Improved Combined Step-size Normalized Sign Algorithm with Novel Variable Mixing Factors

The performance of the convex combination of two adaptive filters is heavily dependent on the mixing factor. This paper proposes novel variable mixing factors to combine two normalized sign algorithms robust against impulsive noises with improving the performance. The variable mixing factors resolve the trade-off problem between the convergence rate and steady-state misalignment by updating the mixing parameters at each iteration. The proposed variable mixing factors use a modified arctangent activation function and a modified rectified linear unit activation function used in various fields. These proposed mixing factors are updated by optimizing the absolute value of the system output error to get the robustness to impulsive noises. The proposed algorithm using a modified arctangent activation function has better performance; otherwise, the proposed algorithm using a modified rectified linear unit activation function has lower computational complexity. Simulations are conducted to verify the proposed algorithms in various system identification scenarios. The simulation results show that the proposed algorithms outperform the traditional algorithms.