Although HOS-based adaptive SISO blind algorithms can be effective under ap propriate initialization, they exhibit two major drawbacks. First, local convergence is a possibility for many adaptive blind equalization algorithms based on HOS, which typically results from the use of multi-modal cost functions. Moreover, their con vergence can be quite slow and may require long streams of output data. Similarly, many non-adaptive algorithms based on explicit use of HOS, while not necessarily having local convergence problems, also require many channel output data in order to obtain accurate time-average approximates of the needed higher order statistics. The requirement of large data samples can pose a potentially serious obstacle to the application of blind equalization in fast time-varying environment.