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

This paper presents a systematic theoretical performance analysis of the Real-Valued root-MUSIC (RV-root-MUSIC) algorithm under non-asymptotic conditions. However, RV-root-MUSIC suffers from the problem of estimation ambiguity for the mirror roots, therefore the conventional beamforming (CBF) technique is typically employed to filter out the mirror roots. Through the equivalent subspace based on the conjugate extension method and the equivalence of perturbations for both true roots and mirror roots , this paper provides a comprehensive investigation of three critical aspects: noise subspace perturbation, true root perturbation, and mirror root perturbation characteristics in the RV-root-MUSIC algorithm. The statistical model is established and the generalized expression of perturbation is further developed. The simulation results show the correctness and validity of the derived statistical characteristics. The results provide a solid theoretical foundation for optimizing the parameter selection of DOA estimation in practical applications, particularly in radar systems, communication networks, and intelligent sensing technologies.