A new gradient search interpretation of super-exponential algorithm

In this letter, the super-exponential algorithm (SEA) is interpreted as a gradient search of an extremum of the inverse filter criteria, and the optimal gradient search step-size is presented as the root of a quartic equation. Different from the gradient search interpretation presented by Mboup and Regalia in the combined channel-equalizer space, the interpretation here is directly related with the realization of SEA in the equalizer space and uncovers more convergence details of SEA under unideal conditions.