Recursive General Mixed Norm Algorithm for Censored Regression: Performance Analysis and Channel Equalization Application
Haiquan Zhao, Gen Wang, Feng Zhao, Dongxu Liu, Pucha Song
Abstract
The recursive general mixed-norm (RGMN) algorithm achieved excellent convergence performance in traditional unknown parameter identification application. However, it produces obvious estimation bias when dealing with the censored data collected from many practical scenarios. In this article, an RGMN algorithm for censored regression (CR-RGMN) is proposed for censored signal processing scenarios. The CR-RGMN algorithm utilizes a probit regression model to compensate for the sample bias caused by the sampling device. Then, a general form of the adaptive filter algorithm based on minimizing the convex mixture of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{a}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{b}$ </tex-math></inline-formula> norms of the error is developed to identify the unknown parameter. The theoretical steady-state analysis in mean sense proves that the proposed CR-RGMN algorithm is unbiased, and the steady-state mean square deviation (MSD) is derived to predict the convergence behavior of the proposed algorithm. The computational complexities of the CR-RGMN and other algorithms are provided as well. Computer simulation results under robust parameter identification and channel equalization applications show that the proposed CR-RGMN algorithm achieves better performance in terms of convergence speed and steady-state MSD than the RGMN algorithm in censored data processing. And the theoretical analysis results are also verified.