Asymptotic Analysis of Subspace

Asymptotic analysis methods for performance prediction of so-called subspace direction-of-arrival estimation methods has been developed earlier, assuming that a large-enough number of array measurements, or snapshots, is collected. This paper also addresses the problem of making performance predictions, but for beamspace-based subspace methods. The novel approach in this paper assumes the number of array elements to be large, while the number of snapshots is arbitrary. The perturbation eeect, due to additive sensor noise, on a certain subspace is used for establishing the asymptotic behavior of direction-of-arrival estimates. The asymptotic estimation errors for the estimators resulting from Signal Sub-space Fitting methods, such as WSF, and Noise Subspace Fitting (NSF) methods, such as MUSIC and a multi-dimensional counterpart to WSF, are shown to be asymptotically unbi-ased and normally distributed. Provided that the array response vectors become orthogonal when the number of array elements increases, the NSF methods are shown to give consistent estimates even in the case of fully coherent emitter signals, and the WSF method is shown to be consistent for coherent emitter signals even without this assumption. Comparisons with results for Maximum-Likelihood methods yield conditions for guaranteeing eeciency of the methods. Some simulation examples are also included.