Analysis of the combined effects of finite samples and model errors on array processing performance

The principal sources of estimation error in sensor array signal processing applications are the finite sample effects of additive noise and imprecise models for the antenna array and spatial noise statistics. While the effects of these errors have been studied individually, their combined effect has not yet been rigorously analyzed. The authors undertake such an analysis for the class of so-called subspace fitting algorithms. In addition to deriving first-order asymptotic expressions for the estimation error, they show that an overall optimal weighting exists for a particular array and noise covariance error model. In a companion paper, the optimally weighted subspace fitting method is shown to be asymptotically equivalent with the more complicated maximum a posteriori estimator. Thus, for the model in question, no other method can yield more accurate estimates for large samples and small model errors. Numerical examples and computer simulations are included to illustrate the obtained results and to verify the asymptotic analysis for realistic scenarios