Blind Equalization Based on Direction Gradient Algorithm under Impulse Noise Environment

A new constant modulus blind equalization based on direction gradient algorithm was proposed, which can obtain robust convergence performance under impulse noise environment. The impulse noise has no more than two order moments, so constant modulus algorithm (CMA) based on stochastic gradient descent algorithm is often ill-convergence or divergence. The direction gradient algorithm uses the reliability of the output of the blind equalizer to determine the equalizer weights updating strategy, and the reliable region called decision circle is set according to the scatterplot of the send signal. If the output signal drops in the decision circle, the equalizer weights update according to the traditional CMA, otherwise it only keeps the sign of the output error, and the previous step instantaneous gradient is used to update the equalizer weights. The direction gradient algorithm can suppress the impulse noise interference effectively, which shows robust convergence performance under the impulse noise environment. Simulation results show that, compared with the fractional lower order CMA and the nonlinear transform CMA, the blind equalization based on direction gradient algorithm has the fastest convergence rate and the lowest steady state error. Key-Words: blind equalization, direction gradient algorithm, impulse noise, constant modulus algorithm, decision circle