The New Family of Adaptive Filter Algorithms for Block-Sparse System Identification

Background and Objectives: In order to improve the performance of normalized subband adaptive filter algorithm (NSAF) for identifying the block-sparse (BS) systems, this paper introduces the novel adaptive algorithm which is called BSNSAF. In the following, an improved multiband structured subband adaptive filter (IMSAF) algorithms for BS system identification is also proposed. The BS IMSAF has faster convergence speed than BS-NSAF. Since the computational complexity of BS-IMSAF is high, the selective regressor (SR) and dynamic selection (DS) approaches are utilized and BS-SR-IMSAF and BS-DS-IMSAF are introduced. Furthermore, the theoretical steady-state performance analysis of the presented algorithms is studied. Methods: All algorithms are established based on the 𝐿2,0-norm constraint to the proposed cost function and the method of Lagrange multipliers is used to optimize the cost function. Results: The good performance of the proposed algorithms is demonstrated through several simulation results in the system identification setup. The algorithms are justified and compared in various scenarios and optimum values of the parameters are obtained. Also, the computational complexity of different algorithms is studied. In addition, the theoretical steady state values of mean square error (MSE) values are compared with simulation values. Conclusion: The BS-NSAF algorithm has better performance than NSAF for BS system identification. The BSIMSAF algorithm has better convergence speed than BS-NSAF. To reduce the computational complexity, the BS-SR-IMSAF and BS-DSRIMSAF algorithms are developed. These algorithms have close performance to BS-IMSAF.