Mean-Square Performance of a Family of Affine Projection Algorithms

TLDR

Affine projection algorithms accelerate LMS convergence, yet existing analyses assume special regression models or Gaussian data and treat filters separately. The paper offers a unified analysis of mean‑square error, tracking, and transient performance for a family of affine projection algorithms. The analysis uses energy‑conservation arguments without restricting regressors to specific models or Gaussian distributions. Simulations confirm the derived performance expressions and illustrate the analysis.

Abstract

Affine projection algorithms are useful adaptive filters whose main purpose is to speed the convergence of LMS-type filters. Most analytical results on affine projection algorithms assume special regression models or Gaussian regression data. The available analysis also treat different affine projection filters separately. This paper provides a unified treatment of the mean-square error, tracking, and transient performances of a family of affine projection algorithms. The treatment relies on energy conservation arguments and does not restrict the regressors to specific models or to a Gaussian distribution. Simulation results illustrate the analysis and the derived performance expressions.