Blind Adaptive Equalization in Additive Impulsive Noise Using the Logarithmic Product Fractional-Moment (LP-FM) Criterion

The blind mitigation of inter-symbol interference in additive white impulsive noise modeled by a symmetric $\alpha$-stable (S$\alpha$S) distribution is investigated. A novel logarithmic product fractional-moment statistics (LP-FMS) criterion is proposed by combining complementary fractional-moment statistics with logarithmic normalization in a constrained optimization framework. Based on this criterion, a normalized blind equalization algorithm for symmetric alpha-stable noise (NBEA-SAS) is derived using stochastic gradient ascent with recursive fractional-moment estimation and Bussgang-consistent constrained adaptation. Simulation results for $64$-APSK signaling over fractionally spaced multipath microwave channels show that the proposed algorithm converges faster than FLOS-CMA, RAW-CMA, and NBEA-GG while achieving a comparable steady-state residual intersymbol interference floor under both moderately and highly impulsive S$\alpha$S noise conditions. The results demonstrate that the proposed LP-FMS criterion provides a robust framework for blind adaptive equalization in impulsive noise environments.