On the asymptotic performance analysis of subspace DOA estimation in the presence of modeling errors: case of MUSIC

• Published in: IEEE transactions on signal processing Vol. 54; no. 3; pp. 907 - 920
• Main Authors: Ferreol, A., Larzabal, P., Viberg, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Antennas; Applied sciences; Asymptotic properties; Bias; Calibration; Closed-form solution; Computer aided software engineering; Detection, estimation, filtering, equalization, prediction; direction of arrival (DOA) estimation; Direction of arrival estimation; Error analysis; Errors; Estimation error; Exact sciences and technology; Exact solutions; Information, signal and communications theory; Mathematical analysis; modeling errors; Multiple signal classification; MUSIC; Performance analysis; Radiocommunications; Random variables; Root mean square; Signal and communications theory; Signal, noise; Stochastic processes; Studies; Telecommunications; Telecommunications and information theory; Performance evaluation; Estimation error; Second order; MUSIC; direction of arrival (DOA) estimation; modeling errors; Direction-of-arrival estimation; Parameter estimation; Error estimation; Hermite interpolation; Asymptotic behavior; Signal estimation; Subspace method; Calibration; Perturbation; Algorithm; Modeling; Mean square error; Simulation; First order; Antenna array; performance analysis
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2005.861798

This paper provides a new analytic expression of the bias and RMS error (root mean square) error of the estimated direction of arrival (DOA) in the presence of modeling errors. In , first-order approximations of the RMS error are derived, which are accurate for small enough perturbations. However, the previously available expressions are not able to capture the behavior of the estimation algorithm into the threshold region. In order to fill this gap, we provide a second-order performance analysis, which is valid in a larger interval of modeling errors. To this end, it is shown that the DOA estimation error for each signal source can be expressed as a ratio of Hermitian forms, with a stochastic vector containing the modeling error. Then, an analytic expression for the moments of such a Hermitian forms ratio is provided. Finally, a closed-form expression for the performance (bias and RMS error) is derived. Simulation results indicate that the new result is accurate into the region where the algorithm breaks down.