On the asymptotic distribution of Time-Reversal MUSIC null spectrum

In this paper we derive the asymptotic (viz. high signal-to-noise ratio) distribution of the null spectrum of the well-known Multiple Signal Classification (MUSIC) in its computational Time-Reversal (TR) form. The analysis builds upon classical results on the first-order perturbation of the singular value decomposition. These allow to obtain a simple characterization of the moments (up to the second order) of the spectrum and thus provide also a consistent form of the asymptotic “noisiness” measure in the TR case. The present study refers to a single-frequency case in a multistatic co-located scenario. The proposed analysis also enables a simple comparison of TR-MUSIC null-spectrum properties when linear and non linear (i.e. with mutual interaction effects) scattering models are assumed. Finally, a numerical analysis is provided to confirm the theoretical findings.