Subspace estimation along a frequency band through projection matrix approximation

Abstract

In this paper, we present a method to estimate the signal subspace at all the frequencies in a given band, which is computed from the usual set of frequency-bin sample covariance matrices in wideband subspace estimation. Fundamentally, the method exploits the similarity between the signal subspace at any two near-by frequencies to produce an improved subspace estimate along the band. Its key idea consists of modeling the signal subspace by means of a projection matrix function which is approximated by a polynomial. The method provides two improvements: a reduced-size representation of the signal subspace along the 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). 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.