A PERFORMANCE ANALYSIS OF SUBSPACE-BASED METHODS IN THE PRESENCE OF MODEL ERRORS .1. THE MUSIC ALGORITHM

Application of subspace-based algorithms to narrowband direction-of-arrival (DOA) estimation requires that certain modeling assumptions be made. Most importantly, both the array response in all directions of interest and the spatial covariance of the noise must be known. In practice, however, neither of these quantities is known precisely. Depending on the degree to which they deviate from their nominal values, serious performance degradation may result. In this two-part paper, the performance of subspace-based algorithms is examined for situations in which the noise covariance and array response are perturbed from their assumed values. Part I focuses on the popular MUSIC algorithm. Theoretical expressions for the error in the MUSIC DOA estimates are derived and compared with simulations performed for several representative cases, and with the appropriate Cramer-Rao bound. In addition, an optimally weighted version of MUSIC is proposed for a particular class of array errors. In the companion paper, a similar analysis is performed for various multidimensional algorithms.