Summary: Variable Step-Size Affine Projection Algorithm
with a Weighted and Regularized Projection
Tao Dai, Andy Adler, and Behnam Shahrrava
Abstract--This paper presents a forgetting factor scheme for
variable step-size affine projection algorithms (APA). The proposed
scheme uses a forgetting processed input matrix as the projection
matrix of pseudo-inverse to estimate system deviation. This method
introduces temporal weights into the projection matrix, which is
typically a better model of the real error's behavior than homogeneous
temporal weights. The regularization overcomes the ill-conditioning
introduced by both the forgetting process and the increasing size
of the input matrix. This algorithm is tested by independent trials
with coloured input signals and various parameter combinations.
Results show that the proposed algorithm is superior in terms of
convergence rate and misadjustment compared to existing algorithms.
As a special case, a variable step size NLMS with forgetting factor
is also presented in this paper.
Keywords--Adaptive signal processing, affine projection algo-
rithms, variable step-size adaptive algorithms, regularization.