Analysis of the decision delay effect on the convergence of gradient recursive decision feedback equalizers

In this paper we investigate the relationship between the decision delay and the convergence properties of DFE equalizers when using gradient algorithms to perform the coefficient adaptation. We show how the delay affects the structure of the input data correlation matrix and how a poor choice of the decision delay may dramatically increase its eigenvalue spread which in tum causes a significant increase in the convergence time. Rules are derived showing how the delay can be selected to minimize, or at least greatly reduce, the eigenvalue spread while at the same time keep the steady-state mean squared error (MSE) level low.