Min-norm interpretations and consistency of MUSIC, MODE and ML

The multiple signal characterization (MUSIC) approach, its generalization to correlated signals known as the method of direction estimation (MODE), and the deterministic maximum likelihood (ML) approach for bearing estimation in array processing are shown to be signal subspace fitting approaches in a minimum norm sense. MODE, for example, is shown to be an approach in which the array manifold is linearly estimated from principal empirical eigenvectors in a minimum weighted Frobenius norm sense. Using the min-norm interpretations, a unified proof for strong consistency of the three approaches is provided for stationary and ergodic signals.