Blind equalization based on pdf fitting and convergence analysis

In this paper, we address M-QAM blind equalization by fitting the probability density functions (pdf) of the equalizer output with the constellation symbols. We propose two new cost functions, based on kernel pdf approximation, which force the pdf at the equalizer output to match the known constellation pdf. The kernel bandwidth of a Parzen estimator is updated during iterations to improve the convergence speed and to decrease the residual error of the algorithms. Unlike related existing techniques, the new algorithms measure the distance error between observed and assumed pdfs for the real and imaginary parts of the equalizer output separately. The advantage of proceeding this way is that the distributions show less modes, which facilitates equalizer convergence, while as for multi-modulus methods phase recovery keeps being preserved. The proposed approaches outperform CMA and classical pdf fitting methods in terms of convergence speed and residual error. We also analyse the convergence properties of the most efficient proposed equalizer via the ordinary differential equation (ODE) method.