Blind system identification using the empirical characteristic function´s derivative

High-order statistics have become a common tool in blind identification of nonminimum phase systems. In this paper we present a new, alternative tool, namely the first-order derivatives of the observations´ second characteristic function, evaluated at arbitrary (off-origin) locations. The estimation of these derivatives reduces plainly into specially-weighted empirical averages, from which the identification of the system´s zeros is nearly straightforward. We show that despite the addition of some nuisance parameters, this approach generates more equations than unknowns, and thus enables a well-averaged least-squares solution. We demonstrate, using simulation results, the potential improvement in estimation accuracy over cumulants-based estimation.