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

TL;DR

This work tackles non-asymptotic DOA estimation with RV-root-MUSIC, addressing mirror-root ambiguity through a perturbation-based framework that separately analyzes noise-subspace, true-root, and mirror-root perturbations. It derives generalized expressions for DOA deviations, including a closed-form true-DOA bias $\Delta\theta_k = C_k\,\mathrm{Im}(\Delta r_k/r_k)$ with $C_k = \frac{\lambda}{2\pi d\cos\theta_k}$, and shows how even-element ULAs induce root degeneracy that can be mitigated by a correction factor $R(a)$. Monte Carlo simulations validate the theory under finite snapshots and SNR, demonstrating tight agreement with predicted RMSE trends and guiding practical parameter choices. The results provide a rigorous, non-asymptotic foundation for optimizing RV-root-MUSIC in radar, communications, and sensing systems, including guidance on array design and mirror-root suppression strategies.

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.

Figures (3)

• Figure 1: Roots of RV-root-MUSIC in varying array elements
• Figure 2: The trend of estimation RMSE in SNR variation
• Figure 3: The trend of estimation RMSE in Snapshots variation