Performance Analysis of Fractional Learning Algorithms

Fractional learning algorithms are trending in signal processing and adaptive filtering recently. However, it is unclear whether their proclaimed superiority over conventional algorithms is well-grounded or is a myth as their performance has never been extensively analyzed. In this article, a rigorous analysis of fractional variants of the least mean squares and steepest descent algorithms is performed. Some critical schematic kinks in fractional learning algorithms are identified. Their origins and consequences on the performance of the learning algorithms are discussed and swift ready-witted remedies are proposed. Apposite numerical experiments are conducted to discuss the convergence and efficiency of the fractional learning algorithms in stochastic environments. The analysis substantiates that the fractional learning algorithms have no advantage over the conventional least mean squares algorithm.