A variable multiple step-size LMS algorithm with l0-norm

In this paper, a novel variable multiple step-size least mean square (VMSSLMS) adaptive filter algorithm with the l
₀
-norm constraint is proposed, which both allows the step-size to vary for different taps and includes a sparsity constraint in the cost function. When channel changes suddenly, the filter can track the specific tap-weight fast to adapt to the variation of the channel. The l
₀
-norm constraint can take advantage of the sparse property, thus it can improve the performance of the sparse channel estimation. Simulations show that compared with the existing algorithms, the proposed algorithm performs better in the sparse channels with a faster convergence rate and a lower misadjustment. System identification tests with the proposed algorithm for the channel obtained from South ocean also show superior performance.