Analysis and implementation of the max-NLMS adaptive filter

We provide an efficient implementation and a statistical analysis of the max-NLMS adaptive filter. This adaptive filter only adjusts the coefficient associated with the data element that has the maximum absolute value in the filter memory at each iteration. Our method for determining this maximum absolute data value requires many fewer compares and storage locations on average as compared to other techniques. We then provide statistical and stability analyses of the max-NLMS algorithm for several input data models. Theory and simulations show that the max-NLMS adaptive filter is statistically more efficient than other adaptive filters with similar computational complexity for some input signals; however, its stability behavior is very sensitive to skew in the input data probability distribution.