Rank Test Based Blind Equalization Schemes for Impulsive Environment

Most blind channel equalization schemes assume that the additive noise is Gaussian distributed owing to central limit theorem. Experimental measurements, on the other hand, demonstrate that many practical sources of noise are impulsive and heavy-tailed like low-frequency atmospheric noise, automobile and industrial noise, underwater acoustic noise, and electro-magnetic noise in urban mobile-radio channels. Non-Gaussianity often results in significant performance degradation for blind equalizers optimized under Gaussian assumption. A well-known example is the constant modulus algorithm based equalizer for coherent equalization of transmitted signal in Gaussian white noise. The weight update process of CMA which depends on the modulus (that is magnitude) of the deconvolved sequence tends to diverge and becomes unstable when impulsive channel observation is used directly. Heuristic approaches to avoid divergence have been incorporated in the past which include the normalization of equalizer input (regressor), equalizer output or the error function, or the use of fractional moments in dispersion based cost function. Although these heuristic modifications do work under given several heavy-tailed distributions including -stable noise scenarios but it is a matter of academic interest to explore if there exists any analytical way to design an optimal or near optimal blind equalization cost functions for the given impulsive environment. In this project, we aim to exploit methods rank test in order to design scale-invariant blind equalization cost functions to promote uniformity against impulsive noise which is distributed as symmetric -stable or Generalized-Gaussian distribution. In simple words, for linear time-invariant channels, we attempt to obtain equalizer coefficients which modifies the heavy-tailed probability distribution of received signal into uniform distribution. We aim to obtain new algorithms, evaluate their analytical performance in terms of their stability bounds and excess mean square error, compare those with existing known solutions, and draw conclusions.