Performance analysis of smoothed subspace-based estimation methods

A formal approach is presented to carry out a performance analysis of subspace-based estimation techniques applied to the problem of the direction of arrival of plane waves. This approach was inspired by the operator formalism, on account of its algebraic simplicity. It is a generalized approach that can be easily modified to analyze any subspace-based technique, as it uses a series expansion of projection operators on the signal and noise subspaces. A perturbation analysis is performed on the operators, thus avoiding a direct use of the eigenvectors and eigenvalues. This allows the analysis to be carried out to any desired order. This is made possible by using an original recurrence formula developed for the higher order terms in the expansion of the projection operators. This method is applied to study the root-min-norm algorithm with uncorrelated signals impinging from distinct directions on a uniform linear array and then extended to the correlated signal scenario. Simulations which verify the analytical derivations are provided