Development of Amari Alpha Divergence-Based Gradient-Descent Least Mean Square Algorithm

In this brief, a new least mean square (LMS) adaptive filtering algorithm based on Amari-Alpha information theoretic divergence is proposed which is named as Amari-Alpha LMS (AALMS). The local convergence and stability analysis show the upper bound of step size for tractable analysis. The steady-state performance of the proposed algorithm is analyzed, and the mean-square deviation (MSD) at steady-state is derived. Error-in-variable (EIV) model where input and desired signals both are corrupted with Gaussian noise is considered in this brief. Simulation results and computational complexity analysis show that the proposed AALMS algorithm performs better in comparison to well-known algorithms in terms of MSD in stationary and non-stationary scenarios. Comparison of different distance measures that can be derived from Amari-Alpha divergence is also carried out in terms of the MSD.

Automated summary

In this paper, a new least mean square (LMS) adaptive filtering algorithm called Amari-Alpha LMS (AALMS) based on Amari-Alpha information theoretic divergence is proposed. The upper bound of step size for tractable analysis is obtained through local convergence and stability analysis. The steady-state performance of the algorithm is analyzed, and the mean-square deviation (MSD) at steady-state is derived. The proposed AALMS algorithm outperforms well-known algorithms in terms of MSD in both stationary and non-stationary scenarios, as shown by simulation results and computational complexity analysis. Comparison of different distance measures derived from Amari-Alpha divergence is also conducted in terms of MSD.