An enhanced mixed norm error criterion adaptive filtering algorithm for sparse channel estimation

Mixed norm error (MNE) criterion has been successfully used to develop adaptive filtering algorithms. Recently, adaptive filter algorithms based on MNE has an excellent performance for system identification, including channel estimation. In this paper, an enhanced sparse mixed l₂ and l_p norm error criterion algorithm is proposed by the use of a soft parameter function to modify the basic cost function of l₂ and l_p algorithm to generate a desired zero attractor. The proposed sparse MNE algorithm can well explore the essential sparsity in multi-path wireless channel because of the designed zero attractor. The proposed sparse MNE algorithm is analyzed and mathematically derived in detail. Simulation examples are presented to verify its behavior via a sparse wireless multi-path channel. Additionally, we will also investigate the parameter affects on the proposed algorithm. The obtained results confirm that the excellent behavior of the proposed sparse MNE algorithm is achieved in terms of both convergence and steady-state error in comparison with the LMS/F, L2LP and their corresponding sparse algorithms.