Date of Award


Degree Type



Electrical Engineering

First Advisor

Richard J. Vaccaro


In the last decade, the subspace approach has found prominence in the problem of estimating directions of arrival using an array of sensors. Many subspace methods have been proposed and improved; the most attractive ones among these are MUSIC, Min-Norm, State-Space Realization (TAM) and ESPRIT. However, performance analyses are required for justifying and comparing these methods before applying them. Early performance justifications and comparisons were based on simulations. In recent years, many excellent analytical studies have been reported, but these studies have one or more of the following restrictions: (i) assume asymptotic measurements, (ii) analyze some specific parameter perturbation directly instead of through the perturbation of the appropriate subspace, (iii) evaluate individual algorithms using different approximations (so it is hard to compare the analyses of different methods), (iv) involve complicated mathematics and statistics which result in difficult expressions. In our attempt to obtain a unified, nonasymptotic analysis to subspace processing algorithms in a greatly simplified and self-contained fashion, we

  1. classify these algorithms into category by the subspace they use - orthogonalsubspace processing and signal-subspace processing. We then derive expressions for the first-order perturbation of the signal and orthogonal subspaces using a matrix approximation technique. These formulas provides a common foundation for our analysis of all the DOA estimation algorithms mentioned above.
  2. define three approaches by the numerical procedure these algorithms exploit - extrema-searching, polynomial-rooting approach, matrix-shifting approach. We establish a common model for each approach and analyze these common models (instead of individual algorithms), and specialize the results for each algorithm.
  3. provide a first-order relationship between subspace perturbations and direction-of-arrival perturbations.
  4. use the perturbation formulas to derive variance expressions for DOA estimates for all the algorithms. We make the comparisons and discussions among these algorithms and approaches with our theoretical prediction and numerical simulations.

The tractable formulas derived in this analysis provide insight into the performance of the algorithms. Simulations verify the analysis.