On the equivalence between the super-exponential algorithm and a gradient search method
Mamadou Mboup, P.A. Regalia · 1999
This paper reviews the super-exponential algorithm proposed by Shalvi and Weinstein (1993) for blind channel equalization. We show that the algorithm coincides with a gradient search of a maximum of a cost function, which belongs to a family of functions very relevant in blind channel equalization. This family traces back to Donoho's (1981) work on minimum entropy deconvolution, and also underlies the Godard (1980) (or constant modulus) and the Shalvi-Weinstein algorithms. Using this gradient search interpretation, we give a simple proof of convergence for the super-exponential algorithm. Finally, we show that the gradient step-size choice giving rise to the super-exponential algorithm is optimal.