Unified analysis for DOA estimation algorithms in array signal processing

In this paper, a unified statistical performance analysis using perturbation expansions is applied to subspace-based algorithms for direction-of-arrival (DOA) estimation in array signal processing. The analysis assumes that only a finite amount of array data is available at high signal-to-noise ratio. The MUSIC, Min-Norm, State-Space Realization (TAM) and ESPRIT algorithms are analyzed in a common framework. A significant feature of this analysis is that it includes different types of error sources, such as the finite sample effect induced by additive observation noise, the sensor error effect induced by the inaccurate knowledge of sensor response and location, and the effect of a coherent noise field with unknown structure. All of the algorithms considered in this paper are based on a singular value decomposition of a data matrix. A general expression for the perturbation of singular vectors as a function of data matrix perturbations is derived and used to obtain an analytical expression for the mean-squared DOA estimation error in a simple and self-contained fashion. The tractable formulas provide insight into the algorithms. Simulation results verify the analytically predicted performance. © 1991