A family of normalized dual sign algorithms

The classical sign algorithm (SA) has attracted much attention in many applications because of its low computational complexity and robustness against impulsive noise. However, its steady-state mean-square derivation (MSD) is large when a large step-size is used to guarantee a relatively fast convergence rate. To address this problem, the dual sign algorithm (DSA) was developed by using a piecewise cost function in the literature. In this paper a family of normalized DSAs (NDSAs) is proposed to further improve the performance of the DSA in terms of MSD. Specifically, two sparse NDSAs are firstly developed, by using the ℓ₁-norm and ℓ₀-norm constraints, respectively; on this basis, some variable step-size algorithms are then proposed based on mean-square a posteriori error minimization. Finally, simulation results are provided to show the superior performance of our proposed algorithms.