Subspace Estimation Along a Frequency Band Through Projection Matrix Approximation

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.This work was supported by the Spanish Ministry of Science and Innovation, the State Agency of Research (AEI) and the European Funds for Regional Development (EFRD) under Project PID2020-117303GB-C22