A New LMS Algorithm Based on Sparsity and lp - Norm Constraint

A novel adaptive algorithm is proposed by combing the sparseness ξ(n) with the value of p applied in l_p - Norm constraint. The convergence process of p is built by estimating and updating the value of p in each iteration, which produces two items, the error item and the constraint item, cooperating with the convergence of W(n). The parameter k is a factor to balance the two items, which is a trade-off between the convergence rate and the steady-state misalignment. The new algorithm is improved by selecting different value of k in different stages of the convergence process. The parameter k is selected by the value p, which can describe the stage of the convergence process. The numerical simulation indicates that the new algorithm gets a better performance than l₀ norm and l₁ norm constraint LMS algorithm and a faster convergence rate and a lower steady-state misalignment can be obtained at the same time.