A sparse system identification algorithm based on fractional order LMS

In this paper, a zero-attracting fractional order least mean squares (ZA-FLMS) algorithm is proposed for adaptive sparse system identification.l(1)-norm of the filter coefficients is considered and zero-attracting correction is introduced into the updating equation. The extension of the algorithm is also proposed for distributed local sensors of information-centric IoT. The convergence speed and MSE performance are investigated in the simulations, which show effective improvement for sparse system identification compared with traditional LMS, zero-attracting LMS and fractional order LMS, especially with lower sparsity and smaller fractional order. But the decrement of fractional order and step size will lead to slower convergence speed, while the bigger fractional order and step size will lead to bigger variation of MSE. Therefore, optimised ZA-FLMS is further introduced, which uses l0-norm in the initial stage of the algorithm and shows improvement of convergence speed for smaller fractional order.