A family of affine projection-type least lncosh algorithms and their step-size optimization

The Least lncosh (Llncosh) algorithm is a promising adaptive algorithm due to its robustness in impulsive interference and has a faster convergence rate than the classical sign algorithm (SA). However, when the input signal is correlated, it may still suffer from a slow convergence rate. To address this problem, this paper incorporates the method of data-reusing into the lncosh cost function to develop a family of affine projection-type Llncosh (AP-Llncosh) algorithms. To promote its performance for sparse system identification, a low-order norm constraint is also considered. Moreover, to address the problem of tradeoff between fast convergence rate and small steady-state misalignment, we optimize its step-size by minimizing the mean-square deviation (MSD). Simulation results are provided to verify the superior performance of the proposed algorithms.