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Analytical performance assessment of multi-dimensional matrix- and tensor-based ESPRIT-type algorithms

: Römer, Florian; Haardt, Martin; Galdo, Giovanni del


IEEE transactions on signal processing 62 (2014), Nr.10, S.2611-2625
ISSN: 0096-3518
ISSN: 0018-9278
ISSN: 0096-1620
ISSN: 1053-587X
Fraunhofer IIS ()
Richtungsschätzung (DoA)

In this paper we present a generic framework for the asymptotic performance analysis of subspace-based parameter estimation schemes. It is based on earlier results on an explicit first-order expansion of the estimation error in the signal subspace obtained via an SVD of the noisy observation matrix. We extend these results in a number of aspects. Firstly, we demonstrate that an explicit first-order expansion of the Higher-Order SVD (HOSVD)-based subspace estimate can be derived. Secondly, we show how to obtain explicit first-order expansions of the estimation error of arbitrary ESPRIT-type algorithms and provide the expressions for R-D Standard ESPRIT, R-D Unitary ESPRIT, R-D Standard Tensor-ESPRIT, as well as R-D Unitary Tensor-ESPRIT. Thirdly, we derive closed-form expressions for the mean square error (MSE) and show that they only depend on the second-order moments of the noise. Hence, to apply this framework we only need the noise to be zero mean and possess finite second order moments. Additional assumptions such as Gaussianity or circular symmetry are not needed.