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.