Parameter estimation and blind channel identification in impulsive signal environments

New methods for parameter estimation and blind channel identification in impulsive signal environments are presented, where the signals/noise are modeled as symmetric /spl alpha/-stable (S/spl alpha/S) processes. First, we present methods for estimating the parameters (characteristic exponent /spl alpha/ and dispersion /spl gamma/) of a S/spl alpha/S distribution from a time series. The fractional lower order moments, with both positive and negative orders, and their applications to signal processing are introduced. Then we present a new algorithm for blind channel identification using the output fractional lower order moments, and the /spl alpha/-Spectrum, a new spectral representation for impulsive signals, is introduced. From the /spl alpha/-Spectrum, we establish the blind identifiability conditions of any FIR channel (mixed-phase, unknown order) with i.i.d. S/spl alpha/S (/spl alpha/>1) input. As a byproduct, a simple algorithm for recovering the phase of any type of a signal from the magnitude of its z-transform is presented. The novelty of our paper is in parameter estimation and blind identification of the FIR channel based on fractional lower order moments of its output data. Monte Carlo simulations clearly demonstrate the performance of the new methods.