A Modified Recursive Regularization Factor Calculation for Sparse RLS Algorithm with <i>l</i>₁-Norm

• Main Authors: Junseok Lim, Keunhwa Lee, Seokjin Lee
• Format: Article
• Language: English
• Published: MDPI AG 2021-07-01
• Series: Mathematics
• Subjects: sparse impulse response system; sparse system estimation; <i>l</i>₁-RLS; regularization factor
• Online Access: https://www.mdpi.com/2227-7390/9/13/1580

In this paper, we propose a new calculation method for the regularization factor in sparse recursive least squares (SRLS) with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mn>1</mn></msub></semantics></math></inline-formula>-norm penalty. The proposed regularization factor requires no prior knowledge of the actual system impulse response, and it also reduces computational complexity by about half. In the simulation, we use Mean Square Deviation (MSD) to evaluate the performance of SRLS, using the proposed regularization factor. The simulation results demonstrate that SRLS using the proposed regularization factor calculation shows a difference of less than 2 dB in MSD from SRLS, using the conventional regularization factor with a true system impulse response. Therefore, it is confirmed that the performance of the proposed method is very similar to that of the existing method, even with half the computational complexity.