Substituting the cumulants in the super-exponential blind equalization algorithm

The Shalvi-Weinstein super-exponential algorithm for blind channel equalization employs empirical high-order cross-cumulants between the equalizer\´s input and output for iterative updates of the equalizer. When the source signal has (nearly) null cumulants of the required order, the algorithm\´s performance may be severely degraded. Rather than resort to even higher-order cumulants in such cases, we propose to employ an alternative statistic, based on second-order derivatives (Hessians, evaluated away from the origin) of the joint log-characteristic function of the equalizer\´s input and output. These Hessians admit straightforward empirical estimates, maintain the "philosophy of operation" of the algorithm, and, as we demonstrate in simulation, can significantly improve its performance in such (and in other) cases.