Non-Asymptotic Performance Analysis of DOA Estimation Based on Real-Valued Root-MUSIC

Abstract

This paper presents a systematic theoretical performance analysis of the Real-Valued root-MUSIC (RV-root-MUSIC) algorithm under non-asymptotic conditions. A well-known limitation of RV-root-MUSIC is the estimation ambiguity caused by mirror roots, which are typically suppressed using conventional beamforming (CBF). By leveraging the equivalent subspace constructed through the conjugate extension method and exploiting the equivalence of perturbations for true and mirror roots, this work provides a comprehensive study of three key aspects: noise subspace perturbation, true-root perturbation, and mirror-root perturbation. A statistical model is established, and generalized perturbation expressions are derived. Monte Carlo simulations confirm the correctness and effectiveness of the theoretical results. The analysis provides a rigorous foundation for parameter optimization in Direction-of-Arrival (DOA) estimation, with applications in radar, wireless communications, and intelligent sensing.