Fast blind equalization using subgradient-based algorithms

Abstract

ABSTRACT In this thesis, several novel blind equalization methods based on subgradient search over a convex cost surface are presented. These subgradient-based methods are alternatives to the existing iterative blind equalization approaches (such as the Constant Modulus Algorithm (CMA)) which mostly suffer from the convergence problems caused by their nonconvex cost functions. The proposed methods are variations of on an iterative algorithm (called SubGradient based Blind Algorithm (SGBA) ) for both real and complex constellations. SGBA is based on the minimization of the loo norm of the equalizer output under a linear constraint on the equalizer coefficients using subgradient iterations. The algorithm has a nice convergence behavior attributed to the convex loo cost surface as well as the step size selection rules connected with the subgradient search. We study four different variations of the SGBA algorithm: Fixed Window SGBA, Moving Window SGBA, Weighted SGBA and the Fractionally-Spaced SGBA. The performances of these algorithms are illustrated using examples in both complex and real constellations, where it is shown that the convergence behaviors of the proposed algorithms are in general less sensitive to initial point selection and fast convergence speeds can be achieved with a wise selection of step sizes. Furthermore, the amount of data required for the training of these equalization algorithms and their complexities are significantly low. IV