A short-sort M-Max NLMS partial-update adaptive filter with applications to echo cancellation

Partial-update algorithms reduce adaptive filter complexity by updating only a subset of taps at each iteration. However, they suffer a processing overhead in tap selection that can substantially reduce the computational advantages of partial-update schemes. Short-sort M-Max NLMS (SM-NLMS) addresses this problem by having the advantages of other partial-update schemes but with very low computational overhead in tap selection. SM-NLMS uses a low-complexity short-sort procedure to perform tap selection and updates the selection periodically. We show a performance analysis based on contraction mapping for SM-NLMS using a time-varying unknown system and quantify its characteristics. Simulation results and the performance analysis show that SM-NLMS performs almost as well as NLMS but with substantially lower computational cost involved in tap selection and updating compared to other schemes. The straightforward structure and low complexity of SM-NLMS make it well suited to real-time and high-density applications such as echo cancellation and equalization.