Sparse-befap: A fast implementation of fast affine projection avoiding explicit regularisation

It is well known that régularisation of the covariance matrix is necessary in Affine Projection Algorithm (APA) based adaptive filters. A technique to achieve régularisation is using non-successive equations in the system of equations that is solved in the APA-algorithm, leading to the Sparse-APA algorithm [5] [4]. In this paper, a fast exact frequency domain implementation of Sparse-APA is derived which does not rely on any of the approximations which are found in the classical fast affine projection algorithms, while only a very small number of extra computations is needed.