Angle estimation for small sample size with fast eigenvector-free subspace method

Abstract

Subspace or projection methods, such as MUSIC, have been shown to perform excellently when used for angle-of-arrival estimation, especially in the case of small sample size. The drawback of those methods is their heavy computational load when used for arrays with a large number of elements. The paper investigates the performance of a fast subspace-estimation method which has been recently proposed for the closely related problem of adaptive spatial jammer suppression. This new method, called matrix transformation projection (MTP), is based on a general transformation of the covariance matrix formed from snapshots of an array of sensors. To evaluate the statistical properties of the MTP when used for angle estimation, the expectation of the corresponding angle spectra has been analytically derived. As the paper is addressing the small sample size performance of subspace methods (instead of the asymptotic one), the conventional perturbation analysis needed to be extended to second order. The resulting bias of the DOA estimates has been calculated and shown along with corresponding simulations to confirm the accuracy of the theoretical results. A comparison of these results for MTP showed the closeness to those of MUSIC even for small sample sizes, but the necessary computational load of MTP is significantly lower.