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

2025-09-02

AI Summary

To address the direction-of-arrival (DOA) estimation ambiguity in real-valued root-MUSIC (RV-root-MUSIC) caused by spurious mirror roots under non-asymptotic conditions, this paper proposes a conjugate-expanded equivalent subspace construction method. It systematically models the joint perturbations induced by noise, true roots, and mirror roots. For the first time, it establishes the theoretical equivalence between mirror-root and true-root perturbations in the non-asymptotic regime and derives a generalized statistical model for root-location bias. By integrating subspace analysis and matrix perturbation theory with conventional beamforming (CBF), the method effectively suppresses mirror roots. Simulation results validate both the accuracy of the proposed perturbation model and the efficacy of the algorithm. The work provides an analytically tractable and broadly applicable theoretical framework for DOA estimation performance analysis and parameter optimization in radar, wireless communications, and intelligent sensing systems.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Analyzing RV-root-MUSIC algorithm performance under non-asymptotic conditions
• Addressing estimation ambiguity problem caused by mirror roots
• Establishing statistical perturbation model for true and mirror roots

Innovation

• Real-Valued root-MUSIC algorithm analysis
• Conjugate extension method for subspace equivalence
• Statistical perturbation model for mirror roots