Stochastic blind equalization based on PDF fitting using Parzen estimator

This work presents a new blind equalization approach that aims to force the probability density function (pdf) at the equalizer output to match the known constellation pdf. Quadratic distance between pdf´s is used as the cost function to be minimized. The proposed method relies on the Parzen window method to estimate the data pdf and is implemented by a stochastic gradient descent algorithm. The kernel size of the Parzen estimator allows a dual mode switch or a soft switch between blind and decision-directed equalization. The proposed method converges faster than the constant modulus algorithm (CMA) working at the symbol rate, with a similar computational burden, and reduces the residual error of the CMA in multilevel modulations at the same time. A comparison with the most common blind techniques is presented.