Adaptive method for blind equalization of QAM signals utilizing unconstrained function

Aiming at the problem of blind equalization and carrier-phase recovery of Quadrature Amplitude Modulation (QAM) signal. Based on the analysis of blind equalization algorithms that optimize the equalizer output energy, a new unconstrained cost function for blind equalization and carrier-phase recovery of QAM using the relationships of vector norm is proposed in this paper. Then, the convergence and the uniqueness of solution of the cost function are discussed, and we show that a perfect equalization solution and carrier-phase recovery can be achieved at the optimum of the objective function. By reformulating the unconstrained cost function, an adaptive algorithm that can be optimized via stochastic gradient descent method is obtained. The new proposed algorithm can provide better performance in comparison to some existing adaptive methods, such as CMA and MMA, moreover, the validity of the new proposed algorithm is verified through computer simulations of blind equalization and carrier-phase recovery of higher-order QAM signals.