Optimum and Adaptive Complex-Valued Bilinear Filters

Abstract

The identification of nonlinear systems is a frequent task in digital signal processing. Such nonlinear systems may be grouped into many sub-classes, whereby numerous nonlinear real-world systems can be approximated as bilinear (BL) models. Therefore, various optimum and adaptive BL filters have been introduced in recent years. Moreover, in many applications, such as communications and radar, complex-valued (CV) BL systems in combination with CV signals may occur. Hence, in this work, we investigate the extension of real-valued (RV) BL filters to CV BL filters. First, we derive CV BL filters by applying two or four RV BL filters, and compare them with respect to their computational complexity and performance. Second, we introduce novel fully CV BL filters, such as the CV BL Wiener filter (C-BWF), the CV BL least squares (C-BLS) filter, the CV BL least mean squares (C-BLMS) filter, the CV BL normalized least mean squares (C-BNLMS) filter, and the CV BL recursive least squares (C-BRLS) filter. Finally, these filters are applied to identify CV multiple-input-single-output (MISO) systems and CV Hammerstein models.