Generalization of the Wide-Sense Markov Concept to a Widely Linear Processing

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Espinosa-Pulido, Juan Antonio^1 ; Navarro-Moreno, Jesús^1 ; Fernández-Alcalá, Rosa María^1 ; Ruiz-Molina, Juan Carlos^1 ; Oya-Lechuga, Antonia^1 ; Ruiz-Fuentes, Nuria^1

Department of Statistics and Operations Research, University of Jaén, Campus Las Lagunillas, 23071 Jaén, Spain^1

关键词: Complex signal;    Markovian representation;    On state;    Recursive algorithms;    Second orders;    Widely Linear;    Widely-linear processing;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012061/pdf
DOI  :  10.1088/1742-6596/490/1/012061

来源: IOP

【 摘 要 】

In this paper we show that the classical definition and the associated characterizations of wide-sense Markov (WSM) signals are not valid for improper complex signals. For that, we propose an extension of the concept of WSM to a widely linear (WL) setting and the study of new characterizations. Specifically, we introduce a new class of signals, called widely linear Markov (WLM) signals, and we analyze some of their properties based either on second-order properties or on state-space models from a WL processing standpoint. The study is performed in both the forwards and backwards directions of time. Thus, we provide two forwards and backwards Markovian representations for WLM signals. Finally, different estimation recursive algorithms are obtained for these models.