Improved Fast NLMS algorithm based on variable forgetting factor technique for acoustic echo cancellation

The recursive least squares (RLS) algorithm is widely used in various adaptive filtering applications, mostly due to its rapid convergence rate. The forgetting factor is a crucial parameter in this algorithm. For a fixed value for this parameter, there is a tradeoff between misalignment and tracking. Nevertheless, the use of a variable forgetting factor (VFF) approach gives a better compromise between the performance criteria of the RLS algorithm. Nonetheless, the algorithm's computational complexity presents a notable challenge, particularly in scenarios that involve lengthy adaptive filters, such as acoustic echo cancellation (AEC). This paper incorporates the concept of a variable forgetting factor into the fast normalized least mean squares (FNLMS) algorithm. The FNLMS algorithm demonstrates performances comparable to the RLS algorithm while maintaining a computational complexity similar to that of the normalized least mean squares (NLMS) algorithm. Based on simulation results in the context of AEC, the proposed VFF-FNLMS algorithm exhibits better performances in terms of convergence speed and tracking ability when compared to both FNLMS and NLMS algorithms.