Affine projection exponential hyperbolic sine algorithm designed for impulsive noise environments

The performance of the affine projection algorithm (APA) is negatively affected when confronted with non-Gaussian noises and impulsive background noises. In order to mitigate this problem, this paper introduces the Affine Projection Exponential Hyperbolic Sine Algorithm (APEHSA), which employs a cost function that is derived from the exponential hyperbolic sine-based error function. The proposed algorithm is effectively adopted in adaptive filtering due to its ability to handle non-Gaussian and impulsive background noises. To enhance the rate of convergence and address the issue of steady-state misalignment in the APEHSA, the incorporation of the variable scaling parameter method has been introduced. Hence, the Variable Scaling Parameter APEHSA (VSP-APEHSA) is proposed. Furthermore, the mean square stability and the steady-state performance of the proposed algorithm are analyzed. In order to assess the effectiveness of the APEHSA, a series of simulation studies were conducted in the context of system identification scenarios and acoustic echo cancellation (AEC) system. The results of these studies demonstrate that the APEHSA algorithm exhibits superior steady state performance and enhanced convergence capabilities compared to other established algorithms, including APA, Exponential Hyperbolic Sine Adaptive Filter (EHSAF), affine projection tanh algorithm (APTA), and Affine Projection Sign Algorithm (APSA), particularly in impulsive noise environments.