Transient analysis of l0-LMS and l0-NLMS algorithms

• An accurate transient analysis of both l0-LMS and l0-NLMS algorithms is advanced.
• A stochastic model for predicting their MSD and MSE learning behaviors is proposed.
• The analysis employs weaker conditions, e.g., input signal whiteness is not required.
• Learning properties of these algorithms are revealed by the proposed framework.
• Steady-state results can be predicted as limiting cases of the transient analysis.

Sparsity-aware adaptive algorithms present some advantages over standard ones, specially due to the fact that they have faster convergence rate. This paper proposes a stochastic model for both l0-LMS and l0-NLMS algorithms, and carries out an accurate transient analysis of these algorithms without requiring the input signal to be white. Some previously unreported learning properties of these algorithms are revealed by the proposed framework, which are confirmed by experimental evidence.