Essentially Bivariate Nonlinear Units for Complex-Valued Adaptive Filter

This letter proposes a novel complex-valued nonlinear function (CVNF) approximation method for adaptive nonlinear filter, which is used to digitally cancel the weak nonlinearity, a commonly observed feature in most communication systems. The method approximates CVNF through a two-dimensional piecewise linear surface (2D-PLS), which is linear combination of nonlinear basis functions essentially of two variables. The finding is that such basis functions of two variables have stronger ability to express nonlinearity than the tensor product of two functions of one variable. Experiment using data collected from the transceiver in wireless communication show that the proposed method outperforms the other two methods dealing with nonlinear system identification on complex-valued signals in approximating accuracy as well as computational complexity.