The Contour Algorithm for Self-Training Adaptive Equalization

We present a new algorithm to adjust the coefficients of a transversal equalizer in a self-training mode, where initial equalizer convergence is achieved without requiring the transmission of a known reference signal. The generation of the adjustment terms depends on whether the equalizer output signal is found outside or within a region bounded by a contour line connecting the outer points of the input symbol constellation. To characterize the convergence properties of the self-training equalization algorithm, a functional, the derivatives of which are closely related to the employed stochastic gradient, is introduced. This functional can exhibit only a set of equivalent global minima, which correspond to points of perfect equalization for different equalizer delays and signs of the output signal. A joint robust carrier-phase recovery algorithm is also presented. The convergence behavior of the algorithm is illustrated by simulations.