A closed-form solution to blind equalization

Abstract

Abstract In some recent papers new algorithms for blind adaptive equalization were proposed. These algorithms are based on the stochastic gradient method and thus can be regarded as a ‘blind’ counterpart to the classic LMS (least mean squares) algorithms. It is well known that these algorithms show relatively slow convergence speed. The classic solution to get fast convergence is the RLS (recursive least squares) algorithm which makes use of the closed-form solution. The purpose of this paper is to derive a closed-form solution in the sense of blind equalization. It will be shown that the equalizer coefficients can be uniquely derived from the eigenvectors of a specific 4th-order cumulant matrix of the received signal. By means of some examples it will be demonstrated that the eigenvector solution is near the ideal MSE (mean square error) solution.