Convergence analysis of a modified Armijo rule step-size LMF algorithm

In this work, we make use of the Armijo rule for the selection of the learning rate to introduce the Armijo rule learning rate least mean fourth (ALRLMF) algorithm. The algorithm is derived by incorporating the modified version of the Armijo rule line search to the class of stochastic gradient algorithm that minimizes the mean fourth error. The convergence behavior of the algorithm is analyzed and bounds guaranteeing convergence are explicitly derived. Finally, simulation results presented in a system identification scenario are found to corroborate the theoretical findings.