Convergence analysis of a new blind equalization algorithm with M-ary PSK channel inputs

In our previously proposed equalization criterion with MPSK modulated channel inputs (see Proc. of 10th IEEE Workshop on Statistical Signal and Array Processing p.692-6, Pocono Manor, PA, USA, August 2000), perfect equalization was guaranteed in principle under constrained optimization. The algorithm was implemented based on stochastic gradient method. In this paper, we investigate the convergence property of that algorithm. By carefully examining all stationary points of the objective function, we prove that all other points are unstable except the desired solution. The effects of the ary number M and the background noise on the performance of the proposed equalizer are studied in detail in our simulations. Satisfactory bit error rate performance and output constellation are observed