Proportionate-Type Steepest Descent and NLMS Algorithms

In this paper, a unified framework for representing proportionate type algorithms is presented. This novel representation enables a systematic approach to the problem of design and analysis of proportionate type algorithms. Within this unified framework, the feasibility of predicting the performance of a stochastic proportionate algorithm by analyzing the performance of its associated deterministic steepest descent algorithm is investigated, and found to have merit. Using this insight, various steepest descent algorithms are studied and used to predict and explain the behavior of their counterpart stochastic algorithms. In particular, it is shown that the μ-PNLMS algorithm possesses robust behavior. In addition to this, the -PNLMS algorithm is proposed and its performance is evaluated.