A novel set membership fast NLMS algorithm for acoustic echo cancellation

In order to improve the performances of the Fast Normalized Least Mean Square type (FNLMS) adaptive filtering algorithm in the context of Acoustic Echo Cancellation (AEC), this work proposes an Improved Set Membership version by exploiting, firstly, the theory of set membership identification (SMI) to the FNLMS algorithm to get more complexity reduction, then by using the estimated output error to update the step size which results to better convergence speed and tracking ability. The obtained algorithm is called the Improved Set Membership FNLMS (ISM-FNLMS) algorithm. Simulation results have demonstrated the superiority and the good performances of the proposed algorithm compared with NLMS, SM-NLMS, FNLMS, SM-FNLMS and SM-NLMS with Robust Error Bound (SMREB-NLMS) algorithms in terms of convergence speed, steady-state mean square filtering error (MSE), tracking capability and computational complexity performances.