Performance Analysis of Spatial Smoothing Schemes in the Context of Large Arrays

International audienceThis paper addresses the statistical behaviour of spatial smoothing subspace DoA estimation schemes using a sensor array in the case where the number of observations N is significantly smaller than the number of sensors M , and that the number of virtual arrays L is such that M and N L are of the same order of magnitude. This context is modelled by an asymptotic regime in which N L and M both converge towards ∞ at the same rate. As in recent works devoted to the study of (unsmoothed) subspace methods in the case where M and N are of the same order of magnitude, it is shown that it is still possible to derive improved DoA estimators termed as Generalized-MUSIC (G-MUSIC). The key ingredient of this work is a technical result showing that the largest singular values and corresponding singular vectors of low rank deterministic perturbation of certain Gaussian block-Hankel large random matrices behave as if the entries of the latter random matrices were independent identically distributed. 1. INTRODUCTION The statistical analysis of subspace DoA estimation methods using an array of sensors is a topic that has received a lot of attention since the seventies. Most of the works were devoted to the case where the number of available samples N of the observed signal is much larger than the number of sensors M of the array (see e.g. [11] and the references therein), The case where M and N are large and of the same order of magnitude was addressed for the first time in [9] using large random matrix theory. [9] was followed by various works such as [5], [14], [7]. In this paper, the number of observations may also be much smaller than the number of sensors. In this context, it is well established that spatial smoothing schemes, originally developed to address coherent sources ([1], [13], [12]), can be used to artificially increase the number of snapshots (see e.g. [11] and the references therein, see also the recent related contributions [3], [4] devoted to the case where N = 1). Spatial smoothing consists in considering L < M overlapping arrays with M − L + 1 sensors , and allows to generate artificially N L snapshots observed on a virtual array of M − L + 1 sensors. (M − L + 1) × N L matrix