Joint conditional and steady-state probability densities of weight deviations for proportionate-type LMS algorithms

In this paper, 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. Additionally, the application of using the conditional probability density function to calculate the steady-state joint conditional probability density function is examined along with several examples showing the feasibility of the approach. In the process of calculating the steady-state joint conditional probability density function a proof showing that the weight deviation vectors form a Markov chain is presented.