Finding misconvergences in blind equalizers and new variance constraint cost functions to mitigate the problem

We show that the equalizer weights that cause the overall channel-equalizer response to approximate a pure delay (in a mean square error sense) are within the region of convergence of a stable local minimum of the Bussgang cost function. For any nontrivial channel the approximations for some delay values are poor. If a Bussgang algorithm is initialized with these weights it misconverges. A Monte-Carlo simulation created misconvergence as predicted. We propose the variance constraint (VC) algorithms that have more robust convergence properties than the Bussgang algorithms. The VC cost functions are similar to the well-known Godard cost functions. They incorporate estimates of the channel-equalizer overall gain and use a linear constraint on the weights. These two modifications push the bad stable points farther away in weight space from the stable points with good performance (i.e., low intersymbol interference). A Monte-Carlo simulation of nearly 2000 channels shows no misconvergence.