2023/02/22 by Yang, Zai, Wang, Kaijie
#FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2302.11209
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 C1\fracmax\σ2, C2\√(L) with overwhelming probability, where L is the snapshot number, σ2 is the Gaussian noise power, and C1,C2 are constants independent of L and σ2, 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.