Dynamic Limited Variable Step-Size Algorithm Based on the MSD Variation Cost Function

The steady-state and convergence performances are important indicators to evaluate adaptive algorithms. The step-size affects these two important indicators directly. Many relevant scholars have also proposed some variable step-size adaptive algorithms for improving performance. However, there are still some problems in these existing variable step-size adaptive algorithms, such as the insufficient theoretical analysis, the imbalanced performance and the unachievable parameter. These problems influence the actual performance of some algorithms greatly. Therefore, we intend to further explore an inherent relationship between the key performance and the step-size in this paper. The variation of mean square deviation (MSD) is adopted as the cost function. Based on some theoretical analyses and derivations, a novel variable step-size algorithm with a dynamic limited function (DLF) was proposed. At the same time, the sufficient theoretical analysis is conducted on the weight deviation and the convergence stability. The proposed algorithm is also tested with some typical algorithms in many different environments. Both the theoretical analysis and the experimental result all have verified that the proposed algorithm equips a superior performance.