Global Stabilization of the Least Mean Fourth Algorithm

The least mean fourth algorithm has several stability problems. Its stability depends on the variance and distribution type of the adaptive filter input, the noise variance, and the initialization of the filter weights. The present correspondence provides a global solution to all these stability problems. This is achieved by normalizing the weight vector update term by a term that is fourth order in the regressor and second order in the estimation error. The former property stabilizes the algorithm against the variance and distribution type of the filter input, while the latter stabilizes the algorithm against the noise variance and the weight initialization. The obtained algorithm is stable for all values of the step-size between 0 and 2. The stability of the algorithm is supported by simulations.