Blind Equalization Via Polynomial Optimization

A polynomial optimization based blind equalizer (POBE) is proposed. Different from the popular constant modulus algorithm and its variants, the POBE adopts an eighth-order multivariate polynomial as the loss function. Since the loss function is sensitive to phase rotation, the POBE can achieve automatic carrier phase recovery. A gradient descent method with optimal step size is developed for solving the optimization problem. We reveal that this optimal step size is one root of a seventh-order univariate polynomial and hence, can be computed easily. Compared with the blind equalizers based on stochastic gradient descent with empirical step size, which suffers from slow convergence or even divergence, the POBE significantly accelerates the convergence rate. Moreover, it attains a much lower inter-symbol interference (ISI), resulting in a noticeable improvement of equalization performance. Simulation results demonstrate the superiority of POBE over several representative blind equalizers.