On convergence analysis of fractionally spaced adaptive blind equalizers

We study the convergence analysis of fractionally-spaced adaptive blind equalizers. We show that based on the trivial and nontrivial nullspaces of a channel convolution matrix, all equilibria, can be classified as channel dependent equilibria (CDE) or algorithm dependent equilibria (ADE). Because oversampling provides channel diversity, the nullspace of the channel convolution matrix is affected. We show that fractionally spaced equalizers (FSE) does not possess any CDE if a length-and-zero condition is satisfied. We characterize the global convergence ability of several popular blind adaptive algorithms simply based on their ADE. We also present an FSE implementation of the super-exponential algorithm. We show that the FSE implementation does not introduce any non-ideal approximation.