Adaptive algorithm based on a new hyperbolic sine cost function

This paper introduces a stochastic gradient algorithm, which uses an exclusive hyperbolic sine objective function. The algorithm belongs to the variable step size (VSS) class. The algorithms in this class are shown to be very stable and effective in many applications, e.g., echo-cancellation, equalization, and others. In this algorithm, as opposed to other existing VSS algorithms, only one tuning parameter is needed. Experimental results show that with a sub-optimal selection of the tuning parameter, the algorithm provides very promising results in both stationary and tracking scenarios. Analytic convergence and steady state error performance analysis are provided to demonstrate the excellent performance. Also, an optimal solution, based on the least hyperbolic sine error, is derived to confirm the convergence of the proposed algorithm towards the Wiener solution.