Probability Density of Weight Deviations Given Preceding Weight Deviations for Proportionate-Type LMS Adaptive Algorithms

In this work, the conditional probability density function of the current weight deviations given the preceding weight deviations is generated for a wide array of proportionate type least mean square algorithms. The conditional probability density function is derived for colored input signals when noise is present as well as when noise is absent. Additionally, the marginal conditional probability density function for weight deviations is derived. Finally, potential applications of the derived conditional probability distributions are discussed and an example finding the steady-state probability distribution is presented.