An improper random vector approach for ESPRIT and unitary ESPRIT frequency estimation

The problem of estimating the frequencies of a complex signal corrupted by noise is addressed in this paper. Solving the problem by a subspace approach induce an inevitable maximum overlap between windowed observation vectors. It appears therefore that traditional second order statistics do not describe totally the second order behavior and the notion of improper random vector is recommended. Based on this, we analyze an ESPRIT and a Unitary ESPRIT-based methods established with improper random vectors assumption. Numerical simulations and a real application are brought for embellishing the discussion.