On the whereabouts of local minima for blind adaptive equalizers

The lack of global convergence of existing blind equalization algorithms prompts the need for studying their mean cost functions and the whereabouts of local and global minima. The authors explore the location of minima for several general families of cost functions for blind equalization. It is shown that minima are unique along any radial direction in the equalizer parameter space. The authors characterize the resident manifold on which all minima and all saddle points of the cost function must reside. This information can be helpful in designing initialization strategies and parameter constraints to avoid convergence under adaptation to undesirable local minima