Combined Regularization Parameter Affine Projection Algorithm

The conventional affine projection algorithm with a fixed regularization parameter confronts the tradeoff between fast convergence and low steady-state misalignment. A combined regularization parameter affine projection algorithm (CRP-APA) is presented to address this problem. The proposed algorithm adaptively combines two different regularization parameters by employing a mixing parameter that is derived by minimizing the energy of the priori error. For the sake of a better tracking capability, the mixing factor is conducted by using a modified sigmoidal activation function. Particularly, the mathematical analyses including the steady-state behavior and computational complexity are also performed. A series of simulations for system identification and echo cancellation scenarios demonstrate the significant merits of the proposed CRP-APA and support the theoretical analysis.