Performance Analysis of Hammerstein Block-Oriented Functional Link Adaptive Filters

Nonlinear adaptive filters (NAFs) exhibit superior modeling capabilities compared to conventional linear adaptive filters, especially in practical applications involving nonlinear input-output relationships. The functional link adaptive filter (FLAF) is an NAF that uses nonlinear functional expansions to achieve nonlinear modelling, however, at the expense of high computational complexity. In response, a low-complexity Hammerstein-type block-oriented functional link adaptive filter (HBO-FLAF) was recently developed, which requires less computation than that of the traditional FLAF. To shed more light on its behaviour and design, we provide a steady-state theoretical analysis of the HBO-FLAF in this paper. We derive the conditions for steady-state mean and mean square convergence of the weight update equations, specifically, an upper bound on the step-size parameter, an expression for the steady-state excess mean square error (EMSE) and a lower bound on the steady-state EMSE of the HBO-FLAF. Numerical simulation results show a close relation with the derived results, thus validating the theoretical analysis.