Local convergence of `globally convergent´ blind adaptive equalization algorithms

It is shown, through the analysis of nullspace for the channel convolution matrix, that the behavior of a finitely parameterized Godard equalizer in general can never achieve or approximate the desirable global convergence performance of an infinitely parameterized noncausal Godard equalizer. Nullspace theory is supported by a simple example showing ill-convergence of the Godard algorithm