Mean-square performance of a family of affine projection algorithms

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.