A New Optimality Property of the Capon Estimator

A new derivation of the Capon spectral estimator is provided in this letter enriching the set of its possible interpretations. Specifically, it is shown that it defines the best rank-one approximation (according to any distance measure induced by a unitary invariant norm) of the data covariance matrix along the dyadic product specified by the useful signal direction. Remarkably, the Capon power estimate is obtained as solution to a convex optimization problem, which represents the starting point toward the development of a new class of robust estimators.