Recursive General Mixed Norm Algorithm for Censored Regression: Performance Analysis and Channel Equalization Application
针对删失数据场景，提出一种递归广义混合范数算法（CR-RGMN），利用probit回归补偿采样偏差，理论证明无偏性并推导稳态均方偏差，在参数识别和信道均衡中收敛更快、稳态误差更低。
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.