DIRECTION-OF-ARRIVAL ESTIMATION USING RANK REVEALING QR FACTORIZATION

In recent years, signal subspace algorithms have emerged as a class of very powerful techniques for bearing estimation. All these algorithms obtain and use a set of vectors which are orthogonal to the direction vectors by performing an eigen-decomposition of the array covariance matrix. Eigen-decomposition, however, requires a considerable amount of computations. Here we discuss a new technique, 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, are 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.