L1-Norm Penalized Bias Compensated Linear Constrained Affine Projection Algorithm

This paper presents an l1-norm penalized bias compensated linear constrained affine projection (l1-BC-CAP) algorithm for sparse system identification having linear phase aspectin the presence of noisy colored input. The motivation behind the development of the proposed algorithm is formulated on the concept of reusing the previous projections of input signal in affine projection algorithm (APA) that makes it suitable for colored input. At First, l1-CAP algorithm is derived by adding zero attraction based on l1-norm into constrained affine projection (CAP) algorithm. Then, the proposed l1-BC-CAP algorithm is derived by adding a bias compensator into the filter coefficient update equation of l1-norm constrained affine projection (l1-CAP) algorithm to alleviate the adverse consequence of input noise on the estimation performance. Hence, the resulting l1-BC-CAP algorithm excels the estimation performance when applied to linear phase sparse system in the existence of noisy colored input. Further, this work also examines the stability concept of the proposed algorithm