Attraction of saddles and slow convergence in CMA adaptation

We show that the most widely used blind equalization algorithm, the constant modulus algorithm, CMA, can be attracted during one convergence trajectory to the vicinity of more than one of the saddles in its error performance surface where it exhibits very slow convergence. We also establish bounds on the attraction and escape rates at a saddle and show that the saddles associated with lower energy levels have slower escape rates than the saddles with higher energy levels. These results highlight the need for intelligent initialization schemes for the CMA algorithm. We suggest a step normalisation technique to improve convergence speed in the vicinity of a saddle. © 1997 Elsevier Science B.V