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.

翻译：本文对非渐近条件下的实值根MUSIC（RV-root-MUSIC）算法进行了系统的理论性能分析。RV-root-MUSIC的一个已知局限是由镜像根引起的估计模糊问题，该问题通常通过常规波束形成（CBF）进行抑制。通过利用共轭扩展方法构建的等价子空间，并利用真实根与镜像根扰动的等价性，本研究对三个关键方面进行了全面分析：噪声子空间扰动、真实根扰动和镜像根扰动。建立了统计模型，并推导了广义扰动表达式。蒙特卡洛仿真验证了理论结果的正确性与有效性。该分析为波达方向（DOA）估计中的参数优化提供了严格的理论基础，可应用于雷达、无线通信及智能感知等领域。