A Novel Variable Step-Size Algorithm Derived from the Noise-Free Posterior Error Cost Function

The least mean square algorithm has attracted a lot of attention among the various adaptive algorithms due to its simple structure and good computational complexity. The step-size is a key factor affecting some critical performance and the variable step-size strategy has become an important branch of research. However, some methods lack systematic theoretical derivation and appropriate analysis. The difficulty of obtaining prior parameters and the common performance make some algorithms less practical. Therefore, a variable step-size algorithm which is based on the energy of the posterior error without noise and combined with a dynamic restricted function is proposed in this paper. This algorithm takes the energy of the noiseless posterior error as the cost function and uses the basic theoretical formula to obtain the variable step-size expression. The parameters of the proposed algorithm can be obtained by an iterative smooth calculation without requiring any prior information. The specific mean square deviation performance analysis of the algorithm is also provided. Various experimental results show that the proposed algorithm can accurately adjust the step-size according to the convergence state of the system.