Convergence condition of adaptive algorithm of nonlinear adaptive digital filter

In this brief, we consider the adaptive algorithm and the convergence condition of the nonlinear adaptive digital filter (ADF) that has a general transfer function. The adaptive algorithm is based on the orthogonality principle, and the updating value of the algorithm is the correlation of the input signal to the weights and the estimation error. The sufficient condition of the unknown system for which the weight vector of the ADF converges to the weight vector of the unknown system is derived.