A Robust Decision Directed Algorithm for Blind Equalization Under $\alpha$-Stable Noise

This paper reports a solution to a linear blind equalizer used in communication systems under the effect of two factors: i) An unknown linear inter symbol interference and ii) the impulsive noise satisfying the
$\alpha$
-stable distribution. First, a constellation matching error-based cost function associated with the linear equalizer is designed to effectively compensate for the inter symbol interference and suppress the influence of the impulsive noise. Second, an improved form of the proposed cost function is derived through the finite alphabet property of information symbols. The theoretical analysis shows that the improved cost function significantly reduces the local minima and converges more stably in high-order modulation systems. Furthermore, based on the special structure of the designed cost function, a modified Newton scheme is constructed to quickly minimize it, and then the corresponding optimal blind equalizer can be obtained. Finally, computer simulations are presented to demonstrate the robust equalization performance and fast convergence of the novel algorithm under both impulsive and Gaussian noise environments.