Local minima escape transients of CMA

We examine the implications of our recent analysis of the local minima escape behavior of the Godard (or CMA) blind equalizer. This analysis suggests asymptotic estimates for the expected value of the escape time when leaving the region of attraction of local equilibria. For a particular source, channel, and equalizer local minimum parameterization, the log of the inverse of the mean escape time is estimated to be proportional to a weighted sum of the stepsize and the channel noise variance. We examine the validity of the functional form of this relationship for two examples. This experimental evidence corroborates our earlier analysis and suggests that the mean time to escape can be very large for the Godard (1980) algorithm (also known as the constant modulus algorithm)