On convergence analysis of fractionally spaced adaptive blind equalizers

In this paper, 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 (FSEs) do not possess any CDE if a length-zero condition is satisfied. The convergence behavior of these FSE are clearly determined by the specific choice of cost function alone. We characterize the global convergence ability of several popular 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 nonideal approximation. Simulation results are also presented to illustrate the robustness and the improved performance of FSE under the super-exponential algorithm.