Derivation of the theoretical performance of a Tensor MUSIC algorithm

Philippe Forster (1) , Guillaume Ginolhac (2) , Mélanie Boizard (1)

1 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie
2 LISTIC - Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance

In this paper, we derive the theoretical performance of a Tensor MUSIC algorithm based on the Higher Order Singular Value Decomposition (HOSVD) that was previously developed to estimate the Direction Of Arrival (DOA) and the polarization parameters of polarized sources. The derivation of this result is done via a perturbation analysis and allows to obtain the theoretical Mean Square Error (MSE) on the DOA and the polarization parameters. The proposed result is also shown to be valid for the Long Vector MUSIC algorithm, i.e. when the multidimensional samples are unfolded into a long vector. The agreement between theoretical and empirical MSEs is illustrated through Monte Carlo simulations.

Mots clés: Tensor MUSIC; HOSVD; DOA; Polarization sources; Theoretical Mean Square Error; Perturbation analysis

Domaines: Traitement du signal et de l'image [eess.SP]

Philippe Forster, Guillaume Ginolhac, Mélanie Boizard. Derivation of the theoretical performance of a Tensor MUSIC algorithm. Signal Processing, 2016, 129 (12), pp.97-105. ⟨10.1016/j.sigpro.2016.05.033⟩. ⟨hal-01391933⟩