FIR blind equalizers: no local minima issue?

Blind equalization was shown to be perfectly achievable within some channel identifiability conditions and no additive channel noise. Under these conditions some approaches such as constant modulus, known to have local minima when using a FIR equalizer, were proved to have only minima corresponding to perfect equalization performances. We extend, under the channel identifiability conditions, the results of perfect equalization existing for doubly infinite length equalizers to the case of FIR equalizers. Moreover, when the channel is corrupted by a small amount of additive noise, the optimal receivers are still in the vicinity of the Wiener receivers. Blind equalization criteria can then achieve almost as good performance as the non-blind optimal Wiener filter!