Abstract:

The direction-finding (DF) success probability is an important specification of the eigen-structure algorithm. We derive the DF success probability of the MUSIC algorithm in the presence of modeling errors. A closed-form expression of DF error and its statistical properties are obtained from the first-order Taylor expansion of the spatial spectrum function. Two classes of DF success definitions are given for single-source DF and holistic DF based on these definitions and statistical characteristics of the modeling errors. The calculation formulas of the DF success probability are derived. The theoretical analysis is validated through simulation using a uniform circular array (UCA) and a uniform linear array (ULA).

Key words: direction-finding, modeling errors, MUSIC algorithm, direction-finding success probability, Taylor expansion, quadratic form of Gaussian vector