Improving the convergence of adaptive Hammerstein filters

The implementation of adaptive Hammerstein filters involves updating the coefficients of two cascaded blocks, namely, a memoryless nonlinearity and a linear filter. Such an update process presents important numerical problems mainly due to the non-uniqueness of the coefficient values that lead to optimum performance. These problems can be circumvented by keeping constant (not adapting) one of the filter coefficients, which however may significantly slow down the convergence of the adaptive algorithm. In this context, this paper presents a novel approach to implement adaptive Hammerstein filters in which a coefficient normalization strategy is used to overcome the aforementioned numerical problems. Thus, enhanced convergence speed is obtained with a small increase in the computational burden. Simulation results are presented to corroborate the effectiveness of the proposed strategy.