Recursive Inverse Adaptive Filtering Algorithm With Low Computational Complexity On Sparse System Identification

Abstract

This paper studies the performance of Recursive Inverse (RI) adaptive filtering for the identification of sparse systems. A new adaptive algorithm utilizing a modified autocorrelation matrix and a modified weight vector which are both reduced in size, is introduced. This algorithm is called Reduced Complexity Sparse RI (RCS-RI). The low computational complexity is the most significant feature of RCS-RI. Due to the low computational complexity, it performs better by doing faster computations compared with Recursive Inverse (RI) and Zero Attracting Recursive Inverse (ZA-RI) algorithms. Additionally, the convergence of the algorithm is faster compared with the RI algorithm with respect to the steady state Mean Square Error (MSE). The RCS-RI also outperforms the Zero Attracting Variable Step Size Least Mean Square (ZA-VSSLMS) in the steady state Mean Square Deviation (MSD). Its convergence rate and MSD performance in the steady state conditions are approximately equal to that of ZA-RI. Consequently, RCS-RI improves the performance of identifying the sparse system by faster and more efficient computations due to lower complexity and MSE. RCS_RI’s steady state MSE is significantly reduced when compared to LMS-type system identification algorithms.