This paper introduces a variable regularization method for the fast affine projection algorithm (VR-FAP). It is inspired by a recently introduced technique for variable regularization of the classical, affine projection algorithm (VR-APA). In both algorithms, the regularization parameter varies as a function of the excitation, measurement noise, and residual error energies. Because of the dependence on the last parameter, VR-APA and VR-FAP demonstrate the desirable property of fast convergence (via a small regularization value) when the convergence is poor and deep convergence/immunity to measurement noise (via a large regularization value) when the convergence is good. While the regularization parameter of APA is explicitly available for on-line modification, FAP\u27s regularization is only set at initialization. To overcome this problem we use noise-injection with the noise-power proportional to the variable regularization parameter. As with their fixed regularization versions, VR-FAP is considerably less complex than VR-APA and simulations verify that they have the very similar convergence propertie
