# Non-colocated Time-Reversal MUSIC: High-SNR Distribution of Null Spectrum

## TL;DR

This paper derives the asymptotic distribution of the null spectrum in Time-Reversal MUSIC for high-SNR scenarios, providing insights into spectrum stability and validating findings through numerical analysis.

## Contribution

It introduces a theoretical framework for the null spectrum distribution in TR-MUSIC, enhancing understanding of its stability in high-SNR conditions.

## Key findings

- Null spectrum moments characterized up to second order
- Spectrum stability analyzed and compared
- Numerical results confirm theoretical predictions

## Abstract

We derive the asymptotic distribution of the null spectrum of the well-known Multiple Signal Classification (MUSIC) in its computational Time-Reversal (TR) form. The result pertains to a single-frequency non-colocated multistatic scenario and several TR-MUSIC variants are here investigated. The analysis builds upon the 1st-order perturbation of the singular value decomposition and allows a simple characterization of null-spectrum moments (up to the 2nd order). This enables a comparison in terms of spectrums stability. Finally, a numerical analysis is provided to confirm the theoretical findings.