection matrix estimate and a numerical assessment of the method and its combination with the previous two DOA estimators.