Nonasymptotic Performance Analysis of Direct-Augmentation and Spatial-Smoothing ESPRIT for Localization of More Sources Than Sensors Using Sparse Arrays
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Direction augmentation (DA) and spatial smoothing (SS), followed by a subspace method such as ESPRIT or MUSIC, are two simple and successful approaches that enable localization of more uncorrelated sources than sensors with a proper sparse array. In this paper, we carry out nonasymptotic performance analyses of DA-ESPRIT and SS-ESPRIT in the practical finite-snapshot regime. We show that their absolute localization errors are bounded from above by C_1max{σ^2, C_2}/√(L) with overwhelming probability, where L is the snapshot number, σ^2 is the Gaussian noise power, and C_1,C_2 are constants independent of L and σ^2, if and only if they can do exact source localization with infinitely many snapshots. We also show that their resolution increases with the snapshot number, without a substantial limit. Numerical results corroborating our analysis are provided.
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