Adaptive blind equalization through quadratic pdf matching

In this paper we propose a new cost function for blind equalization which aims at forcing a given probability density at the output of the equalizer. In previous works based on this idea, the Kullback-Leibler distance was used as an appropriate measure of the distance between densities. Here we consider the Euclidean (quadratic) distance between the current pdf at the output of the equalizer and the target pdf. Using Parzen windowing with Gaussian kernels for pdf estimation, this quadratic distance can be easily evaluated from data. The adaptive equalization algorithm minimizes the cost function employing a stochastic gradient descent approach. The algorithm is evaluated in different scenarios through computer simulations, and its performance is compared to that of a minimum Renyi´s entropy approach, which is related to the proposed algorithm, and also to the conventional constant modulus algorithm (CMA).