Stochastic mean-square performance analysis of an adaptive Hammerstein filter

This paper presents an almost sure (a.s.) mean-square performance analysis of an adaptive Hammerstein filter for the case when the measurement noise in the desired response signal is a martingale difference sequence. The system model consists of a series connection of a memoryless nonlinearity followed by a recursive linear filter. It is shown under the conditions of the analysis that the long-term time average of the squared excess estimation error of the adaptive filter can be made arbitrarily close to zero.