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.