Semi-blind constant modulus equalization with optimal step size

Channel equalization is an important problem in digital communications. The paper studies a hybrid equalization criterion combining the constant modulus (CM) property and the minimum mean square error (MMSE) between the equalizer output and the known pilot sequence. An efficient semi-blind block gradient-descent algorithm is proposed, in which the step size globally minimizing the cost function along the search direction is algebraically computed at each iteration. The use of the optimal step size notably accelerates convergence and can further reduce the impact of local extrema on the semi-blind algorithm´s performance. The proposed approach is not restricted to the CM-MMSE principle, but it can benefit other equalization criteria as well.