Direction-of-arrival estimation using rank revealing QR factorization

Abstract

The authors describe a novel technique for direction-of-arrival estimation based on computing a permutation matrix E and a QR factorization RE=HB of the permuted covariance matrix R, such that a possible rank deficiency of R is revealed in the triangular factor B having a minimum norm lower right block. A subset of the columns of the orthogonal matrix, H, is shown to be orthogonal to the direction vectors of sources and hence can be used to estimate their bearings. The cost of this algorithm is only slightly more than that of one QR factorization, but is much lower than that of an eigen-decomposition. Simulation results are included to show that the proposed method performs nearly as well as MUSIC in terms of signal resolution, bias, and variance of the estimated bearings.